A comparative study of several smoothing methods in density estimation
Computational Statistics & Data Analysis
A comparison of hybrid strategies for Gibbs sampling in mixed graphical models
Computational Statistics & Data Analysis
A Bayesian approach to bandwidth selection for multivariate kernel density estimation
Computational Statistics & Data Analysis
Robust NL-means filter with optimal pixel-wise smoothing parameter for statistical image denoising
IEEE Transactions on Signal Processing
Kernel bandwidth optimization in spike rate estimation
Journal of Computational Neuroscience
A flexible extreme value mixture model
Computational Statistics & Data Analysis
Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions
Computational Statistics & Data Analysis
Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation
Computational Statistics & Data Analysis
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A new procedure is proposed for deriving variable bandwidths in univariate kernel density estimation, based upon likelihood cross-validation and an analysis of a Bayesian graphical model. The procedure admits bandwidth selection which is flexible in terms of the amount of smoothing required. In addition, the basic model can be extended to incorporate local smoothing of the density estimate. The method is shown to perform well in both theoretical and practical situations, and we compare our method with those of Abramson (The Annals of Statistics 10: 1217–1223) and Sain and Scott (Journal of the American Statistical Association 91: 1525–1534). In particular, we note that in certain cases, the Sain and Scott method performs poorly even with relatively large sample sizes.We compare various bandwidth selection methods using standard mean integrated square error criteria to assess the quality of the density estimates. We study situations where the underlying density is assumed both known and unknown, and note that in practice, our method performs well when sample sizes are small. In addition, we also apply the methods to real data, and again we believe our methods perform at least as well as existing methods.