Translator Disclaimer
June, 1993 Inadmissibility of Studentized Tests for Normal Order Restricted Models
Arthur Cohen, H. B. Sackrowitz
Ann. Statist. 21(2): 746-752 (June, 1993). DOI: 10.1214/aos/1176349148

Abstract

Consider the model where $X_{ij}, i = 1,\ldots, k; j = 1,2,\ldots, n_i; n_i \geq 2$, are observed. Here $X_{ij}$ are independent $N(\theta_i,\sigma^2), \theta_i, \sigma^2$ unknown. Let $X_i = \sum^n_{j = 1}X_{ij}/n_i, \mathbf{X}' = (X_1,\ldots, X_k), \mathbf{\theta}' = (\theta_1,\ldots,\theta_k), V = \sum^k_{i = 1} \sum^{n_i}_{j = 1}X^2_{ij} - n \sum^k_{i = 1}X^2_i$. Let $\mathbf{A}_1$ be a $(k - m) \times k$ matrix of rank $(k - m) \geq 2$ and test $H: \mathbf{A}_1\mathbf{\theta} = \mathbf{0}$ versus $K - H$ where $K: \mathbf{A}_1\mathbf{\theta} \geq \mathbf{0}$. Suppose we assume $\sigma^2$ known and consider a constant size $\alpha$ test $(\alpha < 1/2)$ which is admissible for $H$ versus $K - H$ based on $\mathbf{X}$. Next assume $\sigma^2$ is unknown. Consider the same test but now as a function of $\mathbf{X}/V^{1/2}$ (i.e., Studentize the test). The resulting test is inadmissible. Examples are noted.

Citation

Arthur Cohen. H. B. Sackrowitz. "Inadmissibility of Studentized Tests for Normal Order Restricted Models." Ann. Statist. 21 (2) 746 - 752, June, 1993. https://doi.org/10.1214/aos/1176349148

Information

Published: June, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0779.62006
MathSciNet: MR1232516
Digital Object Identifier: 10.1214/aos/1176349148

Subjects:
Primary: 62F03
Secondary: 62C15  