Model-Check Based on Residual Partial Sums Process of Heteroscedastic spatial Linear Regression Models - Wayan Somayasa (Jurnal Matematika, 2011)
It is common in practice to evaluate the correctness of an assumed linear regressionmodel by conducting a model-check method in which the residuals of the observations areinvestigated. In the asymptotic context instead of observing the vector of the residuals directly,one investigates the partial sums of the observations. In this paper we derive a functional centrallimit theorem for a sequence of residual partial sums processes when the observations comefrom heteroscedastic spatial linear regression models. Under a mild condition it is shown thatthe limit process is a function of Brownian sheet. Several examples of the limit processes arealso discussed. The limit theorem is then applied in establishing an asymptotically Kolmogorovtype test concerning the adequacy of the fitted model. The critical regions of the test for finitesample sizes are constructed by Monte Carlo simulation.