Comparing tests appear in model-check for normal regression with spatially correlated observations

[摘要] The problem of investigating the appropriateness of an assumed model in regression analysis was traditionally handled by means of F test under independent observations. In this work we propose a more modern method based on the so-called set-indexed partial sums processes of the least squares residuals of the observations. We consider throughout this work univariate and multivariate regression models with spatially correlated observations, which are frequently encountered in the statistical modelling in geosciences as well as in mining. The decision is drawn by performing asymptotic test of statistical hypothesis based on the Kolmogorov-Smirnov and Cramér-von Misses functionals of the processes. We compare the two tests by investigating the power functions of the test. The finite sample size behavior of the tests are studied by simulating the empirical probability of rejections of H0. It is shown that for univariate model the KS test seems to be more powerful. Conversely the Cramér-von Mises test tends to be more powerful than the KS test in the multivariate case.

[发布机构] Department of Mathematics, Halu Oleo University, Kendari; 93232, Indonesia^1

[效力级别] 物理学

[关键词] Correlated observations;Empirical probabilities;Finite sample sizes;Kolmogorov-Smirnov;Multivariate regression models;Statistical hypothesis;Statistical modelling;Univariate models