Asymptotically efficient estimation based on wavelet of expectation value in a partial linear model

Hua Liang; Lixing Zhu; Yong Zhou

doi:10.1080/03610929908832405

Asymptotically efficient estimation based on wavelet of expectation value in a partial linear model

Hua Liang^*
, Lixing Zhu
, Yong Zhou

^*Corresponding author for this work

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

6 Scopus citations

Abstract

This paper is concerned with a semiparametric regression model Y_i = θ₁+θ₂(T_i)+ε_i, i = 1, ⋯, n where the error ε_i is independent of T_i for each i, θ₁ is an unknown constant of interest, and θ₂ is an unknown function on [0, 1]. In order to obtain an asymptotically efficient estimate θ̂_1wof θ₁, θ₂(t) is generally in the literature assumed to be a continuously differentiable function on [0, 1]. In this paper, it is constructed assuming only that θ₂ is an unknown piecewise differentiable function on [0, 1]. In the process of construction, wavelet expansion is employed.

Original language	English
Pages (from-to)	2045-2055
Number of pages	11
Journal	Communications in Statistics - Theory and Methods
Volume	28
Issue number	9
DOIs	https://doi.org/10.1080/03610929908832405
State	Published - 1999
Externally published	Yes

Keywords

Asymptotic efficiency
Partly linear model
Wavelet estimate

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10.1080/03610929908832405

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title = "Asymptotically efficient estimation based on wavelet of expectation value in a partial linear model",

abstract = "This paper is concerned with a semiparametric regression model Yi = θ1+θ2(Ti)+εi, i = 1, ⋯, n where the error εi is independent of Ti for each i, θ1 is an unknown constant of interest, and θ2 is an unknown function on [0, 1]. In order to obtain an asymptotically efficient estimate {\^θ}1wof θ1, θ2(t) is generally in the literature assumed to be a continuously differentiable function on [0, 1]. In this paper, it is constructed assuming only that θ2 is an unknown piecewise differentiable function on [0, 1]. In the process of construction, wavelet expansion is employed.",

keywords = "Asymptotic efficiency, Partly linear model, Wavelet estimate",

author = "Hua Liang and Lixing Zhu and Yong Zhou",

year = "1999",

doi = "10.1080/03610929908832405",

language = "英语",

volume = "28",

pages = "2045--2055",

journal = "Communications in Statistics - Theory and Methods",

issn = "0361-0926",

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TY - JOUR

T1 - Asymptotically efficient estimation based on wavelet of expectation value in a partial linear model

AU - Liang, Hua

AU - Zhu, Lixing

AU - Zhou, Yong

PY - 1999

Y1 - 1999

N2 - This paper is concerned with a semiparametric regression model Yi = θ1+θ2(Ti)+εi, i = 1, ⋯, n where the error εi is independent of Ti for each i, θ1 is an unknown constant of interest, and θ2 is an unknown function on [0, 1]. In order to obtain an asymptotically efficient estimate θ̂1wof θ1, θ2(t) is generally in the literature assumed to be a continuously differentiable function on [0, 1]. In this paper, it is constructed assuming only that θ2 is an unknown piecewise differentiable function on [0, 1]. In the process of construction, wavelet expansion is employed.

AB - This paper is concerned with a semiparametric regression model Yi = θ1+θ2(Ti)+εi, i = 1, ⋯, n where the error εi is independent of Ti for each i, θ1 is an unknown constant of interest, and θ2 is an unknown function on [0, 1]. In order to obtain an asymptotically efficient estimate θ̂1wof θ1, θ2(t) is generally in the literature assumed to be a continuously differentiable function on [0, 1]. In this paper, it is constructed assuming only that θ2 is an unknown piecewise differentiable function on [0, 1]. In the process of construction, wavelet expansion is employed.

KW - Asymptotic efficiency

KW - Partly linear model

KW - Wavelet estimate

UR - https://www.scopus.com/pages/publications/2342590346

U2 - 10.1080/03610929908832405

DO - 10.1080/03610929908832405

M3 - 文章

AN - SCOPUS:2342590346

SN - 0361-0926

VL - 28

SP - 2045

EP - 2055

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 9

ER -

Asymptotically efficient estimation based on wavelet of expectation value in a partial linear model

Abstract

Keywords

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