Estimation and variable selection in partial linear single index models with error-prone linear covariates

Zhang, Jun; Wang, Xiaoguang; Yu, Yao; Gai, Yujie

doi:10.1080/02331888.2013.800519

Cited by 16 publications

(4 citation statements)

References 41 publications

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“…Lemma 1 can be immediately proved from the result obtained by Mack and Silverman [23], see also in [50].…”

Section: Lemma 1 Suppose E(t |U = U) = M(u) and Its Derivatives Up Tmentioning

confidence: 89%

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Statistical inference on partial linear additive models with distortion measurement errors

Gai

Zhang

et al. 2015

Statistical Methodology

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“…Lemma 1 can be immediately proved from the result obtained by Mack and Silverman [23], see also in [50].…”

Section: Lemma 1 Suppose E(t |U = U) = M(u) and Its Derivatives Up Tmentioning

confidence: 89%

“…Important semiparametric regression models include partial linear models [8,10,22,42], partial linear single index models [1,18,45,50], and partial linear varying-coefficient models [7,14,55]. In this article, we focus the partial linear additive models (PLAMs).…”

Section: Introductionmentioning

confidence: 99%

Statistical inference on partial linear additive models with distortion measurement errors

Gai

Zhang

et al. 2015

Statistical Methodology

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“…The asymptotic variance of the proposed estimator for ( β 0 , γ 0 ) depends on neither the bandwidth nor the kernel function. Hence, we can use the rule of thumb suggested by SILVERMAN (), ZHOU and LIANG (), and ZHANG et al (). That is,

h_{*} = {\overset{σ}{true}}_{U} n^{- 1 / 3}

, and

{\overset{σ}{true}}_{U}

is the sample deviation of U .…”

Section: Profile Least Squares Estimators For β0 and γ0mentioning

confidence: 99%

Statistical inference on restricted partial linear regression models with partial distortion measurement errors

Zhang

Zhou

Sun

et al. 2016

Statistica Neerlandica

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We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed under the null hypothesis. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure, and a real example is analyzed for an illustration.

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“…Apanasovich, Carroll & Maity () derived the limiting distribution of Simulation Extrapolation (SIMEX) in semiparametric problems, where the variable X is subject to measurement error and modelled parametrically, nonparametrically or as a combination of both. Zhang et al () investigated the sample property in efficient variable selection problems and developed a semiparametric profile least‐square based estimation procedure to estimate the parameters in partial linear single index models. Measurement error problems have attracted researchers from other scientific research fields as well.…”

Section: Introductionmentioning

confidence: 99%

Locally efficient semiparametric estimators for a class of Poisson models with measurement error

Liu

2019

Can J Statistics

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The presence of measurement error may cause bias in parameter estimation and can lead to incorrect conclusions in data analyses. Despite a large body of literature on general measurement error problems, relatively few works exist to handle Poisson models. In this article we thoroughly study Poisson models with errors in covariates and propose consistent and locally efficient semiparametric estimators. We assess the finite sample performance of the estimators through extensive simulation studies and illustrate the proposed methodologies by analyzing data from the Stroke Recovery in Underserved Populations Study. The Canadian Journal of Statistics 47: 157–181; 2019 © 2019 Statistical Society of Canada

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Estimation and variable selection in partial linear single index models with error-prone linear covariates

Cited by 16 publications

References 41 publications

Statistical inference on partial linear additive models with distortion measurement errors

Statistical inference on partial linear additive models with distortion measurement errors

Statistical inference on restricted partial linear regression models with partial distortion measurement errors

Locally efficient semiparametric estimators for a class of Poisson models with measurement error

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