%0 Journal Article %J Stat %D 2017 %T Adaptively-Tuned Particle Swarm Optimization with Application to Spatial Design %A Simpson, M. %A Wikle, C.K. %A Holan, S.H. %X Particle swarm optimization (PSO) algorithms are a class of heuristic optimization algorithms that are attractive for complex optimization problems. We propose using PSO to solve spatial design problems, e.g. choosing new locations to add to an existing monitoring network. Additionally, we introduce two new classes of PSO algorithms that perform well in a wide variety of circumstances, called adaptively tuned PSO and adaptively tuned bare bones PSO. To illustrate these algorithms, we apply them to a common spatial design problem: choosing new locations to add to an existing monitoring network. Specifically, we consider a network in the Houston, TX, area for monitoring ambient ozone levels, which have been linked to out-of-hospital cardiac arrest rates. Published 2017. This article has been contributed to by US Government employees and their work is in the public domain in the USA %B Stat %V 6 %P 145–159 %G eng %U http://onlinelibrary.wiley.com/doi/10.1002/sta4.142/abstract %N 1 %R 10.1002/sta4.142 %0 Journal Article %J Journal of the American Statistical Association %D 2017 %T Bayesian Hierarchical Multi-Population Multistate Jolly-Seber Models with Covariates: Application to the Pallid Sturgeon Population Assessment Program %A Wu, G. %A Holan, S.H. %X Estimating abundance for multiple populations is of fundamental importance to many ecological monitoring programs. Equally important is quantifying the spatial distribution and characterizing the migratory behavior of target populations within the study domain. To achieve these goals, we propose a Bayesian hierarchical multi-population multistate Jolly–Seber model that incorporates covariates. The model is proposed using a state-space framework and has several distinct advantages. First, multiple populations within the same study area can be modeled simultaneously. As a consequence, it is possible to achieve improved parameter estimation by “borrowing strength” across different populations. In many cases, such as our motivating example involving endangered species, this borrowing of strength is crucial, as there is relatively less information for one of the populations under consideration. Second, in addition to accommodating covariate information, we develop a computationally efficient Markov chain Monte Carlo algorithm that requires no tuning. Importantly, the model we propose allows us to draw inference on each population as well as on multiple populations simultaneously. Finally, we demonstrate the effectiveness of our method through a motivating example of estimating the spatial distribution and migration of hatchery and wild populations of the endangered pallid sturgeon (Scaphirhynchus albus), using data from the Pallid Sturgeon Population Assessment Program on the Lower Missouri River. Supplementary materials for this article are available online. %B Journal of the American Statistical Association %V 112 %P 471-483 %G eng %U http://www.tandfonline.com/doi/abs/10.1080/01621459.2016.1211531 %N 518 %R 10.1080/01621459.2016.1211531 %0 Journal Article %J Statistica Sinica %D 2017 %T The Cepstral Model for Multivariate Time Series: The Vector Exponential Model %A Holan, S.H. %A McElroy, T.S. %A Wu, G. %K Autocovariance matrix %K Bayesian estimation %K Cepstral %K Coherence %K Spectral density matrix %K stochastic search variable selection %K Wold coefficients. %X Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to work with a stable, or at least stationary, representation. To fit such models, one must impose restrictions on the coefficient matrices to ensure that certain determinants are nonzero; which, except in special cases, may prove burdensome. To circumvent these difficulties, we propose a flexible frequency domain model expressed in terms of the spectral density matrix. Specifically, this paper treats the modeling of covariance stationary vector-valued (i.e., multivariate) time series via an extension of the exponential model for the spectrum of a scalar time series. We discuss the modeling advantages of the vector exponential model and its computational facets, such as how to obtain Wold coefficients from given cepstral coefficients. Finally, we demonstrate the utility of our approach through simulation as well as two illustrative data examples focusing on multi-step ahead forecasting and estimation of squared coherence. %B Statistica Sinica %V 27 %P 23-42 %G eng %U http://www3.stat.sinica.edu.tw/statistica/J27N1/J27N12/J27N12.html %R 10.5705/ss.202014.0024 %0 Report %D 2017 %T Computationally Efficient Multivariate Spatio-Temporal Models for High-Dimensional Count-Valued Data. (With Discussion). %A Bradley, J.R. %A Holan, S.H. %A Wikle, C.K. %K Aggregation %K American Community Survey %K Bayesian hierarchical model %K Big Data %K Longitudinal Employer-Household Dynamics (LEHD) program %K Markov chain Monte Carlo %K Non-Gaussian. %K Quarterly Workforce Indicators %X We introduce a Bayesian approach for multivariate spatio-temporal prediction for high-dimensional count-valued data. Our primary interest is when there are possibly millions of data points referenced over different variables, geographic regions, and times. This problem requires extensive methodological advancements, as jointly modeling correlated data of this size leads to the so-called "big n problem." The computational complexity of prediction in this setting is further exacerbated by acknowledging that count-valued data are naturally non-Gaussian. Thus, we develop a new computationally efficient distribution theory for this setting. In particular, we introduce a multivariate log-gamma distribution and provide substantial theoretical development including: results regarding conditional distributions, marginal distributions, an asymptotic relationship with the multivariate normal distribution, and full-conditional distributions for a Gibbs sampler. To incorporate dependence between variables, regions, and time points, a multivariate spatio-temporal mixed effects model (MSTM) is used. The results in this manuscript are extremely general, and can be used for data that exhibit fewer sources of dependency than what we consider (e.g., multivariate, spatial-only, or spatio-temporal-only data). Hence, the implications of our modeling framework may have a large impact on the general problem of jointly modeling correlated count-valued data. We show the effectiveness of our approach through a simulation study. Additionally, we demonstrate our proposed methodology with an important application analyzing data obtained from the Longitudinal Employer-Household Dynamics (LEHD) program, which is administered by the U.S. Census Bureau. %B arXiv %G eng %U https://arxiv.org/abs/1512.07273 %0 Journal Article %J Journal of the Royal Statistical Society -- Series B. %D 2017 %T Regionalization of Multiscale Spatial Processes using a Criterion for Spatial Aggregation Error %A Bradley, J.R. %A Wikle, C.K. %A Holan, S.H. %K American Community Survey %K empirical orthogonal functions %K MAUP %K Reduced rank %K Spatial basis functions %K Survey data %X The modifiable areal unit problem and the ecological fallacy are known problems that occur when modeling multiscale spatial processes. We investigate how these forms of spatial aggregation error can guide a regionalization over a spatial domain of interest. By "regionalization" we mean a specification of geographies that define the spatial support for areal data. This topic has been studied vigorously by geographers, but has been given less attention by spatial statisticians. Thus, we propose a criterion for spatial aggregation error (CAGE), which we minimize to obtain an optimal regionalization. To define CAGE we draw a connection between spatial aggregation error and a new multiscale representation of the Karhunen-Loeve (K-L) expansion. This relationship between CAGE and the multiscale K-L expansion leads to illuminating theoretical developments including: connections between spatial aggregation error, squared prediction error, spatial variance, and a novel extension of Obled-Creutin eigenfunctions. The effectiveness of our approach is demonstrated through an analysis of two datasets, one using the American Community Survey and one related to environmental ocean winds. %B Journal of the Royal Statistical Society -- Series B. %G eng %U https://arxiv.org/abs/1502.01974 %0 Journal Article %J Journal of the American Statistical Association - T&M. %D 2016 %T Bayesian Hierarchical Models with Conjugate Full-Conditional Distributions for Dependent Data from the Natural Exponential Family %A Bradley, J.R. %A Holan, S.H. %A Wikle, C.K. %X We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called "big n problem." The computational complexity of the "big n problem" is further exacerbated when allowing for non-Gaussian data models, as is the case here. Thus, we develop new computationally efficient distribution theory for this setting. In particular, we introduce something we call the "conjugate multivariate distribution," which is motivated by the univariate distribution introduced in Diaconis and Ylvisaker (1979). Furthermore, we provide substantial theoretical and methodological development including: results regarding conditional distributions, an asymptotic relationship with the multivariate normal distribution, conjugate prior distributions, and full-conditional distributions for a Gibbs sampler. The results in this manuscript are extremely general, and can be adapted to many different settings. We demonstrate the proposed methodology through simulated examples and analyses based on estimates obtained from the US Census Bureaus' American Community Survey (ACS). %B Journal of the American Statistical Association - T&M. %G eng %U https://arxiv.org/abs/1701.07506 %0 Journal Article %J Bayesian Analysis %D 2016 %T Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis %A Yang, W.H. %A Holan, S.H. %A Wikle, C.K. %X Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time-frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption). %B Bayesian Analysis %P 977-1003 %G eng %U https://arxiv.org/abs/1408.2757 %0 Journal Article %J Journal of the American Statistical Association %D 2016 %T Bayesian Spatial Change of Support for Count-Valued Survey Data with Application to the American Community Survey %A Bradley, J.R. %A Wikle, C.K. %A Holan, S.H. %X We introduce Bayesian spatial change of support methodology for count-valued survey data with known survey variances. Our proposed methodology is motivated by the American Community Survey (ACS), an ongoing survey administered by the U.S. Census Bureau that provides timely information on several key demographic variables. Specifically, the ACS produces 1-year, 3-year, and 5-year "period-estimates," and corresponding margins of errors, for published demographic and socio-economic variables recorded over predefined geographies within the United States. Despite the availability of these predefined geographies it is often of interest to data users to specify customized user-defined spatial supports. In particular, it is useful to estimate demographic variables defined on "new" spatial supports in "real-time." This problem is known as spatial change of support (COS), which is typically performed under the assumption that the data follows a Gaussian distribution. However, count-valued survey data is naturally non-Gaussian and, hence, we consider modeling these data using a Poisson distribution. Additionally, survey-data are often accompanied by estimates of error, which we incorporate into our analysis. We interpret Poisson count-valued data in small areas as an aggregation of events from a spatial point process. This approach provides us with the flexibility necessary to allow ACS users to consider a variety of spatial supports in "real-time." We demonstrate the effectiveness of our approach through a simulated example as well as through an analysis using public-use ACS data. %B Journal of the American Statistical Association %P 472-487 %G eng %U https://arxiv.org/abs/1405.7227 %0 Journal Article %J Computational Statistics and Data Analysis %D 2016 %T Computation of the Autocovariances for Time Series with Multiple Long-Range Persistencies %A McElroy, T.S. %A Holan, S.H. %X Gegenbauer processes allow for flexible and convenient modeling of time series data with multiple spectral peaks, where the qualitative description of these peaks is via the concept of cyclical long-range dependence. The Gegenbauer class is extensive, including ARFIMA, seasonal ARFIMA, and GARMA processes as special cases. Model estimation is challenging for Gegenbauer processes when multiple zeros and poles occur in the spectral density, because the autocovariance function is laborious to compute. The method of splitting–essentially computing autocovariances by convolving long memory and short memory dynamics–is only tractable when a single long memory pole exists. An additive decomposition of the spectrum into a sum of spectra is proposed, where each summand has a single singularity, so that a computationally efficient splitting method can be applied to each term and then aggregated. This approach differs from handling all the poles in the spectral density at once, via an analysis of truncation error. The proposed technique allows for fast estimation of time series with multiple long-range dependences, which is illustrated numerically and through several case-studies. %B Computational Statistics and Data Analysis %P 44 - 56 %G eng %U http://www.sciencedirect.com/science/article/pii/S0167947316300202 %0 Journal Article %J Journal of the Royal Statistical Society - Series A %D 2016 %T Generating Partially Synthetic Geocoded Public Use Data with Decreased Disclosure Risk Using Differential Smoothing %A Quick, H. %A Holan, S.H. %A Wikle, C.K. %X When collecting geocoded confidential data with the intent to disseminate, agencies often resort to altering the geographies prior to making data publicly available due to data privacy obligations. An alternative to releasing aggregated and/or perturbed data is to release multiply-imputed synthetic data, where sensitive values are replaced with draws from statistical models designed to capture important distributional features in the collected data. One issue that has received relatively little attention, however, is how to handle spatially outlying observations in the collected data, as common spatial models often have a tendency to overfit these observations. The goal of this work is to bring this issue to the forefront and propose a solution, which we refer to as "differential smoothing." After implementing our method on simulated data, highlighting the effectiveness of our approach under various scenarios, we illustrate the framework using data consisting of sale prices of homes in San Francisco. %B Journal of the Royal Statistical Society - Series A %G eng %U https://arxiv.org/abs/1507.05529 %0 Journal Article %J Stat %D 2016 %T Multivariate Spatio-Temporal Survey Fusion with Application to the American Community Survey and Local Area Unemployment Statistics %A Bradley, J.R. %A Holan, S.H. %A Wikle, C.K %X There are often multiple surveys available that estimate and report related demographic variables of interest that are referenced over space and/or time. Not all surveys produce the same information, and thus, combining these surveys typically leads to higher quality estimates. That is, not every survey has the same level of precision nor do they always provide estimates of the same variables. In addition, various surveys often produce estimates with incomplete spatio-temporal coverage. By combining surveys using a Bayesian approach, we can account for different margins of error and leverage dependencies to produce estimates of every variable considered at every spatial location and every time point. Specifically, our strategy is to use a hierarchical modelling approach, where the first stage of the model incorporates the margin of error associated with each survey. Then, in a lower stage of the hierarchical model, the multivariate spatio-temporal mixed effects model is used to incorporate multivariate spatio-temporal dependencies of the processes of interest. We adopt a fully Bayesian approach for combining surveys; that is, given all of the available surveys, the conditional distributions of the latent processes of interest are used for statistical inference. To demonstrate our proposed methodology, we jointly analyze period estimates from the US Census Bureau's American Community Survey, and estimates obtained from the Bureau of Labor Statistics Local Area Unemployment Statistics program. Copyright © 2016 John Wiley & Sons, Ltd. %B Stat %P 224 - 233 %G eng %U http://onlinelibrary.wiley.com/doi/10.1002/sta4.120/full %0 Journal Article %J Statistica Sinica %D 2015 %T Bayesian Analysis of Spatially-Dependent Functional Responses with Spatially-Dependent Multi-Dimensional Functional Predictors %A Yang, W. H. %A Wikle, C.K. %A Holan, S.H. %A Sudduth, K. %A Meyers, D.B. %B Statistica Sinica %V 25 %G eng %U http://www3.stat.sinica.edu.tw/preprint/SS-13-245w_Preprint.pdf %& 205-223 %R 10.5705/ss.2013.245w %0 Journal Article %J Annals of Applied Statistics %D 2015 %T Bayesian Binomial Mixture Models for Estimating Abundance in Ecological Monitoring Studies %A Wu, G. %A Holan, S.H. %A Nilon, C.H. %A Wikle, C.K. %B Annals of Applied Statistics %V 9 %P 1-26 %G eng %U http://projecteuclid.org/euclid.aoas/1430226082 %R 10.1214/14-AOAS801 %0 Journal Article %J Journal of Statistical Planning and Inference %D 2015 %T Bayesian Semiparametric Hierarchical Empirical Likelihood Spatial Models %A Porter, A.T. %A Holan, S.H. %A Wikle, C.K. %B Journal of Statistical Planning and Inference %V 165 %P 78-90 %8 10/2015 %G eng %R 10.1016/j.jspi.2015.04.002 %0 Journal Article %J Journal of the American Statistical Association %D 2015 %T Comment on ``Semiparametric Bayesian Density Estimation with Disparate Data Sources: A Meta-Analysis of Global Childhood Undernutrition" by Finncane, M. M., Paciorek, C. J., Stevens, G. A., and Ezzati, M. %A Wikle, C.K. %A Holan, S.H. %B Journal of the American Statistical Association %G eng %0 Book Section %B Handbook of Discrete-Valued Time Series %D 2015 %T Hierarchical Dynamic Generalized Linear Mixed Models for Discrete-Valued Spatio-Temporal Data %A Holan, S.H. %A Wikle, C.K. %E Davis, R. %E Holan, S. %E Lund, R. %E Ravishanker, N %B Handbook of Discrete-Valued Time Series %I Chapman and Hall/CRC Press %C Boca Raton, FL %@ ISBN 9781466577732 %G eng %U http://www.crcpress.com/product/isbn/9781466577732 %0 Book Section %B Handbook of Discrete--Valued Time Series %D 2015 %T Hierarchical Dynamic Generalized Linear Mixed Models for Discrete--Valued Spatio-Temporal Data %A Holan, S.H. %A Wikle, C.K. %B Handbook of Discrete--Valued Time Series %G eng %0 Book Section %B Handbook of Discrete-Valued Time Series %D 2015 %T Long Memory Discrete--Valued Time Series %A Lund, R. %A Holan, S.H. %A Livsey, J. %Y Davis, R. %Y Holan, S. %Y Lund, R. %Y Ravishanker, N. %B Handbook of Discrete-Valued Time Series %I Chapman and Hall %G eng %U http://www.crcpress.com/product/isbn/9781466577732 %& Long Memoriy Discrete-Valued Time Series %0 Web Page %D 2015 %T Multiscale Analysis of Survey Data: Recent Developments and Exciting Prospects %A Bradley, J.R. %A Wikle, C.K. %A Holan, S.H. %B Statistics Views %G eng %0 Journal Article %J STAT %D 2015 %T Multivariate Spatial Hierarchical Bayesian Empirical Likelihood Methods for Small Area Estimation %A Porter, A.T. %A Holan, S.H. %A Wikle, C.K. %B STAT %V 4 %P 108-116 %8 05/2015 %G eng %U http://dx.doi.org/10.1002/sta4.81 %N 1 %R 10.1002/sta4.81 %0 Journal Article %J Annals of Applied Statistics %D 2015 %T Multivariate Spatio-Temporal Models for High-Dimensional Areal Data with Application to Longitudinal Employer-Household Dynamics %A Bradley, J.R. %A Holan, S.H. %A Wikle, C.K. %X Many data sources report related variables of interest that are also referenced over geographic regions and time; however, there are relatively few general statistical methods that one can readily use that incorporate these multivariate spatio-temporal dependencies. Additionally, many multivariate spatio-temporal areal datasets are extremely high-dimensional, which leads to practical issues when formulating statistical models. For example, we analyze Quarterly Workforce Indicators (QWI) published by the US Census Bureau’s Longitudinal Employer-Household Dynamics (LEHD) program. QWIs are available by different variables, regions, and time points, resulting in millions of tabulations. Despite their already expansive coverage, by adopting a fully Bayesian framework, the scope of the QWIs can be extended to provide estimates of missing values along with associated measures of uncertainty. Motivated by the LEHD, and other applications in federal statistics, we introduce the multivariate spatio-temporal mixed effects model (MSTM), which can be used to efficiently model high-dimensional multivariate spatio-temporal areal datasets. The proposed MSTM extends the notion of Moran’s I basis functions to the multivariate spatio-temporal setting. This extension leads to several methodological contributions including extremely effective dimension reduction, a dynamic linear model for multivariate spatio-temporal areal processes, and the reduction of a high-dimensional parameter space using a novel parameter model. %B Annals of Applied Statistics %V 9 %8 03/2015 %G eng %N 4 %R 0.1214/15-AOAS862 %0 Journal Article %J Australian & New Zealand Journal of Statistics %D 2015 %T Small Area Estimation via Multivariate Fay-Herriot Models With Latent Spatial Dependence %A Porter, A.T. %A Wikle, C.K. %A Holan, S.H. %B Australian & New Zealand Journal of Statistics %V 57 %P 15-29 %G eng %U http://arxiv.org/abs/1310.7211 %0 Generic %D 2014 %T An Approach for Identifying and Predicting Economic Recessions in Real-Time Using Time-Frequency Functional Models, Seminar on Bayesian Inference in Econometrics and Statistics (SBIES) %A Holan, S.H. %8 May %G eng %0 Conference Paper %B Joint Statistical Meetings 2014 %D 2014 %T An Approach for Identifying and Predicting Economic Recessions in Real-Time Using Time-Frequency Functional Models %A Holan, S.H. %B Joint Statistical Meetings 2014 %I Joint Statistical Meetings %C Boston, MA %8 August %G eng %U http://www.amstat.org/meetings/jsm/2014/onlineprogram/AbstractDetails.cfm?abstractid=310841 %R 10.1002/asmb.1954 %0 Generic %D 2014 %T A Bayesian Approach to Estimating Agricultural Yield Based on Multiple Repeated Surveys %A Holan, S.H. %8 March %G eng %0 Conference Paper %B Twelfth World Meeting of ISBA %D 2014 %T Bayesian Dynamic Time-Frequency Estimation %A Holan, S.H. %B Twelfth World Meeting of ISBA %I ISBA %C Cancun, Mexico %8 July %G eng %0 Report %D 2014 %T The Cepstral Model for Multivariate Time Series: The Vector Exponential Model. %A Holan, S.H. %A McElroy, T.S. %A Wu, G. %X

Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to work with a stable, or at least stationary, representation. To fit such models, one must impose restrictions on the coefficient matrices to ensure that certain determinants are nonzero; which, except in special cases, may prove burdensome. To circumvent these difficulties, we propose a flexible frequency domain model expressed in terms of the spectral density matrix. Specifically, this paper treats the modeling of covariance stationary vector-valued (i.e., multivariate) time series via an extension of the exponential model for the spectrum of a scalar time series. We discuss the modeling advantages of the vector exponential model and its computational facets, such as how to obtain Wold coefficients from given cepstral coefficients. Finally, we demonstrate the utility of our approach through simulation as well as two illustrative data examples focusing on multi-step ahead forecasting and estimation of squared coherence.

%I arXiv %G eng %U http://arxiv.org/abs/1406.0801 %9 preprint %0 Conference Paper %B ASA Proceedings of the Joint Statistical Meetings %D 2014 %T Fast Estimation of Time Series with Multiple Long-Range Persistencies %A McElroy, T.S. %A Holan, S.H. %B ASA Proceedings of the Joint Statistical Meetings %I American Statistical Association %C Alexandria, VA %G eng %0 Generic %D 2014 %T Spatial Fay-Herriot Models for Small Area Estimation With Functional Covariates %A Holan, S.H. %8 January %G eng %0 Generic %D 2013 %T A Bayesian Approach to Estimating Agricultural Yield Based on Multiple Repeated Surveys, Institute of Public Policy and the Truman School of Public Affairs %A Holan, S.H. %8 March %G eng %0 Journal Article %J Journal of Agricultural, Biological, and Environmental Statistics %D 2013 %T Ecological Prediction With Nonlinear Multivariate Time-Frequency Functional Data Models %A Yang, W.H., %A Wikle, C.K. %A Holan, S.H. %A Wildhaber, M.L. %B Journal of Agricultural, Biological, and Environmental Statistics %V 18 %G eng %U http://link.springer.com/article/10.1007/s13253-013-0142-1 %& 450-474 %R 10.1007/s13253-013-0142-1 %0 Journal Article %J Journal of Agricultural, Biological, and Environmental Statistics %D 2013 %T Hierarchical Bayesian Spatio-Temporal Conway-Maxwell Poisson Models with Dynamic Dispersion %A Wu, G. %A Holan, S.H. %A Wikle, C.K. %B Journal of Agricultural, Biological, and Environmental Statistics %C Anchorage, Alaska %V 18 %P 335-356 %G eng %U http://link.springer.com/article/10.1007/s13253-013-0141-2 %R 10.1007/s13253-013-0141-2 %0 Generic %D 2013 %T Recent Advances in Spatial Methods for Federal Surveys %A Holan, S.H. %8 September %G eng %0 Report %D 2012 %T Asymptotic Theory of Cepstral Random Fields %A McElroy, T.S. %A Holan, S.H. %X Asymptotic Theory of Cepstral Random Fields McElroy, T.S.; Holan, S.H. Random fields play a central role in the analysis of spatially correlated data and, as a result,have a significant impact on a broad array of scientific applications. Given the importance of this topic, there has been a substantial amount of research devoted to this area. However, the cepstral random field model remains largely underdeveloped outside the engineering literature. We provide a comprehensive treatment of the asymptotic theory for two-dimensional random field models. In particular, we provide recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the necessary autocovariance matrix. Additionally, we establish asymptotic consistency results for Bayesian, maximum likelihood, and quasi-maximum likelihood estimation of random field parameters and regression parameters. Further, in both the maximum and quasi-maximum likelihood frameworks, we derive the asymptotic distribution of our estimator. The theoretical results are presented generally and are of independent interest,pertaining to a wide class of random field models. The results for the cepstral model facilitate model-building: because the cepstral coefficients are unconstrained in practice, numerical optimization is greatly simplified, and we are always guaranteed a positive definite covariance matrix. We show that inference for individual coefficients is possible, and one can refine models in a disciplined manner. Finally, our results are illustrated through simulation and the analysis of straw yield data in an agricultural field experiment. http://arxiv.org/pdf/1112.1977.pdf %I University of Missouri %G eng %U http://hdl.handle.net/1813/34461 %9 Preprint %0 Generic %D 2012 %T Bayesian Multiscale Multiple Imputation With Implications to Data Confidentiality %A Holan, S.H. %G eng %0 Conference Paper %B Joint Statistical Meetings 2012 %D 2012 %T Flexible Spectral Models for Multivariate Time Series %A Holan, S.H. %B Joint Statistical Meetings 2012 %8 August %G eng