Full bandwidth matrix selectors for gradient kernel density
estimate

J 2013

Full bandwidth matrix selectors for gradient kernel density estimate

HOROVÁ, Ivanka, Jan KOLÁČEK a Kamila VOPATOVÁ

Základní údaje

Originální název

Full bandwidth matrix selectors for gradient kernel density estimate

Autoři

HOROVÁ, Ivanka (203 Česká republika, domácí), Jan KOLÁČEK (203 Česká republika, garant, domácí) a Kamila VOPATOVÁ (203 Česká republika, domácí)

Vydání

Computational Statistics & Data Analysis, ELSEVIER, 2013, 0167-9473

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 1.151

Kód RIV

RIV/00216224:14310/13:00067353

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1016/j.csda.2012.07.006

UT WoS

000310403700027

Klíčová slova anglicky

asymptotic mean integrated square error; multivariate kernel density; unconstrained bandwidth matrix

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 4. 4. 2014 12:06, Ing. Andrea Mikešková

Anotace

V originále

The most important factor in a multivariate kernel density estimation is a~choice of a bandwidth matrix. Because of its role in controlling both the amount and the direction of multivariate smoothing, this choice is a particularly important. Considerable attention has been paid to constrained parameterization of the bandwidth matrix such as a diagonal matrix or pre-transformation of the data. General multivariate kernel density derivative estimators has been investigated in paper Chac\'on, Test, p. 375--398, Vol. 19, 2011. The present paper is focused on data-driven selectors of full bandwidth matrices for a density and its gradient. This method is based on an optimally balanced relation between integrated variance and integrated squared bias. The analysis of statistical properties shows the rationale of the proposed method. It is also given the relative rate of convergence to compare the method with cross-validation and plug-in methods. The utility of this method is illustrated through a~simulation study and application to real data.

Návaznosti

LC06024, projekt VaV

Název: Centrum Jaroslava Hájka pro teoretickou a aplikovanou statistiku

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Centrum Jaroslava Hájka pro teoretickou a aplikovanou statistiku

Citovat

HOROVÁ, Ivanka, Jan KOLÁČEK a Kamila VOPATOVÁ. Full bandwidth matrix selectors for gradient kernel density estimate. Computational Statistics & Data Analysis. ELSEVIER, 2013, roč. 57, č. 1, s. 364-376. ISSN 0167-9473. Dostupné z: https://dx.doi.org/10.1016/j.csda.2012.07.006.

@article{969459,
   author = {Horová, Ivanka and Koláček, Jan and Vopatová, Kamila},
   article_number = {1},
   doi = {http://dx.doi.org/10.1016/j.csda.2012.07.006},
   keywords = {asymptotic mean integrated square error; multivariate kernel density; unconstrained bandwidth matrix},
   language = {eng},
   issn = {0167-9473},
   journal = {Computational Statistics & Data Analysis},
   title = {Full bandwidth matrix selectors for gradient kernel density estimate},
   volume = {57},
   year = {2013}
}

TY  - JOUR
ID  - 969459
AU  - Horová, Ivanka - Koláček, Jan - Vopatová, Kamila
PY  - 2013
TI  - Full bandwidth matrix selectors for gradient kernel density estimate
JF  - Computational Statistics & Data Analysis
VL  - 57
IS  - 1
SP  - 364-376
EP  - 364-376
PB  - ELSEVIER
SN  - 01679473
KW  - asymptotic mean integrated square error
KW  - multivariate kernel density
KW  - unconstrained bandwidth matrix
N2  - The most important factor in a multivariate kernel density estimation is a~choice of a bandwidth matrix. Because of its role in controlling both the amount and the direction of multivariate smoothing, this choice is a particularly important. Considerable attention has been paid to constrained parameterization of the bandwidth matrix such as a diagonal matrix or pre-transformation of the data. General multivariate kernel density derivative estimators has been investigated in paper Chac\'on, Test, p. 375--398, Vol. 19, 2011. The present paper is focused on data-driven selectors of full bandwidth matrices for a density and its gradient. This method is based on an optimally balanced relation between integrated variance and integrated squared bias. The analysis of statistical properties shows the rationale of the proposed method. It is also given the relative rate of convergence to compare the method with cross-validation and plug-in methods. The utility of this method is illustrated through a~simulation study and application to real data.
ER  -

HOROVÁ, Ivanka, Jan KOLÁČEK a Kamila VOPATOVÁ. Full bandwidth matrix selectors for gradient kernel density estimate. \textit{Computational Statistics \&{} Data Analysis}. ELSEVIER, 2013, roč.~57, č.~1, s.~364-376. ISSN~0167-9473. Dostupné z: https://dx.doi.org/10.1016/j.csda.2012.07.006.

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