MODEL-CHECKS FOR HOMOSCHEDASTIC SPATIAL LINEAR REGRESSION MODEL BASED ON BOOTSTRAP METHOD

Abstract

In  this  paper  we  propose  Efron  residual  based-bootstrap  approximation  methods in  asymptotic  model-checks  for  homoschedastic  spatial  linear  regression  models.  It  is  shown  that  under  some  regularity conditions given to the known regression functions the bootstrap version of the sequence of least squares residual partial sums processes converges in distribution to a centred Gaussian process having sample paths in the space of continuous functions on  1,0 1,0 :I . Thus, Efron residual based-bootstrap is a consistent approximation in the usual sense. The finite sample performance of the bootstrap level   Kolmogorov-Smirnov (KS) type test is also investigated by means of Monte Carlo simulation.