Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression
Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression
复制标题
DOI：
10.1214/13-ejs847
复制
发表时间：
2013-01-01
影响因子：
1.1
通讯作者：
Basu, Ayanendranath
中科院分区：
文献类型：
--
作者：
Ghosh, Abhik;Basu, Ayanendranath
在现实生活中，我们经常不得不处理这样的情况，即采样的观测值是独立的，并且在其分布中共享共同的参数，但不是同分布的。虽然基于最大似然法的方法为在这种情况下进行统计推断提供了规范的方法，但它通常带有对假设条件的微小偏差缺乏稳健性的包袱。在本文中，我们发展了一种基于最小距离方法的通用估计方法来处理这种情况，该方法利用了密度功率散度度量的稳健性(Basu等人)。1998[2])。我们建立了所提出的估计量的渐近性质，并说明了我们的方法在线性回归情况下的好处。
In real life we often have to deal with situations where the sampled observations are independent and share common parameters in their distribution but are not identically distributed. While the methods based on maximum likelihood provide canonical approaches for doing statistical inference in such contexts, it carries with it the usual baggage of lack of robustness to small deviations from the assumed conditions. In the present paper we develop a general estimation method for handling such situations based on a minimum distance approach which exploits the robustness properties of the density power divergence measure (Basu et al. 1998 [2]). We establish the asymptotic properties of the proposed estimators, and illustrate the benefits of our method in case of linear regression.