Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences

Han Ying Liang; Bing Yi Jing

doi:10.1016/j.jmva.2004.06.004

Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences

Han Ying Liang^*
, Bing Yi Jing^*

^*Corresponding author for this work

Department of Mathematics

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

115 Citations (Scopus)

Abstract

Consider the nonparametric regression model Y_ni = g (x_ni) + ε_ni for i = 1,..., n, where g is unknown, x_ni are fixed design points, and ε_ni are negatively associated random errors. Nonparametric estimator g_n (x) of g(x) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of g_n (x) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors (e.g. see J. Multivariate Anal. 25(1) (1988) 100).

Original language	English
Pages (from-to)	227-245
Number of pages	19
Journal	Journal of Multivariate Analysis
Volume	95
Issue number	2
Early online date	10 Dec 2004
DOIs	https://doi.org/10.1016/j.jmva.2004.06.004
Publication status	Published - Aug 2005

Keywords

Nonparametric regression
Negatively associated random error
Consistency
Complete convergence
Asymptotic normality

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title = "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences",

abstract = "Consider the nonparametric regression model Yni = g (xni) + εni for i = 1,..., n, where g is unknown, xni are fixed design points, and εni are negatively associated random errors. Nonparametric estimator gn (x) of g(x) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of gn (x) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors (e.g. see J. Multivariate Anal. 25(1) (1988) 100).",

keywords = "Nonparametric regression, Negatively associated random error, Consistency, Complete convergence, Asymptotic normality",

author = "Liang, \{Han Ying\} and Jing, \{Bing Yi\}",

year = "2005",

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doi = "10.1016/j.jmva.2004.06.004",

language = "English",

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journal = "Journal of Multivariate Analysis",

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T1 - Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences

AU - Liang, Han Ying

AU - Jing, Bing Yi

PY - 2005/8

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N2 - Consider the nonparametric regression model Yni = g (xni) + εni for i = 1,..., n, where g is unknown, xni are fixed design points, and εni are negatively associated random errors. Nonparametric estimator gn (x) of g(x) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of gn (x) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors (e.g. see J. Multivariate Anal. 25(1) (1988) 100).

AB - Consider the nonparametric regression model Yni = g (xni) + εni for i = 1,..., n, where g is unknown, xni are fixed design points, and εni are negatively associated random errors. Nonparametric estimator gn (x) of g(x) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of gn (x) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors (e.g. see J. Multivariate Anal. 25(1) (1988) 100).

KW - Nonparametric regression

KW - Negatively associated random error

KW - Consistency

KW - Complete convergence

KW - Asymptotic normality

UR - https://www.scopus.com/pages/publications/22944477365

U2 - 10.1016/j.jmva.2004.06.004

DO - 10.1016/j.jmva.2004.06.004

M3 - Journal Article

SN - 0047-259X

VL - 95

SP - 227

EP - 245

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 2

ER -

Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences

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Keywords

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