Consistent Goodness-of-Fit Tests for Gamma Distributions Based on Empirical Hankel Transforms

• Activity Number: 198 - SPEED: Nonparametric Statistics: Estimation, Testing, and Modeling
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 11:35 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Elena Hadjicosta* and Donald Richards
• Companies: Penn State University and Penn State University
• Keywords: Consistent tests; Contiguous alternatives ; Empirical Hankel transform; Gamma distribution; Goodness-of-fit test

Abstract

In recent years, integral transforms have been used widely in statistical inference, especially in goodness-of-fit testing. Gamma distributions with known shape parameters are frequently used as models in many research areas, such as queueing theory, neuroscience, reliability theory, and life testing. In this talk, we apply Hankel transform theory to propose an integral-type test statistic for goodness-of-fit tests for gamma distributions with known shape parameters. We prove that the null asymptotic distribution of the test statistic is a weighted sum of independent chi-square distributed random variables. Further, we show that the proposed test is consistent against each fixed alternative distribution, and we derive the non-null asymptotic distribution of the test statistic under a sequence of contiguous alternatives.