Uniform consistency of automatic and location-adaptive delta-sequence estimators
type: Item
instance of: scholarly article
title: Uniform consistency of automatic and location-adaptive delta-sequence estimators
zbMATH Open document ID: 0644.62041
DOI: 10.1007/BF00318909
author: Deborah Nolan
author: J. S. Marron
publication date: 1989-01-01T00:00:00Z
review text: The class of delta-sequence estimators for a probability density includes the kernel, histogram and orthogonal series types, because each can be characterized as a collection of averages of some function that is indexed by a smoothing parameter. There are two important extensions of this class. The first allows a random smoothing parameter, for example that specified by a cross-validation method. The second allows the smoothing parameter to be a function of location, for example an estimator based on nearest-neighbor distance. In this paper a general method is presented which establishes uniform consistency for all of these estimators.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 4050765
zbMATH Keywords: delta-sequence estimators
zbMATH Keywords: histogram
zbMATH Keywords: smoothing parameter
zbMATH Keywords: cross- validation
zbMATH Keywords: nearest-neighbor distance
zbMATH Keywords: uniform consistency
zbMATH Keywords: density estimation
zbMATH Keywords: kernel estimators
zbMATH Keywords: orthogonal series type estimators
zbMATH Keywords: location-adaptive smoothing
MaRDI profile type: Publication
cites work: Arbitrariness of the pilot estimator in adaptive kernel methods
cites work: On bandwidth variation in kernel estimates. A square root law
cites work: Adaptive density flattening. - A metric distortion principle for combating bias in nearest neighbor methods
cites work: Q5184302
cites work: Q4104731
cites work: Q5639142
cites work: Variable Kernel Estimates of Multivariate Densities
cites work: A data dependent approach to density estimation
cites work: A note on the \(L_ 1\) consistency of variable kernel estimates
cites work: The consistency of automatic kernel density estimates
cites work: The strong uniform convergence of multivariate variable kernel estimates
cites work: Q3868610
cites work: Central limit theorems for empirical measures
cites work: Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties
cites work: Q4057952
cites work: Large sample optimality of least squares cross-validation in density estimation
cites work: On near neighbour estimates of a multivariate density
cites work: Q3749907
cites work: Cross-validation and the smoothing of orthogonal series density estimators
cites work: Extent to which least-squares cross-validation minimises integrated square error in nonparametric density estimation
cites work: On the amount of noise inherent in bandwidth selection for a kernel density estimator
cites work: Variable window width kernel estimates of probability densities
cites work: Uniform consistency of a histogram density estimator and modal estimation
cites work: Weak convergence and efficient density estimation at a point
cites work: A Nonparametric Estimate of a Multivariate Density Function
cites work: Multivariate k-nearest neighbor density estimates
cites work: An asymptotically efficient solution to the bandwidth problem of kernel density estimation
cites work: A comparison of cross-validation techniques in density estimation
cites work: Local data-driven bandwidth choice for density estimation
cites work: Variable bandwidth kernel estimators of regression curves
cites work: U-processes: Rates of convergence
cites work: Convergence of stochastic processes
cites work: Q3330303
cites work: On empirical density function
cites work: Q3966924
cites work: Frequency Polygons: Theory and Application
cites work: Averaged shifted histograms: Effective nonparametric density estimators in several dimensions
cites work: Weak and strong uniform consistency of the kernel estimate of a density and its derivatives
cites work: Q4727203
cites work: An asymptotically optimal window selection rule for kernel density estimates
cites work: Q5369128
cites work: Q3896361
cites work: A histogram method of density estimation
cites work: A Polynomial Algorithm for Density Estimation
cites work: Interpolating spline methods for density estimation. I: Equi-spaced knots
cites work: Data-based optimal smoothing of orthogonal series density estimates
cites work: Probability density estimation using delta sequences
cites work: On Choosing a Delta-Sequence
full work available at URL: https://doi.org/10.1007/bf00318909
OpenAlex ID: W2052666959
Recommended article: Universal consistency of delta estimators
Recommended article: Adaptive sequential confidence intervals for A location Parameter
Recommended article: Uniform large deviations principle for the delta-sequence method density estimator
Recommended article: Improved sequential and accelerated sequential Procedures for estimating the scale parameter in a aniform distribution
Recommended article: Sequential Interval Estimation of a Location Parameter with the Fixed Width in the Uniform Distribution with an Unknown Scale Parameter
Recommended article: UNIFORM CONSISTENCY FOR NONPARAMETRIC ESTIMATORS IN NULL RECURRENT TIME SERIES
Recommended article: Consistency of adaptive estimators on the basis of correlated observations

Uniform consistency of automatic and location-adaptive delta-sequence estimators (Recommended article)
Recommended article: Sequential risk-efficient estimation of the parameter in the uniform density
Similarity Score: 0.8342221
Recommender Run: Recommender Run 3

Uniform consistency of automatic and location-adaptive delta-sequence estimators (published in)
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete