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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 41, Fasc. 1,
pages 115 - 127
DOI: 10.37190/0208-4147.41.1.8
Published online 8.4.2021
 

Link functions for parameters of sequential order statistics and curved exponential families

Grigoriy Volovskiy
Stefan Bedbur
Udo Kamps

Abstract: Estimation of model parameters of sequential order statistics under linear and nonlinear link function assumptions is considered. Utilizing the arising curved exponential family structure, conditions for existence and uniqueness as well as the validity of asymptotic properties of maximum likelihood estimators are stated. Minimal sufficiency and completeness of the associated canonical statistics are discussed.

2010 AMS Mathematics Subject Classification: Primary 62F10; Secondary 62N05, 62N02.

Keywords and phrases: sequential order statistic, maximum likelihood estimation, curved exponential family, link function.

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