Empirical likelihood for linear models with missing responses

Xue, Liugen

doi:10.1016/j.jmva.2008.12.009

Cited by 67 publications

(38 citation statements)

References 16 publications

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“…Then it follows from the central limit theorem that (11) is obtained immediately. In a similar way, we can prove (12).…”

Section: Proofs Of the Main Resultsmentioning

confidence: 57%

“…In fact, missing data are a commonplace in practice due to various reasons such as loss of information caused by uncontrollable factors, unwillingness of some sampled units to supply the desired information, failure on the part of investigators to gather correct information, and so forth. Dating back to the early 1970s, spurred by the advances in computer technology that made it possible to perform laborious numerical calculations, the literature on statistical analysis of real data with missing values has flourished in applied work, see [8][9][10][11][12]. Although missing data analysis has a long history in statistics, little work on QR has taken missing data into account.…”

Section: Introductionmentioning

confidence: 99%

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Empirical likelihood for quantile regression models with response data missing at random

Luo

Pang

2017

Open Mathematics

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This paper studies quantile linear regression models with response data missing at random. A quantile empirical-likelihood-based method is proposed firstly to study a quantile linear regression model with response data missing at random. It follows that a class of quantile empirical log-likelihood ratios including quantile empirical likelihood ratio with complete-case data, weighted quantile empirical likelihood ratio and imputed quantile empirical likelihood ratio are defined for the regression parameters. Then, a bias-corrected quantile empirical log-likelihood ratio is constructed for the mean of the response variable for a given quantile level. It is proved that these quantile empirical log-likelihood ratios are asymptotically 2 distribution. Furthermore, a class of estimators for the regression parameters and the mean of the response variable are constructed, and the asymptotic normality of the proposed estimators is established. Our results can be used directly to construct the confidence intervals (regions) of the regression parameters and the mean of the response variable. Finally, simulation studies are conducted to assess the finite sample performance and a real-world data set is analyzed to illustrate the applications of the proposed method.

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“…Then it follows from the central limit theorem that (11) is obtained immediately. In a similar way, we can prove (12).…”

Section: Proofs Of the Main Resultsmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Empirical likelihood for quantile regression models with response data missing at random

Luo

Pang

2017

Open Mathematics

View full text Add to dashboard Cite

show abstract

“…Following the example given in [3,4] for a linear model, we introduce the forecast of Y i , constructed using the LS estimator for parameter β and a nonparametric estimator for probability π(X i ), withπ(X i ) being a nonlinear estimator for π(X i ), as in the linear regression [4]:…”

Section: Reconstitution Of the Response Variablementioning

confidence: 99%

Empirical likelihood for nonlinear models with missing responses

Ciuperca

2013

Journal of Statistical Computation and Simulation

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In this paper, a nonlinear model with response variables missing at random is studied. In order to improve the coverage accuracy for model parameters, the empirical likelihood (EL) ratio method is considered. On the complete data, the EL statistic for the parameters and its approximation have a χ 2 asymptotic distribution. When the responses are reconstituted using a semi-parametric method, the empirical loglikelihood on the response variables associated with the imputed data is also asymptotically χ 2 . The Wilks theorem for EL on the parameters, based on reconstituted data, is also satisfied. These results can be used to construct the confidence region for the model parameters and the response variables. It is shown via Monte Carlo simulations that the EL methods outperform the normal approximation-based method in terms of coverage probability for the unknown parameter, including on the reconstituted data. The advantages of the proposed method are exemplified on real data.

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“…Most of material on this section comes from Qin et al (2009). Related works can be found in ), Xue (2009a, Yang et al (2009).…”

Section: Empirical Likelihood In Missing Data Problemsmentioning

confidence: 99%

Empirical likelihood in some nonparametric and semiparametric models

Xue

Zhu

2012

Statistics and Its Interface

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In this very selective overview, we summarise the recent developments by our own and other, on the empirical likelihood in some nonparametric and semiparametric regression models. The models include the partially linear model, the single-index model, the partially linear singleindex model, the varying coefficient model, and so on. The focus of this overview is to expatiate the adjustment and "bias correction" methodologies when Wilks' phenomenon does not hold. The adjustment or bias correction can make the limiting distributions tractable such that they can be directly used to construct the confidence regions of parameters of interest without the assistance of Monte Carlo approximation.

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Empirical likelihood for linear models with missing responses

Cited by 67 publications

References 16 publications

Empirical likelihood for quantile regression models with response data missing at random

Empirical likelihood for quantile regression models with response data missing at random

Empirical likelihood for nonlinear models with missing responses

Empirical likelihood in some nonparametric and semiparametric models

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