A review on empirical likelihood methods for regression

Chen, Song Xi; Keilegom, Ingrid Van

doi:10.1007/s11749-009-0159-5

Cited by 135 publications

(60 citation statements)

References 76 publications

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“…In order to reduce computation time, one can estimate γ 0 first by solving (2.2), which results in an explicit function of β, and then apply the empirical likelihood method to (2.4) with γ replaced by this estimator. However, this does not lead to a chi-squared limit due to the plug-in estimator, but rather a weighted sum of independent chi-squared variables, see Chen and Van Keilegom (2009). Recently a jackknife empirical likelihood method was proposed by Jing, Yuan, and Zhou (2009) to deal with non-linear functionals, and Li, Peng, and Qi (2011) employed this idea to reduce the computation of the empirical likelihood method based on estimating equations.…”

Section: Jackknife Empirical Likelihood Methodsmentioning

confidence: 99%

Uniform interval estimation for an AR(1) process with AR errors

Hill¹,

Peng

2017

STAT SINICA

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An empirical likelihood method was proposed in Hill and Peng (2014) to construct a unified interval estimation for the coefficient in an AR(1) model, regardless of whether the sequence was stationary or near integrated. The error term, however, was assumed independent, and this method fails when the errors are dependent. Testing for a unit root in an AR(1) model has been studied in the literature for dependent errors, but existing methods cannot be used to test for a near unit root. In this paper, assuming the errors are governed by an AR(p) process, we exploit the efficient empirical likelihood method to give a unified interval for the coefficient by taking the structure of errors into account. Furthermore, a jackknife empirical likelihood method is proposed to reduce the computation of the empirical likelihood method when the order in the AR errors is not small. A simulation study is conducted to examine the finite sample behavior of the proposed methods.

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Section: Jackknife Empirical Likelihood Methodsmentioning

confidence: 99%

Uniform interval estimation for an AR(1) process with AR errors

Hill¹,

Peng

2017

STAT SINICA

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“…by analogous weak convergence arguments as used to show (5). Combining these results enables us to show…”

Section: A4 Proof Of Theoremmentioning

confidence: 67%

Empirical Likelihood for Random Sets

Adusumilli

Otsu

2017

Journal of the American Statistical Association

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Abstract. We extend the method of empirical likelihood to cover hypotheses involving the Aumann expectation of random sets. By exploiting the properties of random sets, we convert the testing problem into one involving a continuum of moment restrictions for which we propose two inferential procedures. The first, which we term marked empirical likelihood, corresponds to constructing a non-parametric likelihood for each moment restriction and assessing the resulting process. The second, termed sieve empirical likelihood, corresponds to constructing a likelihood for a vector of moments with growing dimension. We derive the asymptotic distributions under the null and sequence of local alternatives for both types of tests and prove their consistency.The applicability of these inferential procedures is demonstrated in the context of two examples on the mean of interval observations and best linear predictors for interval outcomes.

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“…It is unclear how much power one can gain by building tests based on these more sophisticated estimators since our proposed test already attains the minimax optimal power rate. Tests based on other smoothers, such as penalized splines (Craineceanu, et al, 2006), or other principles, such as empirical likelihood (Chen and Van Keilegom, 2009) …”

Section: Discussionmentioning

confidence: 99%

Generalized Quasi-Likelihood Ratio Tests for Semiparametric Analysis of Covariance Models in Longitudinal Data

Tang¹,

Li²,

Guan³

2016

Journal of the American Statistical Association

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We model generalized longitudinal data from multiple treatment groups by a class of semiparametric analysis of covariance models, which take into account the parametric effects of time dependent covariates and the nonparametric time effects. In these models, the treatment effects are represented by nonparametric functions of time and we propose a generalized quasi-likelihood ratio test procedure to test if these functions are identical. Our estimation procedure is based on profile estimating equations combined with local linear smoothers. We find that the much celebrated Wilks phenomenon which is well established for independent data still holds for longitudinal data if a working independence correlation structure is assumed in the test statistic. However, this property does not hold in general, especially when the working variance function is mis-specified. Our empirical study also shows that incorporating correlation into the test statistic does not necessarily improve the power of the test. The proposed methods are illustrated with simulation studies and a real application from opioid dependence treatments.

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A review on empirical likelihood methods for regression

Abstract: We provide a review on the empirical likelihood method for regression type inference problems. The regression models considered in this review include parametric, semiparametric and nonparametric models. Both missing data and censored data are accommodated.

Cited by 135 publications

References 76 publications

Uniform interval estimation for an AR(1) process with AR errors

Uniform interval estimation for an AR(1) process with AR errors

Empirical Likelihood for Random Sets

Generalized Quasi-Likelihood Ratio Tests for Semiparametric Analysis of Covariance Models in Longitudinal Data

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