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Link Functions for Parameters of Sequential Order Statistics and Curved Exponential Families

Volovskiy Grigoriy, Bedbur Stefan, Kamps Udo

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 1

115--127

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.

Empirical likelihood inference for survival rate regression with missing information principle

Zhao Y.

Probability and Mathematical Statistics

2009

Vol. 29, Fasc. 1

73--89

Recently, regression model for the long-term survival probabilities of patients was proposed, and a semiparametric inference procedure was developed based on missing information principle. In this paper, we propose an alternative empirical likelihood method. First, we define an estimated empirical likelihood ratio for the regression parameter. The limiting distribution of the empirical likelihood ratio is shown to have a weighted sum of i.i.d. χ21 ’s. We also define an adjusted empirical likelihood ratio for the regression parameter and the adjusted empirical likelihood ratio is shown to have a central chi-squared limiting distribution. Confidence regions for the vector of regression parameter are obtained accordingly. Furthermore, an extensive simulation study is conducted and it shows the proposed method has better coverage probability. Finally, we use a real data set to illustrate our proposed method.