Parametric statistical modeling by minimum integrated square error
Parametric statistical modeling by minimum integrated square error
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DOI：
10.1198/004017001316975880
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发表时间：
2001-08-01
期刊：
影响因子：
2.5
通讯作者：
Scott, DW
中科院分区：
文献类型：
--
作者：
Scott, DW
似然函数在参数估计和贝叶斯估计以及通过局部多项式建模的非参数函数估计中起着核心作用。然而.积分平方误差作为非参数密度估计中选择的拟合优度准则具有悠久的传统。在这篇文章中。我研究了积分平方误差或L-2距离的使用。作为各种参数统计模型的理论和实际估计工具。我表明，通过最小化综合平方误差或L-2估计（L2 E）标准与最大似然估计的参数估计的渐近无效性大致是中位数与平均值。我证明了著名的结果，最小距离估计。包括L2 E，本质上是鲁棒的;然而。L2 E不需要在鲁棒似然算法中找到的任何调谐因子的规范。L2 E特别适用于分析大规模数据集，其中数据清理是不切实际的，统计效率是次要问题。设置L2 E标准相对简单，即使具有一些非常复杂的模型规范。本文研究的具体问题包括单变量密度估计、混合密度估计、多元回归估计以及均值和协方差的稳健估计。这篇文章是为了纪念他。
The likelihood function plays a central role in parametric and Bayesian estimation, as well as in nonparametric function estimation via local polynomial modeling. However. integrated square error has enjoyed a long tradition as the goodness-of-fit criterion of choice in nonparametric density estimation. In this article. I investigate the use of integrated square error, or L-2 distance. as a theoretical and practical estimation toot for a variety of parametric statistical models. I show that the asymptotic inefficiency of the parameters estimated by minimizing the integrated square error or L-2 estimation (L2E) criterion versus the maximum likelihood estimator is roughly that of the median versus the mean. I demonstrate by example the well-known result that minimum distance estimators. including L2E, are inherently robust; however. L2E does not require specification of any tuning factors found in robust likelihood algorithms. L2E is particularly appropriate for analyzing massive datasets in which data cleaning is impractical and statistical efficiency is a secondary concern. Setting up the L2E criterion is relatively simple even with some very complex model specifications. Specific problems studied in this article include univariate density estimation, mixture density estimation, multivariate regression estimation, and robust estimation of the mean and covariance.John Tukey had a pivotal role in both nonparametric and robust estimation. This article is dedicated to his memory.