Small area estimation

Abstract

Small area estimation techniques with survey data are now widely being investigated in an increasingly crowded field. In forestry, on-the-ground Inventories could collect very intensive grid information, but this is costly. Therefore, utilizing the low-cost auxiliary information from remote sensing sources such as Landsat Thematic Mapper (TM) or topographical (Topo) information is preferred. Since the data is spatially dependent, it is crucial to develop procedures that combine the existing small area methods with spatial models. In the thesis, the following methods are proposed using transformed and untransformed data: spatial multivariate (MV) distributions on transformed data, spatial zero-inflated exponential (SZIE) models, spatial zero-inflated gamma (SZIG) models, spatial zero-inflated Poisson (SZIP) models and spatial zero-inflated negative binomial (SZINB) models. The spatial zero-inflated models are designed to accommodate the excessive number of zeros among the data. Further, the ancillary data is incorporated into simple spatial multivariate models, called spatial multivariate regression models. The comparison of the result from spatial multivariate regression models with general linear models (GLMs) and the Most Similar Neighbor (MSN) procedure was provided. Making predictions for non-sampled locations Is also a subject of this study. In this thesis, a method for predicting an individual plot response at a non-sampled site on the 0.85-mile grid is determined, based on untransformed data and based on transformed data. Also, predictions for individual plot locations and several simulations designed to yield realizations similar to the available data were investigated to see the reliability of mean squared prediction errors proposed. One focus of this thesis is on modeling spatial dependence of the data for Siuslaw National Forest. The plot data used in this study is 1.7-mile lattice data; however, there is subplot data as close as 40.8 meters. Basically, there is little spatial dependence between plot data, but sufficient spatial dependence at the subplot level to be useful in predictions. For spatial models without dealing with numerous zeros in our data, simple spatial multivariate model are considered for transformed data. Moment and maximum pseudo-likelihood (MPL) estimations are used. To obtain MPL estimators, the normality assumption is made. Such models can only make predictions for plots on the 1.7-mile grid. Best linear unbiased predictions (BLUP) are designed to make predictions for plots on shorter distance grids. BLUPs based on untransformed and transformed data, for non-sampled sites are given. Several back-transformed predictors are compared to BLUPs based on untransformed data. Such predictions for non-sampled sites on 0.85-mile grid points were explored using distance-based correlation functions. The mean squared prediction errors (m.s.p.e.s) of the predictions are also provided. To deal with zeros and non-zeros separately, spatial zero-inflated (SZI) models are proposed. Moment estimators for the directional mean parameters are given. Several predictions rules based on spatial zero-inflated models are also provided. Such spatial zero-inflated models cannot make predictions for non-sampled plots on the 0.85-mile grid. The performance of different models in this study have been compared. Spatial multivariate regression models incorporating auxiliary information did not show improvement based on reduced mean-squared errors. For those prediction rules which do not have a simple closed form for their mean squared prediction errors, mean-squared errors, are compared via simulations.