Strong convergence in nonparametric regression with truncated dependent data

Han Ying Liang; Deli Li; Yongcheng Qi

doi:10.1016/j.jmva.2008.04.002

Strong convergence in nonparametric regression with truncated dependent data

Han Ying Liang, Deli Li, Yongcheng Qi

Mathematics & Statistics

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

15 Scopus citations

Abstract

In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The estimation of the covariate's density is considered as well. Under the assumption that the lifetime observations are bounded, we show that, by an appropriate choice of the bandwidth, both estimators of the covariate's density and regression function attain the optimal strong convergence rate known from independent complete samples.

Original language	English (US)
Pages (from-to)	162-174
Number of pages	13
Journal	Journal of Multivariate Analysis
Volume	100
Issue number	1
DOIs	https://doi.org/10.1016/j.jmva.2008.04.002
State	Published - Jan 2009

Bibliographical note

Funding Information:
The authors would like to thank an associate editor and a referee for their careful reading of this manuscript and their helpful comments. This research was supported by the National Natural Science Foundation of China (10571136, 10871146), a grant from the Natural Sciences and Engineering Research Council of Canada, and the NSF grant DMS 0604176.

Keywords

62G07
62G20
Nonparametric regression estimator
Strong convergence
Truncated data
primary
secondary
α-mixing sequence

Publisher link

10.1016/j.jmva.2008.04.002

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abstract = "In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The estimation of the covariate's density is considered as well. Under the assumption that the lifetime observations are bounded, we show that, by an appropriate choice of the bandwidth, both estimators of the covariate's density and regression function attain the optimal strong convergence rate known from independent complete samples.",

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author = "Liang, {Han Ying} and Deli Li and Yongcheng Qi",

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AU - Li, Deli

AU - Qi, Yongcheng

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N2 - In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The estimation of the covariate's density is considered as well. Under the assumption that the lifetime observations are bounded, we show that, by an appropriate choice of the bandwidth, both estimators of the covariate's density and regression function attain the optimal strong convergence rate known from independent complete samples.

AB - In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The estimation of the covariate's density is considered as well. Under the assumption that the lifetime observations are bounded, we show that, by an appropriate choice of the bandwidth, both estimators of the covariate's density and regression function attain the optimal strong convergence rate known from independent complete samples.

KW - 62G07

KW - 62G20

KW - Nonparametric regression estimator

KW - Strong convergence

KW - Truncated data

KW - primary

KW - secondary

KW - α-mixing sequence

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DO - 10.1016/j.jmva.2008.04.002

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EP - 174

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 1

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Strong convergence in nonparametric regression with truncated dependent data

Abstract

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Keywords

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