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-indexed least-squares residual
partial sum processes of observations obtained form a spatiallinear regression
model. For the proof of the result we apply the uniform centrallimit theorem of
Alexander and Pyke [1] and generalize the geometrical approach of Bischoff [7]
and Bischoff and Somayasa [8]. It is shown that the limit process is a
projection of the set-indexed Brownian sheet onto the reproducing kernel
Hilbert space of this process. For that we define the projection via Choquet
integral [14, 15, 17] of the regression function with respect to the
set-indexed Brownian sheet.
Key words: Set-indexed
Brownian sheet, set-indexed partial sum process, spatial linear regression
model, least-squares residual, Choquet integral
Author: Wayan Somayasa
Journal Code: jpmatematikagg110013
