Tests for the skewness parameter of two-piece double exponential distribution in the presence of nuisance parameters. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Subramanian, Leela; Dixit, Vaijayanti U
• Is Part Of: Statistics. Volume 52:Issue 1(2018)
• Page Start: 115
• Page End: 132
• Publication Date: 2018-01-02
• Subjects: Ancillary statistic -- asymmetric Laplace distribution -- likelihood ratio test -- Neyman–Pearson's lemma -- two-piece distribution; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2017.1379523
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: In this paper, tests for the skewness parameter of the two-piece double exponential distribution are derived when the location parameter is unknown. Classical tests like Neyman structure test and likelihood ratio test (LRT), that are generally used to test hypotheses in the presence of nuisance parameters, are not feasible for this distribution since the exact distributions of the test statistics become very complicated. As an alternative, we identify a set of statistics that are ancillary for the location parameter. When the scale parameter is known, Neyman–Pearson's lemma is used, and when the scale parameter is unknown, the LRT is applied to the joint density function of ancillary statistics, in order to obtain a test for the skewness parameter of the distribution. Test for symmetry of the distribution can be deduced as a special case. It is found that power of the proposed tests for symmetry is only marginally less than the power of corresponding classical optimum tests when the location parameter is known, especially for moderate and large sample sizes.