## Taiwanese Journal of Mathematics

### A NOTE ON THE ADMISSIBILITY OF P-VALUE FOR THE ONE-SIDED HYPOTHESIS TEST IN THE NEGATIVE BINOMIAL MODEL

Jine-Phone Chou

#### Abstract

Let X be a random variable with negative binomial density $$f(x|\theta)=\displaystyle{\Gamma (x+r)\over \Gamma (x+1)\Gamma (r)}\theta^x(1-\theta)^r,$$ where $x=0, 1, 2, \cdots , 0 \lt \theta \lt 1,~r \gt 0$. For the hypothesis testing problem $$H_0 : \theta \leq \theta_0~~~~{\rm versus}~~~~H_1 : \theta \gt \theta_0$$ based on observing X$=x$, where $\theta_0$ is specified, we consider it as an estimation problem within a decision-theoretic framework. We prove the admissibility of estimator $p(x)= P_{\theta_0}(X \geq x)$, the $p$-value, for estimating the accuracy of the test, $1_{(0,\theta_0)}(\theta)$, under the squared error loss.

#### Article information

Source
Taiwanese J. Math., Volume 1, Number 1 (1997), 59-63.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500404925

Digital Object Identifier
doi:10.11650/twjm/1500404925

Mathematical Reviews number (MathSciNet)
MR1435497

Zentralblatt MATH identifier
0876.62003

#### Citation

Chou, Jine-Phone. A NOTE ON THE ADMISSIBILITY OF P-VALUE FOR THE ONE-SIDED HYPOTHESIS TEST IN THE NEGATIVE BINOMIAL MODEL. Taiwanese J. Math. 1 (1997), no. 1, 59--63. doi:10.11650/twjm/1500404925. https://projecteuclid.org/euclid.twjm/1500404925