A fully nonparametric diagnostic test for homogeneity of variances

The authors propose a new nonparametric diagnostic test for checking the constancy of the conditional variance function σ²(x) in the regression model Y_i = m(x_i) + σ(x_i)?_i, i = 1,…, m. Their test, which does not assume a known parametric form for the conditional mean function m(x), is inspired by a recent asymptotic theory in the analysis of variance when the number of factor levels is large. The authors demonstrate through simulations the good finite‐sample properties of the test and illustrate its use in a study on the effect of drug utilization on health care costs.