Minimizing L 1 distance in nonparametric density estimation
Peter Hall,Matt P. Wand +1 more
TLDR
A simple algorithm, based on Newton's method, is constructed, which permits asymptotic minimization of L1 distance for nonparametric density estimators and is applicable to multivariate kernel estimator, multivariate histogram estimators, and smoothed histograms estimators such as frequency polygons.About:
This article is published in Journal of Multivariate Analysis.The article was published on 1988-07-01 and is currently open access. It has received 68 citations till now. The article focuses on the topics: Multivariate kernel density estimation & Adaptive algorithm.read more
Citations
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Book
Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning
TL;DR: Techniques covered range from traditional multivariate methods, such as multiple regression, principal components, canonical variates, linear discriminant analysis, factor analysis, clustering, multidimensional scaling, and correspondence analysis, to the newer methods of density estimation, projection pursuit, neural networks, and classification and regression trees.
Journal ArticleDOI
Recent Developments in Nonparametric Density Estimation
TL;DR: In this paper, the authors present a review of recent developments in nonparametric density estimation and include topics that have been omitted from review articles and books on the subject, such as the histogram, kernel estimators, and orthogonal series estimators.
Dissertation
Bandwidth Selection in Kernel Density Estimation
TL;DR: A new bandwidth selector has promising behavior with respect to the visual error criterion, especially in the cases of limited sample sizes, and a new data-driven bandwidth selector is proposed which is thought to be without these drawbacks.
Journal ArticleDOI
Review Papers: Recent Developments in Nonparametric Density Estimation
TL;DR: In this paper, the authors review recent developments in nonparametric density estimation and include topics that have been omitted from review articles and books on the subject and discuss different types of restricted maximum likelihood density estimators, including order-restricted estimators and sieve estimators.
Journal ArticleDOI
A comparative study of several smoothing methods in density estimation
TL;DR: A critical up-to-date review of the main methods currently available can be found in this article, where the authors provide some new insights on the important problem of estimating the minimization criteria and on the choice of pilot bandwidths in bootstrap-based methods.
References
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Book ChapterDOI
Probability Inequalities for sums of Bounded Random Variables
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.
Journal ArticleDOI
An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates
TL;DR: In this paper, a window selection rule is considered, which can be interpreted in terms of cross-validation, under the mild assumption that the unknown density and its one-dimensional marginals are bounded.
Journal ArticleDOI
Extent to which least-squares cross-validation minimises integrated square error in nonparametric density estimation
Peter Hall,James Stephen Marron +1 more
TL;DR: In this article, the authors compare different data-driven approaches to the determination of window size, and show that the observable window ĥ� c>>\s performs as well as the so-called "optimal" but unattainable window h>>\s to both first and second order.