Estimação em regressão espacial inversa

Abstract

In some issues involving regression analysis, it can be interesting to obtain estimates for a value of the independent variable, given a value of the dependent variable. This issue is determined inverse regression or calibration. In literature, there are two more commonly used methods for performing the point estimation in reverse regression models: classic and inverse. Methods to obtain interval estimations for the true value of the independent variable are also available. The main objective of this dissertation is to present the issue of spatial calibration and propose methods for the point and interval estimation in models that consider the spatial dependence structure between neighboring areas. The issue can be divided into two cases: in the first case, we intend to estimate the value of the independent variable belonging to the observed sample, while in the second case, the value of the independent variable to be estimated does not belong to the observed sample. This dissertation develops point and interval estimators for the value of the independent variable for the spatial autoregressive model (SAR). The estimators obtained are applied to real spatial data. The results obtained show the potential of inverse regression for issues in which the information from one region are directly influenced by the information from neighboring regions.