The Optimal Rank Tests for Modal Direction

Abstract

Spatial statistics arises when the data are points in some Euclidean space (usually R2 or R3) or some surface (usually the unit circle S1 or the unit sphere S2). For a general class of unipolar, rotationally symmetric distributions on the multi-dimensional unit spherical surface, a characterization of locally best rotation-invariant test statistics is exploited in the construction of locally best rotation- invariant rank tests for modal location. Allied statistical distributional problems are appraised, and in the light of these assessments, asymptotic relative efficiency of a class of rotation-invariant rank tests (with respect to some of their parametric counterparts) is studied. Finite sample permutational distributional perspectives are also appraised.