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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

Keywords

Multivariate spatial linear regression model multivariate Brownian sheet partial sums process least squares residual model-check

Article Details

How to Cite
Somayasa, W. (2014). ON WEAK CONVERGENCE OF THE PARTIAL SUMS PROCESSES OF THE LEAST SQUARES RESIDUALS OF MULTIVARIATE SPATIAL REGRESSION. Journal of the Indonesian Mathematical Society, 20(2), 77–94. https://doi.org/10.22342/jims.20.2.183.77-94