Estimação em regressão inversa no modelo CAR espacial

Abstract

Inverse regression or statistical calibration is a statistical technique used in situations where, through regression analysis, it is desired to estimate a unknown value of the independent variable given the value of the dependent variable. Methods for the point and interval estimation in the inverse regression for this unknown value are available in the literature. However, it is observed that there are few methods that consider the spatial information of the data in the estimation process in the inverse regression. The main objective of this thesis is to propose inverse spatial regression or spatial calibration by means of methods for the point and interval estimation of the unknown value of the independent variable using a model that considers the spatial dependence structure in area data. These estimators were constructed using spatial error model or autoregressive conditional model (CAR) and applied to real data that characterize a spatial calibration problem. The results show that the inverse spatial regression is appropriate in the spatial dependence data area analysis, providing a useful tool for cases that configure the need to obtain the value of an independent variable by knowing the value of the dependent variable. It is also observed that a great potential that this inverse spatial regression model has is in the fact that it can be an efficient method of imputation, in specific cases, of missing data in the analysis of area data.