Model Assisted Design Based Estimation of a Spatial Mean
Giuseppe Cicchitelli1, Giorgio E. Montanari1
1Economics, Finance and Statistics, University of Perugia, Perugia, Italy; 2Economics, Finance and Statistics, University of Perugia, Perugia, Italy

Spatial populations arise in a number of disciplines, including geology, ecology, and environmental science, in connection with the study of natural phenomena in two-dimensional regions, such as mineral resources, vegetation cover, soil chemical composition, pollution concentration in soil.

Within a design based approach to inference, we propose and study an application of semiparametric methods to the model-assisted approach to the estimation of means or totals of spatial populations using the spatial coordinates as auxiliary variable. The idea is to assume a low-rank spline regression model as working model, and then to employ the resulting fitted values as predictors of the response values in a difference or regression estimator. Our application allows approximately design unbiased and consistent estimators of the target parameters which capitalize on the spatial pattern in the data captured by the fitted spline regression model.

Proof that the estimator is design-consistent and has a normal limiting distribution is provided

The performance of the proposed estimator for finite size samples has been investigated by means of a simulation study based on some artificial populations characterized by different levels of spatial structure. Substantial gains in efficiency with respect to Horvitz-Thompson estimator, under a spatially stratified designs, are provided as long as the sample size is much larger than the number of degrees of freedom of the spline regression model. Under the same condition, the confidence interval coverage is quite near the nominal level.

We notice that the working model we have assumed to predict the response variable supports also auxiliary variables other than the spatial coordinates. The use of these covariates, when available, can give further strength to the proposed estimator.

Keywords: Randomisation distribution; Penalised splines regression model; Horvitz-Thompson estimator

Biography: Giorgio Eduardo Montanari is a full professor of Statistics at the University of Perugia, Italy. His main research interests are sample theory, sample surveys and data analysis. He is a member of the International Association of Survey Statistician.