ON SET-INDEXED RESIDUAL PARTIAL SUM LIMIT PROCESS OF SPATIAL LINEAR REGRESSION MODELS

Abstract

In this paper we derive the limit process of the sequence of set-indexedleast-squares residual partial sum processes of observations obtained form a spatiallinear regression model. For the proof of the result we apply the uniform central limittheorem of Alexander and Pyke (1986) and generalize the geometrical approach ofBischo (2002) and Bischo and Somayasa (2009). It is shown that the limit processis a projection of the set-indexed Brownian sheet onto the reproducing kernel Hilbertspace of this process. For that we dene the projection via Choquet integral of theregression function with respect to the set-indexed Brownian sheet.

DOI : http://dx.doi.org/10.22342/jims.17.2.4.73-83