A Fully Nonparametric Diagnostic Test For Homogeneity of Variances

For the regression model Yi = m(xi) + σ(xi)2i, i = 1, . . . , m, we propose a new nonparametric diagnostic test for checking the constancy of the conditional variance function σ(x). The proposed test does not assume a known parametric form for the conditional mean function m(x). The test statistic is inspired by recent asymptotic theory in analysis of variance when the number of factor levels is large. Simulation studies demonstrate the good finite-sample properties of the test. We apply the proposed test to a study on the effect of drug utilization on health care costs. Title in French: we can supply this Résumé : For the regression model Yi = m(xi) + σ(xi)2i, i = 1, . . . , m, we propose a new nonparametric diagnostic test for checking the constancy of the conditional variance function σ(x). The proposed test does not assume a known parametric form for the conditional mean function m(x). The test statistic is inspired by recent asymptotic theory in analysis of variance when the number of factor levels is large. Simulation studies demonstrate the test has good finite-sample properties. We apply the proposed test to a study on the effect of drug utilization on health care costs.