Journal ArticleDOI
An alternative method of cross-validation for the smoothing of density estimates
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TLDR
An alternative method of cross-validation, based on integrated squared error, recently also proposed by Rudemo (1982), is derived, and Hall (1983) has established the consistency and asymptotic optimality of the new method.Abstract:
Cross-validation with Kullback-Leibler loss function has been applied to the choice of a smoothing parameter in the kernel method of density estimation. A framework for this problem is constructed and used to derive an alternative method of cross-validation, based on integrated squared error, recently also proposed by Rudemo (1982). Hall (1983) has established the consistency and asymptotic optimality of the new method. For small and moderate sized samples, the performances of the two methods of cross-validation are compared on simulated data and specific examples.read more
Citations
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Journal ArticleDOI
A survey of cross-validation procedures for model selection
Sylvain Arlot,Alain Celisse +1 more
TL;DR: This survey intends to relate the model selection performances of cross-validation procedures to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results.
Journal ArticleDOI
A survey of cross-validation procedures for model selection
Sylvain Arlot,Alain Celisse +1 more
TL;DR: In this paper, a survey on the model selection performances of cross-validation procedures is presented, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results, and guidelines are provided for choosing the best crossvalidation procedure according to the particular features of the problem in hand.
Journal ArticleDOI
Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity
TL;DR: A technique is developed, termed geographically weighted regression, which attempts to capture variation by calibrating a multiple regression model which allows different relationships to exist at different points in space by using Monte Carlo methods.
Journal ArticleDOI
A Brief Survey of Bandwidth Selection for Density Estimation
TL;DR: In this article, the authors recommend a "solve-the-equation" plug-in bandwidth selector as being most reliable in terms of overall performance for kernel density estimation.
Book
Local Regression and Likelihood
TL;DR: The Origins of Local Regression, Fitting with LOCFIT, and Optimizing local Regression methods.
References
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Journal ArticleDOI
Cross-Validatory Choice and Assessment of Statistical Predictions (With Discussion)
Empirical Choice of Histograms and Kernel Density Estimators
TL;DR: Methods of choosing histogram width and the smoothing parameter of kernel density estimators by use of data are studied and two closely related risk function estimators are given.
Journal ArticleDOI
Multivariate binary discrimination by the kernel method
John Aitchison,C. G. G. Aitken +1 more
TL;DR: The kernel method of density estimation from continuous to multivariate binary spaces is described, finding its simple nonparametric nature together with its consistency properties make it an attractive tool in discrimination problems, with some advantages over already proposed parametric counterparts.
Journal ArticleDOI
A completely automatic french curve: fitting spline functions by cross validation
Grace Wahba,Svante Wold +1 more
TL;DR: In this paper, the cross validation mean square error technique is used to determine the correct degree of smoothing, in fitting smoothing solines to discrete, noisy observations from some unknown smooth function.
Journal ArticleDOI
On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions
TL;DR: Parzen estimators are often used for nonparametric estimation of probability density functions and a problem-dependent criterion for its value is proposed and illustrated by some examples.