Testing and Estimating Ratios of Scale Parameters

Abstract

Let X ₁, …, X_m and Y ₁, …, Y_n be independent random samples from populations having continuous d.f.'s Ψ((x-μ)/σ) and Ψ ((y-v)/τ) respectively. The classical F-test of a hypothesis concerning λ = τ/σ is known to be non-robust. This paper examines several robust alternative procedures and compares them on the basis of Pitman a.r.e. and Monte Carlo studies of power functions. An approximate permutation test [13] and a “jackknife” procedure [9] are found to be most satisfactory; while a class of “rank-like” tests [10] are found to be “useful inefficient statistics”