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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, D89069 Ulm, Germany Univ Ulm Ulm Germany D89069Univ Ulm, D89069 Ulm, Germany
 Titolo Testata:
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES BSTATISTICAL METHODOLOGY
,
volume: 61,
anno: 1999,
parte:, 2
pagine: 439  458
 SICI:
 13697412(1999)61:<439:MBKAAC>2.0.ZU;2Z
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 NONPARAMETRIC CURVE ESTIMATION; DENSITYESTIMATION; ENDPOINTS; 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. 439458
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 meansquared error or supnorm 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 nonnegative kernels used in the interior onto the boundary. They are obtained as solutions of the same kernelgenerating 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 GaussMarkov 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