Multivariate statistics: a practical approach
Multivariate statistics: a practical approach
The smallest point of a polytope
Journal of Optimization Theory and Applications
Minimum distance density-based estimation
Computational Statistics & Data Analysis
Reweighted kernel density estimation
Computational Statistics & Data Analysis
Maximum likelihood kernel density estimation: On the potential of convolution sieves
Computational Statistics & Data Analysis
A computational strategy for doubly smoothed MLE exemplified in the normal mixture model
Computational Statistics & Data Analysis
Least squares estimation of a k-monotone density function
Computational Statistics & Data Analysis
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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.