Empirical likelihood for linear regression models with missing responses

Qin, Yongsong; Li, Ling; Lei, Qingzhu

doi:10.1016/j.spl.2009.03.002

Cited by 13 publications

(7 citation statements)

References 9 publications

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“…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%

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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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Section: Reconstitution Of the Response Variablementioning

confidence: 99%

“…In [2], EL inferences for the mean of a response variable under regression imputation of missing responses for a linear regression model and random covariates were developed. In [3], an EL statistic on have missing values. In Section 3, we introduce a model, assumptions and some notations.…”

Section: Introductionmentioning

confidence: 99%

Empirical likelihood for nonlinear models with missing responses

Ciuperca

2013

Journal of Statistical Computation and Simulation

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“…To construct the confidence regions for the coefficients in the linear regression model, Chen (1994) proposed a nonparametric method based on empirical likelihood. Qin et al (2009), Xue (2009) and Ciuperca (2011) considered this same problem but for the models with missing response data. Kolaczyk (1994) shows that empirical likelihood is justified as a method of inference for a class of linear models, and shows in particular how empirical likelihood may be used with generalized linear models.…”

Section: Introductionmentioning

confidence: 99%

“…for all 1 ≤ i ≤ n. The MAR assumption is a common condition for statistical analysis with missing data and is reasonable in many practical situations, see Little and Rubin (1987), Qin et al (2009) and Ciuperca (2011).…”

Section: Introductionmentioning

confidence: 99%

Empirical likelihood confidence regions for the parameters of a two phases nonlinear model with and without missing response data

Salloum

2016

Journal of Statistical Theory and Practice

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In this paper, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an asymptotic chi-squared distribution. The result is a nonparametric version of Wilk's theorem. Empirical likelihood method is also used to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with response variables missing at randoms (MAR). In order to construct the confidence regions of the parameter in question, we propose three empirical likelihood statistics : Empirical likelihood based on complete-case data, weighted empirical likelihood and empirical likelihood with imputed values. We prove that all three empirical likelihood ratios have asymptotically chi-squared distributions. The effectiveness of the proposed approaches in aspects of coverage probability and interval length is demonstrated by a Monte-Carlo simulations.

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“…Wang and Rao (2002) develops EL inferences for the mean of a response variable under regression imputation of missing responses for a linear regression model and random covariates. Qin et al (2009) construct an EL statistic on parameter when regressors are deterministic and Xue (2009a) if regressors are random, based on least squares(LS) method for linear model Y = X t β +ε. Sun and Wang (2009) consider the general linear model Y = H(X) t β + ε with H(x) a known vector function and investigate a hypothesis test on the response variable.…”

Section: Introductionmentioning

confidence: 99%

Random nonlinear model with missing responses

Ciuperca

2010

Preprint

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A nonlinear model with response variable missing at random is studied. In order to improve the coverage accuracy, the empirical likelihood ratio (EL) method is considered. The asymptotic distribution of EL statistic and also of its approximation is χ 2 if the parameters are estimated using least squares(LS) or least absolute deviation(LAD) method on complete data. When the response are reconstituted using a semiparametric method, the empirical log-likelihood associated on imputed data is also asymptotically χ 2 . The Wilk's theorem for EL for parameter on response variable is also satisfied. It is shown via Monte Carlo simulations that the EL methods outperform the normal approximation based method in terms of coverage probability up to and including on the reconstituted data. The advantages of the proposed method are exemplified on the real data.

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Empirical likelihood for linear regression models with missing responses

Cited by 13 publications

References 9 publications

Empirical likelihood for nonlinear models with missing responses

Empirical likelihood for nonlinear models with missing responses

Empirical likelihood confidence regions for the parameters of a two phases nonlinear model with and without missing response data

Random nonlinear model with missing responses

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