Search

In this paper we demonstrate the application of partial sums technique in checking the validity of a multivariate linear regression model. In contrast to classical approaches where multivariate normality is always assumed, in this work we propose a test method in which the underlying distribution of the vector of response variables is unknown. In the first step the array of the observations is transformed by using multivariate set-indexed partial sums operator to the corresponding sequence of set-indexed partial sums process. The limit process is shown to be decomposable as a sum of a multivariate deterministic trend function and the p-dimensional set-indexed Brownian sheet. We show that testing the validity of the ordinary model is equivalent with that of the asymptotic model. Hence, the test problem can be handled by investigating that for the asymptotic model. Next, we define likelihood ratio test by computing the ratio between the likelihood of the trend under H0 and under H1 which are derived from the Cameron-Martin-Girsanov formula of the density function of the asymptotic model with respect to the p-dimensional Brownian sheet. The performance of the test is investigated by conducting Monte Carlo simulation. Application of the method to multivariate data is also discussed. [ABSTRACT FROM AUTHOR]