Annals of the Institute of Statistical Mathematics
, Volume 65, Issue 3, pp 589615
First online:
New estimating equation approaches with application in lifetime data analysis
 Keming YuAffiliated withDepartment of Mathematical Sciences, Brunel UniversityBusiness School, Shihezi University
 , Bing Xing WangAffiliated withDepartment of Statistics, Zhejiang Gongshang University Email author
 , Valentin PatileaAffiliated withEcole Nationale de la Statistique et de l’Analyse de l’Information (Ensai), (CRES)
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Estimating equation approaches have been widely used in statistics inference. Important examples of estimating equations are the likelihood equations. Since its introduction by Sir R. A. Fisher almost a century ago, maximum likelihood estimation (MLE) is still the most popular estimation method used for fitting probability distribution to data, including fitting lifetime distributions with censored data. However, MLE may produce substantial bias and even fail to obtain valid confidence intervals when data size is not large enough or there is censoring data. In this paper, based on nonlinear combinations of order statistics, we propose new estimation equation approaches for a class of probability distributions, which are particularly effective for skewed distributions with small sample sizes and censored data. The proposed approaches may possess a number of attractive properties such as consistency, sufficiency and uniqueness. Asymptotic normality of these new estimators is derived. The construction of new estimation equations and their numerical performance under different censored schemes are detailed via Weibull distribution and generalized exponential distribution.
Keywords
Estimation equation Nonlinear combination of order statistics Asymptotic normality Weibull distribution Generalized exponential distribution Title
 New estimating equation approaches with application in lifetime data analysis
 Journal

Annals of the Institute of Statistical Mathematics
Volume 65, Issue 3 , pp 589615
 Cover Date
 201306
 DOI
 10.1007/s1046301203856
 Print ISSN
 00203157
 Online ISSN
 15729052
 Publisher
 Springer Japan
 Additional Links
 Topics
 Keywords

 Estimation equation
 Nonlinear combination of order statistics
 Asymptotic normality
 Weibull distribution
 Generalized exponential distribution
 Industry Sectors
 Authors

 Keming Yu ^{(1)} ^{(2)}
 Bing Xing Wang ^{(3)}
 Valentin Patilea ^{(4)}
 Author Affiliations

 1. Department of Mathematical Sciences, Brunel University, London, UB8 3PH, UK
 2. Business School, Shihezi University, Wujiaqu, China
 3. Department of Statistics, Zhejiang Gongshang University, Hangzhou, 310018, China
 4. Ecole Nationale de la Statistique et de l’Analyse de l’Information (Ensai), (CRES), Rue Blaise Pascal, BP 37203, 35172, BRUZ Cedex, France