Likelihood Ratio Test for Monotonicity Density
- 2019-01-21 (Mon.), 10:30 AM
- 中研院-統計所6005會議室(環境變遷研究大樓A棟)
- 茶 會:上午10:10統計所6005會議室(環境變遷研究大樓A棟)
- Dr. Chuan-Fa Tang (湯泉發博士)
- Department of Biostatistics, University of Washington, USA.
Abstract
We study the likelihood ratio test statistic for a lasting, but unconventional, hypothesis testing problem on whether a random sample follows a distribution with a nonincreasing density function. The obtained test statistic has a surprisingly simple asymptotic null distribution, which is Gaussian, instead of the well-known chi-square for generic likelihood ratio tests. Also, the limiting distribution does not depend on the underlying density but on some universal constants such as the Euler-Mascheroni constant. The underlying density only plays a role in the higher-order effect, whereby modifications to the test statistic are suggested.
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