ON WEAK CONVERGENCE OF THE PARTIAL SUMS PROCESSES OF THE LEAST SQUARES RESIDUALS OF MULTIVARIATE SPATIAL REGRESSION

Abstract

A weak convergence of the sequence of partial sums processes of theresiduals (PSPR) when the observations are obtained from a multivariate spatiallinear regression model (SLRM) is established. The result is then applied in constructingthe rejection region of an asymptotic test of hypothesis based on a type ofCramer-von Mises functional of the PSPR. When the null hypothesis is true, we getthe limit process as a projection of the multivariate Brownian sheet, whereas underthe alternative it is given by a signal plus multivariate noise model. Examples ofthe limit process under the null hypothesis are also studied.

DOI : http://dx.doi.org/10.22342/jims.20.2.183.77-94