Block bootstrapping for kernel density estimators under ψ-weak dependence

Eunju Hwang; Dong Wan Shin

doi:10.1080/03610926.2012.701695

Block bootstrapping for kernel density estimators under ψ-weak dependence

Eunju Hwang, Dong Wan Shin

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Block bootstrap methods are applied to kernel-type density estimator and its derivatives for ψ-weakly dependent processes. Nonparametric density estimation is discussed via moving block bootstrap (MBB) and disjoint block bootstrap (DBB). Asymptotic validity is proved for MBB and DBB. A Monte-Carlo experiment compares confidence intervals based on MBB and DBB with an existing method based on normal approximation (NA) in terms of serial correlation, dynamic asymmetry, and conditional heteroscedasticity. The experiment shows that, in cases of substantial serial correlation, MBB and DBB perform better than NA and, in the other cases, MBB and DBB perform as good as NA.

Original language	English
Pages (from-to)	3751-3761
Number of pages	11
Journal	Communications in Statistics - Theory and Methods
Volume	43
Issue number	17
DOIs	https://doi.org/10.1080/03610926.2012.701695
State	Published - 2014

Bibliographical note

Funding Information:
This work was supported by Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology (NRF-2009-0070618, NRF-2010-0023000).

Keywords

Disjoint block bootstrap
Kernel density estimator
Moving block bootstrap
Nonlinear time series
Weak dependence

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10.1080/03610926.2012.701695

Cite this

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title = "Block bootstrapping for kernel density estimators under ψ-weak dependence",

abstract = "Block bootstrap methods are applied to kernel-type density estimator and its derivatives for ψ-weakly dependent processes. Nonparametric density estimation is discussed via moving block bootstrap (MBB) and disjoint block bootstrap (DBB). Asymptotic validity is proved for MBB and DBB. A Monte-Carlo experiment compares confidence intervals based on MBB and DBB with an existing method based on normal approximation (NA) in terms of serial correlation, dynamic asymmetry, and conditional heteroscedasticity. The experiment shows that, in cases of substantial serial correlation, MBB and DBB perform better than NA and, in the other cases, MBB and DBB perform as good as NA.",

keywords = "Disjoint block bootstrap, Kernel density estimator, Moving block bootstrap, Nonlinear time series, Weak dependence",

author = "Eunju Hwang and Shin, {Dong Wan}",

note = "Funding Information: This work was supported by Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology (NRF-2009-0070618, NRF-2010-0023000).",

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doi = "10.1080/03610926.2012.701695",

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AU - Hwang, Eunju

AU - Shin, Dong Wan

N1 - Funding Information: This work was supported by Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology (NRF-2009-0070618, NRF-2010-0023000).

PY - 2014

Y1 - 2014

N2 - Block bootstrap methods are applied to kernel-type density estimator and its derivatives for ψ-weakly dependent processes. Nonparametric density estimation is discussed via moving block bootstrap (MBB) and disjoint block bootstrap (DBB). Asymptotic validity is proved for MBB and DBB. A Monte-Carlo experiment compares confidence intervals based on MBB and DBB with an existing method based on normal approximation (NA) in terms of serial correlation, dynamic asymmetry, and conditional heteroscedasticity. The experiment shows that, in cases of substantial serial correlation, MBB and DBB perform better than NA and, in the other cases, MBB and DBB perform as good as NA.

AB - Block bootstrap methods are applied to kernel-type density estimator and its derivatives for ψ-weakly dependent processes. Nonparametric density estimation is discussed via moving block bootstrap (MBB) and disjoint block bootstrap (DBB). Asymptotic validity is proved for MBB and DBB. A Monte-Carlo experiment compares confidence intervals based on MBB and DBB with an existing method based on normal approximation (NA) in terms of serial correlation, dynamic asymmetry, and conditional heteroscedasticity. The experiment shows that, in cases of substantial serial correlation, MBB and DBB perform better than NA and, in the other cases, MBB and DBB perform as good as NA.

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KW - Kernel density estimator

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JO - Communications in Statistics - Theory and Methods

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Block bootstrapping for kernel density estimators under ψ-weak dependence

Abstract

Bibliographical note

Keywords

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