Model-Check Based on Residual Partial Sums Process of Heteroscedastic spatial Linear Regression Models
Abstract: It is common in
practice to evaluate the correctness of an assumed linear regression model by
conducting a model-check method in which the residuals of the observations are investigated.
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 central limit theorem for a sequence of residual partial
sums processes when the observations come from 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 are also
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 finite sample sizes are constructed by Monte Carlo
simulation.
Keywords: heteroscedastic
linear regression model, least squares residual, partial sums process, Brownian
sheet, asymptotic model-check
Author: Wayan Somayasa
Journal Code: jpmatematikagg110004
