Exact inference for the linear model with groupwise heteroscedastic spherical disturbances

Abstract

Exact nonparametric inference on a single coefficient in a linear regression model, as considered by Bekker (Working Paper, Department of Economics, University of Groningen, 1997), is elaborated for the case of spherically distributed heteroscedastic disturbances. Instead of approximate inference based on feasible weighted least squares, exact inference is formulated based on partial rotational invariance of the distribution of the vector of disturbances. Thus, classical exact inference based on t-statistics is generalized to exact inference that remains valid in a groupwise heteroscedastic context. The approach is applied to a basic two-sample problem, and to the random- and fixed-effects models for panel data.