The Annals of Statistics

Minimal Sufficiency and Completeness for Dichotomous Quantal Response Models

Michael A. Messig and William E. Strawderman

Full-text: Open access

Abstract

Minimal sufficiency and completeness are examined for the multistage, multihit and Weibull quantal response models. It is shown that the response counts are minimal sufficient statistics and conditions are presented for completeness for the families of these models. These results provide an example of a complete sufficient statistic for a curved exponential family which is of higher dimension than the parameter space. Uniformly minimum variance unbiased (UMVU) estimators may not exist for the probability of response at a given dose if the response counts are not complete sufficient statistics.

Article information

Source
Ann. Statist., Volume 21, Number 4 (1993), 2149-2157.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349415

Digital Object Identifier
doi:10.1214/aos/1176349415

Mathematical Reviews number (MathSciNet)
MR1245786

Zentralblatt MATH identifier
0790.62008

JSTOR
links.jstor.org

Subjects
Primary: 62B05: Sufficient statistics and fields
Secondary: 62F10: Point estimation 62F11 62J12: Generalized linear models

Keywords
Quantal response model minimal sufficiency completeness uniformly minimum variance unbiased estimator

Citation

Messig, Michael A.; Strawderman, William E. Minimal Sufficiency and Completeness for Dichotomous Quantal Response Models. Ann. Statist. 21 (1993), no. 4, 2149--2157. doi:10.1214/aos/1176349415. https://projecteuclid.org/euclid.aos/1176349415


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