Residual Partial Sums Processes to Check Models for Linear Regression

Abstract

In practice it is popular to investigate the partial sums of the least squares residuals to check for linear regression. The partial sums of the least squares residuals can be injectively embedded into the class of continuous functions. These continuous functions are called residual partial sums process. If the number of observations is large enough a Gaussian process can be considered as approximation of the residual partial sums process. This process can be used to establish non-parametric tests of Cram?r-von Mises and Kolmogoroff-Smirnov type to check for linear regression. In this talk we describe the theory in a geometrical way. Recent results, the hybrid problem of testing and estimating and relation to finance are sketched. The talk is illustrated by data and by several simulations.