Local polynomial M-estimation in random design regression with dependent errors

Yixuan Liu; J. R. Wishart

doi:10.1007/978-3-030-28665-1_16

Local polynomial M-estimation in random design regression with dependent errors

Yixuan Liu, J. R. Wishart

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

Abstract

The asymptotic behaviour of the robust local polynomial M-estimator is investigated in the random design nonparametric regression model with short-range dependent and long-range dependent errors. Asymptotic results are established by decomposing the estimator into two terms: a martingale term and a conditional expectation term. The local polynomial M-estimator is asymptotically normal when errors are short-range dependent. When the errors are long-range dependent, a more complex behaviour is observed that depends on the size of the bandwidth. If the bandwidth is small enough, the standard asymptotic normality persists. If the bandwidth is relatively large the asymptotic result is more intricate and the long-range dependent variables dominate. In both cases, the optimal bandwidth is investigated.

Original language	English
Title of host publication	Stochastic models, statistics and their applications
Editors	Ansgar Steland, Ewaryst Rafajłowicz, Ostap Okhrin
Place of Publication	Cham, Switzerland
Publisher	Springer
Pages	219-227
Number of pages	9
ISBN (Electronic)	9783030286651
ISBN (Print)	9783030286644
DOIs	https://doi.org/10.1007/978-3-030-28665-1_16
Publication status	Published - 2019
Event	14th Workshop on Stochastic Models, Statistics and Their Applications - Dresden, Germany Duration: 6 Mar 2019 → 8 Mar 2019

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Publisher	Springer
Volume	294
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	14th Workshop on Stochastic Models, Statistics and Their Applications
Country/Territory	Germany
City	Dresden
Period	6/03/19 → 8/03/19

Keywords

Random design regression
Long-range dependence
M-estimation
Local polynomial
Rates of convergence

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10.1007/978-3-030-28665-1_16

Cite this

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title = "Local polynomial M-estimation in random design regression with dependent errors",

abstract = "The asymptotic behaviour of the robust local polynomial M-estimator is investigated in the random design nonparametric regression model with short-range dependent and long-range dependent errors. Asymptotic results are established by decomposing the estimator into two terms: a martingale term and a conditional expectation term. The local polynomial M-estimator is asymptotically normal when errors are short-range dependent. When the errors are long-range dependent, a more complex behaviour is observed that depends on the size of the bandwidth. If the bandwidth is small enough, the standard asymptotic normality persists. If the bandwidth is relatively large the asymptotic result is more intricate and the long-range dependent variables dominate. In both cases, the optimal bandwidth is investigated.",

keywords = "Random design regression, Long-range dependence, M-estimation, Local polynomial, Rates of convergence",

author = "Yixuan Liu and Wishart, {J. R.}",

year = "2019",

doi = "10.1007/978-3-030-28665-1_16",

language = "English",

isbn = "9783030286644",

series = "Springer Proceedings in Mathematics & Statistics",

publisher = "Springer",

pages = "219--227",

editor = "Ansgar Steland and Ewaryst Rafaj{\l}owicz and Ostap Okhrin",

booktitle = "Stochastic models, statistics and their applications",

note = "14th Workshop on Stochastic Models, Statistics and Their Applications ; Conference date: 06-03-2019 Through 08-03-2019",

}

Liu, Y & Wishart, JR 2019, Local polynomial M-estimation in random design regression with dependent errors. in A Steland, E Rafajłowicz & O Okhrin (eds), Stochastic models, statistics and their applications. Springer Proceedings in Mathematics & Statistics, vol. 294, Springer, Cham, Switzerland, pp. 219-227, 14th Workshop on Stochastic Models, Statistics and Their Applications, Dresden, Germany, 6/03/19. https://doi.org/10.1007/978-3-030-28665-1_16

Local polynomial M-estimation in random design regression with dependent errors. / Liu, Yixuan; Wishart, J. R.
Stochastic models, statistics and their applications. ed. / Ansgar Steland; Ewaryst Rafajłowicz; Ostap Okhrin. Cham, Switzerland: Springer, 2019. p. 219-227 (Springer Proceedings in Mathematics & Statistics; Vol. 294).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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T1 - Local polynomial M-estimation in random design regression with dependent errors

AU - Liu, Yixuan

AU - Wishart, J. R.

PY - 2019

Y1 - 2019

N2 - The asymptotic behaviour of the robust local polynomial M-estimator is investigated in the random design nonparametric regression model with short-range dependent and long-range dependent errors. Asymptotic results are established by decomposing the estimator into two terms: a martingale term and a conditional expectation term. The local polynomial M-estimator is asymptotically normal when errors are short-range dependent. When the errors are long-range dependent, a more complex behaviour is observed that depends on the size of the bandwidth. If the bandwidth is small enough, the standard asymptotic normality persists. If the bandwidth is relatively large the asymptotic result is more intricate and the long-range dependent variables dominate. In both cases, the optimal bandwidth is investigated.

AB - The asymptotic behaviour of the robust local polynomial M-estimator is investigated in the random design nonparametric regression model with short-range dependent and long-range dependent errors. Asymptotic results are established by decomposing the estimator into two terms: a martingale term and a conditional expectation term. The local polynomial M-estimator is asymptotically normal when errors are short-range dependent. When the errors are long-range dependent, a more complex behaviour is observed that depends on the size of the bandwidth. If the bandwidth is small enough, the standard asymptotic normality persists. If the bandwidth is relatively large the asymptotic result is more intricate and the long-range dependent variables dominate. In both cases, the optimal bandwidth is investigated.

KW - Random design regression

KW - Long-range dependence

KW - M-estimation

KW - Local polynomial

KW - Rates of convergence

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M3 - Conference proceeding contribution

SN - 9783030286644

T3 - Springer Proceedings in Mathematics & Statistics

SP - 219

EP - 227

BT - Stochastic models, statistics and their applications

A2 - Steland, Ansgar

A2 - Rafajłowicz, Ewaryst

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T2 - 14th Workshop on Stochastic Models, Statistics and Their Applications

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ER -

Local polynomial M-estimation in random design regression with dependent errors

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Keywords

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