Minimum quadratic distance density estimation using nonparametric mixtures

作者：Chee Chew Seng; Wang Yong^*

来源：Computational Statistics & Data Analysis, 2013, 57(1): 1-16.

DOI：10.1016/j.csda.2012.06.004

• Bandwidth selection
• Double smoothing
• Kernel-based density estimator
• Minimum distance estimation
• Nonparametric mixture
• Quadratic loss

Quadratic loss is predominantly used in the literature as the performance measure for nonparametric density estimation, while nonparametric mixture models have been studied and estimated almost exclusively via the maximum likelihood approach. In this paper, we relate both for estimating a nonparametric density function. Specifically, we consider nonparametric estimation of a mixing distribution by minimizing the quadratic distance between the empirical and the mixture distribution, both being smoothed by kernel functions, a technique known as double smoothing. Experimental studies show that the new mixture-based density estimators outperform the popular kernel-based density estimators in terms of mean integrated squared error for practically all the distributions that we studied, thanks to the substantial bias reduction provided by nonparametric mixture models and double smoothing.

• 出版日期2013-1