Likelihood ratio test for the spacing between two adjacent location parameters

Suppose Yi is an estimator or sufficient statistic for a location parameter θ_i (i = 1, . . ., k) of a location family. Let θ_(i)≤θ0₍₂₎≤ ⋯ ≤θ_(k) be the ordered parameters. This paper deals with the likelihood ratio test for the hypothesis H₀: θ_(k-t+1) - θ_(k-t)≤Δ versus H₁: θ_(k-t-1) - θ_(k-t) > Δ, where θ_(k-t+1) - θ_(k-t) is the spacing between two adjacent location parameters. It is shown that if the density function of the location family has monotone likelihood ratio, the likelihood ratio test statistic is the corresponding sample spacing. However, this result may not be true for other spacings like the range θ_(k) - θ₍₁₎. Copyright © 1996 Published by Elsevier B.V.