Testing for individual sphericity in heterogeneous panels

Abstract

Summary This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate $p$-values in empirical work. The approximation shows substantial improvements over the normal approximation when the cross-sectional dimension is small.