Full bandwidth matrix selectors for gradient kernel density
estimate

J 2013

Full bandwidth matrix selectors for gradient kernel density estimate

HOROVÁ, Ivanka, Jan KOLÁČEK and Kamila VOPATOVÁ

Basic information

Original name

Full bandwidth matrix selectors for gradient kernel density estimate

Authors

HOROVÁ, Ivanka (203 Czech Republic, belonging to the institution), Jan KOLÁČEK (203 Czech Republic, guarantor, belonging to the institution) and Kamila VOPATOVÁ (203 Czech Republic, belonging to the institution)

Edition

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

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 1.151

RIV identification code

RIV/00216224:14310/13:00067353

Organization unit

Faculty of Science

DOI

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

UT WoS

000310403700027

Keywords in English

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

Abstract

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.

Links

LC06024, research and development project

Name: Centrum Jaroslava Hájka pro teoretickou a aplikovanou statistiku

Investor: Ministry of Education, Youth and Sports of the CR, Jaroslav Hájek Center for Theoretical and Applied Statistics

Citovat

HOROVÁ, Ivanka, Jan KOLÁČEK and Kamila VOPATOVÁ. Full bandwidth matrix selectors for gradient kernel density estimate. Computational Statistics & Data Analysis. ELSEVIER, 2013, vol. 57, No 1, p. 364-376. ISSN 0167-9473. Available from: 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 and Kamila VOPATOVÁ. Full bandwidth matrix selectors for gradient kernel density estimate. \textit{Computational Statistics \&{} Data Analysis}. ELSEVIER, 2013, vol.~57, No~1, p.~364-376. ISSN~0167-9473. Available from: https://dx.doi.org/10.1016/j.csda.2012.07.006.

Detailed Information on Publication Record