New estimating equation approaches with application in lifetime data analysis
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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.
- Brown, B. M. (1985). Grouping problems in distribution-free regression. Australian Journal of Statistics, 27, 123–134. CrossRef
- Csörgő, M., Horváth, L. (1990). On the distribution of \(L_p\) norms of weighted quantile processes. Annales de l’I.H.P., section B, 26, 65–85.
- Csörgő, M., Révész, P. (1978). Strong approximations of the quantile process. Annals of Statistics, 6, 882–894.
- Csörgő, M., Yu, H. (1997). Estimation of total time on test transforms for stationary observations. Stochastic Processes and their Applications, 68, 229–253.
- Dodson, B. (1994). Weibull analysis: with software. Milwaukee: ASQ Quality Press.
- Giorgi, G. M. (1999). Income inequality measurement: the statistical approach. In J. Silber (Ed.), Handbook of income inequality measurement (pp. 245–267). Boston: Kluwer. CrossRef
- Gupta, R. D., Kundu, D. (1999). Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41, 173–188.
- Gupta, R. D., Kundu, D. (2001). Generalized exponential distributions: different methods of estimations. Journal of Statistical Computation and Simulation, 69, 315–338.
- Gupta, R. D., Kundu, D. (2003). Closeness of gamma and generalized exponential distribution. Communications in Statistics—Theory and Methods, 32, 705–721.
- Gupta, R. D., Kundu, D. (2006). On the comparison of Fisher information of the Weibull and GE distributions. Journal of Statistical Planning and Inference, 136, 3130–3144.
- Gupta, R. D., Kundu, D. (2007). Generalized exponential distribution: existing results and some recent developments. Journal of Statistical Planning and Inference, 137, 3537–3547.
- Hampel, F. R., Rousseeuw, P. J., Ronchetti, E. M., Stahel, W. (1986). Robust statistics: the approach based on influence functions. New York: Wiley Interscience.
- Hosking, J. R. M. (1990). L-moments: analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society B, 52, 105–124.
- Hosking, J. R. M. (1995). The use of L-moments in the analysis of censored data. In N. Balakrishnan (Ed.), Recent advances in life-testing and reliability (pp. 545–564). Boca Raton: CRC Press.
- Jones, B. L., Zitikis, R. (2003). Empirical estimation of risk measures and related quantities. North American Actuarial Journal, 7, 44–54.
- Kundu, D., Gupta, R. D., Manglick, A. (2005). Discriminating between the log-normal and generalized exponential distribution. Journal of Statistical Planning and Inference, 127, 213–227.
- Lawless, J. F. (1975). Construction of tolerance bounds for the extreme value and Weibull distributions. Technometrics, 17, 255–261. CrossRef
- Lawless, J. F. (2003). Statistical models and methods for lifetime data (2nd ed., pp. 1691–1696). New York: Wiley.
- Maritz, J. S. (1995). Distribution-free statistical methods. London: Chapman& Hall.
- Mitra, S., Kundu, D. (2008). Analysis of the left censored data from the generalized exponential distribution. Journal of Statistical Computation and Simulation, 78, 669–679.
- Raqab, M. Z. (2002). Inferences for generalized exponential distribution based on record statistics. Journal of Statistical Planning and Inference, 104, 339–350. CrossRef
- Wang, B. X., Yu, K., Jones, M. C. (2010). Inference under progressively type II right censored sampling for certain lifetime distributions. Technometrics, 52, 453–460.
- Weerahandi, S. (2004). Generalized inference in repeated measures: exact methods in MANOVA and mixed models. New Jersey: Wiley.
- New estimating equation approaches with application in lifetime data analysis
Annals of the Institute of Statistical Mathematics
Volume 65, Issue 3 , pp 589-615
- Cover Date
- Print ISSN
- Online ISSN
- Springer Japan
- Additional Links
- Estimation equation
- Nonlinear combination of order statistics
- Asymptotic normality
- Weibull distribution
- Generalized exponential distribution
- Industry Sectors
- 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