Book Chapter10.1007/978-94-011-3222-0_19
Root N Bandwidth Selection
James Stephen Marron
- 01 Jan 1991
- pp 251-260
12
TL;DR: A survey and comparison of methods which have the very fast rate of convergence of the square root of the sample size in view of those usually encountered in nonparametric curve estimation problems.
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Abstract: For various data-based bandwidth selectors for a kernel density estimator, the relative rate of convergence of the selected bandwidth is considered. Several methods have recently been found which have the very fast rate of convergence of the square root of the sample size. Such a fast rate of convergence is quite surprising, in view of those usually encountered in nonparametric curve estimation problems. A survey and comparison of methods with this very fast rate of convergence is given.
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Citations
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.
245
•Journal Article
Progress in data-based bandwidth selection for kernel density estimation
TL;DR: A comparison of methods' practical performance demonstrates that improvements to be gained by using the better methods can be, and often are, considerable, and arguably the two best known bandwidth selection methods cannot be advocated for general practical use.
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Universal smoothing factor selection in density estimation: theory and practice - Discussion
TL;DR: A practical implementation of a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, theL1 error of the corresponding kernel estimate is not larger than 3+∈ times theerror of the estimate with the optimal smoothing factors plus a constant times $$sqrt {\log n/n}$$, wheren is the sample size.
102
Empirical functionals and efficient smoothing parameter selection
Peter Hall,Iain M. Johnstone +1 more
TL;DR: In this article, nonparametric information bounds are defined for the smoothing parameter h 0, which minimizes the squared error of a kernel or smoothing spline estimator, and asymptotically efficient estimators of h 0 are presented.
82
An automatic bandwidth selector for kernel density estimation
TL;DR: In this paper, the authors proposed to select the cut-off frequency by a generalization of cross-validation, which has a relative convergence rate n-, which is much faster than the rate n 1110 for the bandwidth estimate selected by cross-valuation.
55
References
Density estimation for statistics and data analysis
Bernard W. Silverman
- 01 Jan 1986
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
Applied Nonparametric Regression.
Peter M. Robinson,W. Haerdle +1 more
TL;DR: Applied Nonparametric Regression as mentioned in this paper is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable, including kernel smoothing, spline smoothing and orthogonal polynomials.
1.3K
Nonparametric density estimation : the L[1] view
Luc Devroye,László Györfi +1 more
TL;DR: Differentiation of Integrals Consistency Lower bounds for rates of convergence rates of Convergence in L1 and Pointwise Convergence estimates Related to the Kernel Estimate and the Histogram Estimate Simulation, Inequalities, and Random Variate Generation The Transformed Kernel Estimation Applications in Discrimination Operations on Density Estimates Estimators Based on Orthogonal Series Index as mentioned in this paper.
957
Biased and Unbiased Cross-Validation in Density Estimation
David Scott,George R. Terrell +1 more
TL;DR: In this article, biased cross-validation criteria for selection of smoothing parameters for kernel and histogram density estimators, closely related to one investigated in Scott and Factor (1981), were introduced.