Insensitivity regions for testing hypotheses in mixed models with constraints. (English) Zbl 1001.62011

Lešanská, Eva

Tatra Mt. Math. Publ. 22, 209-222 (2001).

The author considers a regular mixed linear model with constraints. A small change of the true value of the second order parameter \((\vartheta ^{\star }\) into \(\vartheta ^{\star }+ \triangle)\) causes a change of the statistic used for testing the null hypotheses \(H_0 \: {\operatorname H}\beta ^{\star } + h=0\) concerning the true value \(\beta ^{\star }\) of the first order parameter. A region \(\mathcal R_{\varepsilon }\) of all shifts \(\triangle \) such that they do not cause increase of the risk of the test larger than a given \(\varepsilon \) is determined.
Further an insensitivity region \(\mathcal H_{\varepsilon , \xi }\) of all shifts \(\triangle \) around \(\vartheta ^{\star }\) such that they do not cause decrease of the power of the test at a chosen point \(\xi = {\operatorname H}\beta ^{\star } + h\) larger than a given \(\varepsilon \) is determined.
A joint insensitivity region \(\mathcal H_{\varepsilon , \xi }\) for all \(\xi \) having the same chosen power \(k\), i.e., for all \(\xi \) located on the boundary of the threshold ellipsoid, is given.

Reviewer: Pavla Kunderová (Olomouc)

MSC:

62F03	Parametric hypothesis testing
62F30	Parametric inference under constraints
62F25	Parametric tolerance and confidence regions
62J10	Analysis of variance and covariance (ANOVA)

Keywords:

mixed linear models with constraints; insensitivity regions; threshold ellipsoids