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

Wayan Somayasa (Department of Mathematics, Haluoleo University)

Journal of the Indonesian Mathematical Society
Volume 20 Number 2 (October 2014)

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