Some parametric tests based on sample spacings

Abstract

Assume that we have a random sample from an absolutely continuous distribution (univariate or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests symmetrically based on sample spacings. Asymptotic properties of these tests have been investigated under the simple null hypothesis and the sequence of local alternatives converging to the null hypothesis. The asymptotic properties of the proposed tests have also been studied under composite null hypothesis. It is observed that these tests have similar properties as the likelihood ratio test. For assessment of finite sample performance of the proposed tests, we have performed an extensive numerical study. The proposed tests can be used in some situations where likelihood ratio tests do not exist due to unboundedness of likelihood function.