Asymptotic modelling of corn plant data using moving sums (MOSUM) technique

Abstract

Empirical model building using linear regression has been widely used in agricultural study. The validity of an assumed model is usually check using either F of likelihood ratio test under normally distributed observations. In this paper an asymptotic method based on the moving sums (MOSUM) of triangular array of ordinary least squares (OLS) residuals is proposed. Reasonable tests statistics for detecting valid model are defined as the Kolmogorov-Smirnov (KS) and Cramér-von Mises (MvM) functionals of the residual MOSUM process. The limit process is obtained for the condition under H0 and under H1 by applying the continuous mapping theorem to the existing limit theorem for partial sums of the residuals. The quantiles of the KS and CvM statistics under H0 are approximated by simulation. The application of the method in obtaining a valid model for the speed of growth of corn plants results in the conclusion that a first-order polynomial regression model is shown to be plausible.