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Titolo:
Multivariate boundary kernels and a continuous least squares principle
Autore:
Muller, HG; Stadtmuller, U;
Indirizzi:
Univ Calif Davis, Div Stat, Davis, CA 95616 USA Univ Calif Davis Davis CAUSA 95616 Davis, Div Stat, Davis, CA 95616 USA Univ Ulm, D-89069 Ulm, Germany Univ Ulm Ulm Germany D-89069Univ Ulm, D-89069 Ulm, Germany
Titolo Testata:
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
, volume: 61, anno: 1999,
parte:, 2
pagine: 439 - 458
SICI:
1369-7412(1999)61:<439:MBKAAC>2.0.ZU;2-Z
Fonte:
ISI
Lingua:
ENG
Soggetto:
NONPARAMETRIC CURVE ESTIMATION; DENSITY-ESTIMATION; END-POINTS; REGRESSION;
Keywords:
curve estimation; density estimation; edge effects; kernel estimator; local least squares; smoothing;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
24
Recensione:
Indirizzi per estratti:
Indirizzo: Muller, HG Univ Calif Davis, Div Stat, 1 Shields Ave, Davis, CA 95616 USA Univ Calif Davis 1 Shields Ave Davis CA USA 95616 CA 95616 USA
Citazione:
H.G. Muller e U. Stadtmuller, "Multivariate boundary kernels and a continuous least squares principle", J ROY STA B, 61, 1999, pp. 439-458

Abstract

Whereas there are many references on univariate boundary kernels, the construction of boundary kernels for multivariate density and curve estimation has not been investigated in detail. The use of multivariate boundary kernels ensures global consistency of multivariate kernel estimates as measured by the integrated mean-squared error or sup-norm deviation for functions with compact support. We develop a class of boundary kernels which work for any support, regardless of the complexity of its boundary. Our construction yields a boundary kernel for each point in the boundary region where the function is to be estimated. These boundary kernels provide a natural continuation of non-negative kernels used in the interior onto the boundary. They are obtained as solutions of the same kernel-generating variational problemwhich also produces the kernel function used in the interior as its solution. We discuss the numerical implementation of the proposed boundary kernels and their relationship to locally weighted least squares. Along the way we establish a continuous least squares principle and a continuous analogue of the Gauss-Markov theorem.

ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 30/03/20 alle ore 09:09:08