A nonparametric hypothesis test for heteroscedasticity in multiple regression

Abstract This article presents a new method to test for heteroscedasticity in a general multiple nonparametric regression model. The test statistic is based on a high‐dimensional one‐way ANOVA constructed with the absolute value of the residuals, and its asymptotic distribution is derived under the null hypothesis of homoscedasticity and local alternative. The properties of the proposed test statistic are preserved when a correctly specified parametric mean function is used to obtain the residuals. Unlike most methods in the literature no parametric form is required for the multivariate variance function. Extensive simulations suggest that the proposed test detects heteroscedasticity in all models considered while classical methods fail in some cases. Two real data applications are examined.The Canadian Journal of Statistics45: 425–441; 2017 © 2017 Statistical Society of Canada