A Likelihood Ratio Test for Shape-Constraint Density

• Activity Number: 316 - Emerging Advances of Innovative Computational Skills with Unconventional Likelihoods
• Type: Invited
• Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Kwun Chuen Gary Chan*
• Companies: University of Washington
• Keywords: Grenander estimator; spacings; generalized maximum likelihood

Abstract

We study a likelihood ratio test statistic for a non-standard hypothesis testing problem of whether the data are generated from a distribution with a non-increasing density function. The test statistic has a surprisingly simple asymptotic null distribution, which is Gaussian and does not depend on the underlying density. We also show that the underlying density only has a higher order effect, and suggest corresponding modifications to the test statistic.