Locally Efficient Estimators for Semiparametric Models With Measurement Error

Ma, Yanyuan; Carroll, Raymond J.

doi:10.1198/016214506000000519

Cited by 45 publications

(65 citation statements)

References 13 publications

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“…The case where the error distribution is unknown has been treated in Diggle and Hall (1993), Neumann (1997) and Li and Vuong (1998). More recently the model (1) with repeated measurements has been studied in Delaigle, Hall, and Meister (2007), see also Ma and Carroll (2006) and Neumann (2007). The model with replicated data is well suited to applications and data of this type are available in various fields: (Jaech, 1985) gives an example where uranium concentration is measured for several fuel pellets, examples of measurement errors in surveys are given in Biemer, Groves, Lyberg, Mathiowetz, and Sudman (2004).…”

Section: Density Estimation From Contaminated Datamentioning

confidence: 99%

Multiscale density estimation with errors in variables

Cavalier

Raimondo

2010

Journal of the Korean Statistical Society

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a b s t r a c tWe present an adaptive method for density estimation when the observations X = (X 1 , . . . , X n ) are contaminated by additive errors Y = X + Z. The error distribution is not specified by the model but is estimated using repeated measurements (Y i ) i=1,2,3 of X. In this setting, we propose a wavelet method for density estimation which adapts both to the degree of ill posedness of the problem (smoothness of the error distribution) and to the regularity of the target density. Our method is implemented in the Fourier domain via a square-root transformation of the empirical characteristic function and yields fast translation invariant non-linear wavelet approximations with data-driven choices of fine tuning parameters. When the variable X is observed without errors our method provides a natural implementation of direct density estimation in the Meyer wavelet basis. We illustrate the adaptiveness properties of our estimator with a range of finite sample examples drawn from population with smooth and less smooth density functions.

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Section: Density Estimation From Contaminated Datamentioning

confidence: 99%

Multiscale density estimation with errors in variables

Cavalier

Raimondo

2010

Journal of the Korean Statistical Society

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“…See Carroll et al (2006) for more detailed discussions on a variety of estimation and inference methods for nonlinear measurement errors models. Ma and Carroll (2006), Ma and Tsiatis (2006) and Tsiatis and Ma (2004) investigated estimation efficiency for semiparametric models with measurement errors. Hall and Ma (2007) studied semiparametric estimators of functional measurement error models.…”

Section: Introductionmentioning

confidence: 99%

Generalized varying coefficient partially linear measurement errors models

Zhang

Feng

et al. 2015

Ann Inst Stat Math

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We study generalized varying coefficient partially linear models when some linear covariates are error prone, but their ancillary variables are available. We first calibrate the error-prone covariates, then develop a quasi-likelihood-based estimation procedure. To select significant variables in the parametric part, we develop a penalized quasi-likelihood variable selection procedure, and the resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Moreover, to select significant variables in the nonparametric component, we investigate asymptotic behavior of the semiparametric generalized likelihood ratio test. The limiting null distribution is shown to follow a Chi-square distribution, and a new Wilks phenomenon Electronic supplementary material The online version of this article (is unveiled in the context of error-prone semiparametric modeling. Simulation studies and a real data analysis are conducted to evaluate the performance of the proposed methods.

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“…First of all, (4) contains two integral equations that typically have to be solved numerically. While this is feasible and it has already been done in the literature (see, for example, Tsiatis andMa 2004, Ma andCarroll 2006), it considerably slows down the implementation. However, a more serious issue is that the efficient score contains the quantities µ 3 (x) ≡ E( 3 | x) and…”

Section: Locally Efficient Estimationmentioning

confidence: 99%

Semiparametric Estimation and Inference of Variance Function with Large Dimensional Covariates

Zhu

2019

STAT SINICA

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We investigate the simultaneous estimation and inference of the central mean subspace and central variance subspace to reduce the effective number of covariates that predict respectively the mean and variability of the response variable. We study the estimation, inference and efficiency properties under different scenarios, and further propose a class of locally efficient estimators when the truly efficient estimator is not practically available. This partially explains the necessity of some dimension-reduction assumptions which were commonly imposed on the conditional mean function in estimating the central variance subspace. Comprehensive simulation studies and a real-data analysis are performed to demonstrate the finite sample performance and efficiency gain of the locally efficient estimators in comparison with existing estimation procedures.

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Locally Efficient Estimators for Semiparametric Models With Measurement Error

Cited by 45 publications

References 13 publications

Multiscale density estimation with errors in variables

Multiscale density estimation with errors in variables

Generalized varying coefficient partially linear measurement errors models

Semiparametric Estimation and Inference of Variance Function with Large Dimensional Covariates

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