Minimum negative exponential disparity estimation of mixture proportions
- 作者：McCann ; Melinda ; Sarkar ; Sahadeb
- 关键词：62F10 ; 62F35 ; Minimum disparity estimation ; Hellinger distance ; Robustness ; Simulation ; Relative efficiency
- 刊名：Journal of Statistical Planning and Inference
- 出版年：2000
- 期刊代码：36_03783758
- 类别：mt
- 出版时间：June 1, 2000
- 卷：87
- 期：2
- 页码：187-197
- 文件大小：173 K
摘要
In this paper we investigate the problem of estimating the mixing proportion in the mixture of densities using the minimum negative exponential disparity estimator (MNEDE) introduced by Lindsay (1994, Ann. Statist. 22, 1081–1114). Woodward et al. (1995, J. Amer. Statist. Assoc. 79, 590–598) examined a minimum Hellinger distance estimator (MHDE) for the same setting. Theoretical results such as strong consistency and asymptotic normality of the MNEDE are established by verifying conditions given in Basu et al. (1997, J. Statist. Plann. Inference) when there are two known component densities. Through simulations asymptotic relative efficiency of the MNEDE to the MHDE and MLE are examined in special cases when the two known densities are pdf's of scale and location transformations, respectively, of (a) a standard normal random variable and (b) a t random variable with four degrees of freedom. Simulations are also carried out when the two component distributions are obtained as transformations of a normal or t distribution as mentioned above, but are assumed to have unknown means and variances. It is shown that the MNEDE is an attractive robust estimator that compares well with the MHDE.