Abstract
Minimum Hellinger distance estimation (MHDE) for parametric model is obtained by minimizing the Hellinger distance between an assumed parametric model and a nonparametric estimation of the model. MHDE receives increasing attention for its efficiency and robustness. Recently, it has been extended from parametric models to semiparametric models. This manuscript considers a two-sample semiparametric location-shifted model where two independent samples are generated from two identical symmetric distributions with different location parameters. We propose to use profiling technique in order to utilize the information from both samples to estimate unknown symmetric function. With the profiled estimation of the function, we propose a minimum profile Hellinger distance estimation (MPHDE) for the two unknown location parameters. This MPHDE is similar to but dif- ferent from the one introduced in Wu and Karunamuni (2015), and thus the results presented in this work is not a trivial application of their method. The difference is due to the two-sample nature of the model and thus we use different approaches to study its asymptotic properties such as consistency and asymptotic normality. The efficiency and robustness properties of the proposed MPHDE are evaluated empirically though simulation studies. A real data from a breast cancer study is analyzed to illustrate the use of the proposed method.
Highlights
Minimum distance estimation of unknown parameters in a parametric model is obtained by minimizing the distance between a nonparametric distribution esti- mation and an assumed parametric model
We focus on model (1) in this paper and work on the inference for the location parameter θ
To investigate the robustness properties of the proposed minimum profile Hellinger distance estimation (MPHDE) and make comparison, we examine the performance of the three methods under data con- tamination
Summary
Minimum distance estimation of unknown parameters in a parametric model is obtained by minimizing the distance between a nonparametric distribution esti- mation (such as empirical, kernel, etc) and an assumed parametric model. The MHDE usually re- quires an estimate of infinite-dimensional nuisance parameter in semiparametric models, which leads to computational difficulty. To solve this problem, Wu and Karunamuni (2015) proposed a minimum profile Hellinger distance estimation (MPHDE). For one-sample case, Wu and Karunamuni (2015) used the Hellinger distance between the location model and its nonpara- metric estimation This method does not work for our two-sample case because it cannot utilize the information for the nuisance parameter contained in both samples. To handle the two-sample estimation, we propose a new Hellinger distance between the location-shifted model and its estimation that involves the nuisance density estimation and the location parameters of our interest.
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