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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.

K. Ahmadi, M. Rezaei and F. Yousefzadeh, Progressively type-II censored competing risks data for exponential distributions based on sequential order statistics, Comm. Statist. Theory Methods 47 (2018), 1276-1296.

N. Balakrishnan, E. Beutner and U. Kamps, Modeling parameters of a load-sharing system through link functions in sequential order statistics models and associated inference, IEEE Trans. Reliab. 60 (2011), 605-611.

S. Bedbur, UMPU tests based on sequential order statistics, J. Statist. Plann. Inference 140 (2010), 2520-2530.

S. Bedbur, E. Beutner and U. Kamps, Generalized order statistics: an exponential family in model parameters, Statistics 46 (2012), 159-166.

S. Bedbur, M. Burkschat and U. Kamps, Inference in a model of successive failures with shape-adjusted hazard rates, Ann. Inst. Statist. Math. 68 (2016), 639-657.

S. Bedbur, M. Johnen and U. Kamps, Inference from multiple samples of Weibull sequential order statistics, J. Multivariate Anal. 169 (2019), 381-399.

S. Bedbur, U. Kamps and M. Kateri, Meta-analysis of general step-stress experiments under repeated Type-II censoring, Appl. Math. Model. 39 (2015), 2261-2275.

R. H. Berk, Consistency and asymptotic normality of MLE's for exponential models, Ann. Math. Statist. 43 (1972), 193-204.

E. Beutner, Nonparametric inference for sequential k-out-of-n systems, Ann. Inst. Statist. Math. 60 (2008), 605-626.

E. Beutner, Nonparametric model checking for k-out-of-n systems, J. Statist. Plann. Inference 140 (2010), 626-639.

M. Bieniek, M. Burkschat and T. Rychlik, Comparisons of the expectations of system and component lifetimes in the failure dependent proportional hazard model, Methodol. Comput. Appl. Probab. 22 (2020), 173-189.

L. D. Brown, Fundamentals of Statistical Exponential Families: With Applications In Statistical Decision Theory, Institute of Mathematical Statistics, Hayward, CA, 1986.

M. Burkschat and J. Navarro, Dynamic signatures of coherent systems based on sequential order statistics, J. Appl. Probab. 50 (2013), 272-287.

E. Cramer and U. Kamps, Sequential k-out-of-n systems, in: Handbook of Statistics, Vol. 20, Advances in Reliability, N. Balakrishnan and C. R. Rao (eds.), Elsevier, Amsterdam, 2001, 301-372.

M. Doostparast, M. Hashempour and E. Velayati Moghaddam, Weibull analysis with sequential order statistics under a power trend model for hazard rates, arXiv:1912.07967 (2019).

M. Esmailian and M. Doostparast, Estimation based on sequential order statistics with random removals, Probab. Math. Statist. 34 (2014), 81-95.

M. Esmailian and M. Doostparast, Estimates based on sequential order statistics with the two-parameter Pareto distribution, Bull. Malays. Math. Sci. Soc. 42 (2018), 2897-2914.

U. Kamps, A concept of generalized order statistics, J. Statist. Plann. Inference 48 (1995), 1-23.

U. Kamps, A Concept of Generalized Order Statistics, Teubner, Stuttgart, 1995.

V. Kretschmer, The uniqueness of extremum estimation, Statist. Probab. Lett. 77 (2007), 942-951.

E. L. Lehmann and G. Casella, Theory of Point Estimation, 2nd ed., Springer, New York, 1998.

M. A. Messig and W. E. Strawderman, Minimal sufficiency and completeness for dichotomous quantal response models, Ann. Statist. 21 (1993), 2149-2157.

F. Mies and S. Bedbur, Exact semiparametric inference and model selection for load-sharing systems, IEEE Trans. Reliab. 69 (2020), 863-872.

J. Pfanzagl, Parametric Statistical Theory, De Gruyter, Berlin, 1994.

T. Rychlik, Evaluations of generalized order statistics from bounded populations, Statist. Papers 51 (2010), 165-177.

A. Schmiedt, Statistical modeling of non-metallic inclusions in steels and extreme value analysis, Ph.D. thesis, RWTH Aachen Univ., 2012.

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