Some parametric tests based on sample spacings

TL;DR

This paper introduces new parametric tests based on sample spacings for assessing hypotheses about known distribution forms with unknown parameters, offering alternatives to likelihood ratio tests especially when likelihoods are unbounded.

Contribution

The paper develops and analyzes new tests based on symmetric functions of m-step disjoint sample spacings, extending previous spacing-based tests and providing alternatives to likelihood ratio tests.

Findings

Tests have similar asymptotic properties to likelihood ratio tests.

Finite sample performance is favorable in simulations.

Real data application demonstrates practical utility.

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 based on statistics that are symmetric functions of $m$-step disjoint sample spacings. Asymptotic properties of these tests have been investigated under the simple null hypothesis and under a sequence of local alternatives converging to the null hypothesis. The asymptotic properties of the proposed tests have also been studied under the composite null hypothesis. We observed that these tests have similar asymptotic properties as the likelihood ratio test. Finite sample performances of the proposed tests are assessed numerically. A data analysis based on real data is also reported. The proposed tests provide alternative to similar tests based on simple spacings (i.e., $m=1$), that were proposed earlier in the literature. These tests also provide an alternative to likelihood ratio tests in situations where likelihood function may be unbounded and hence, likelihood ratio tests do not exist.