A penalized empirical likelihood method in high dimensions

Lahiri, Soumendra N.; Mukhopadhyay, Subhadeep

doi:10.1214/12-aos1040

Cited by 41 publications

(20 citation statements)

References 33 publications

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“…Their frameworks also consider that the number of parameters is allowed to diverge with the sample size at some polynomial rate of the sample size. Lahiri and Mukhopadhyay (2012) considered a different formulation EL with penalization that can accommodate higher dimensional model parameters that can exceed the sample size. Their definition of EL is different and the penalty is introduced as a deviation function of the parameter defined.…”

Section: Current Challenges For Elmentioning

confidence: 99%

Peter Hall's Contribution to Empirical Likelihood

Chang¹,

Guo²,

Tang³

2018

STAT SINICA

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We deeply mourn the loss of Peter Hall. Peter was the premier mathematical statistician of his era. His work illuminated many aspects of statistical thought. While his body of work on bootstrap and nonparametric smoothing is widely known and appreciated, less well known is his work in many other areas. In this article, we review Peter's contribution to empirical likelihood (EL). Peter has done fundamental work on studying the coverage accuracy of confidence regions constructed with EL.

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Section: Current Challenges For Elmentioning

confidence: 99%

Peter Hall's Contribution to Empirical Likelihood

Chang¹,

Guo²,

Tang³

2018

STAT SINICA

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“…To overcome the convex hull constraint violation problem, Bartolucci (2007) dropped the convex hull constraint in the formulation of EL for the mean of a random sample and defined the likelihood by penalizing the unconstrained EL by using the Mahalanobis distance. Recently, Lahiri and Mukhopadhyay (2012) introduced a modified version of Bartolucci's (2007) PEL in the mean case. Under the assumption that the observations are IID and the components of each observation are dependent, Lahiri and Mukhopadhyay (2012) derived asymptotic distributions of the PEL ratio statistic in the high dimensional setting.…”

Section: Penalized Blockwise Empirical Likelihoodmentioning

confidence: 99%

“…Following the terminology in Tsao and Wu (2013), the finite sample coverage bound problem is due to the mismatch between the domain of the EL and the parameter space, so it is also called a mismatch problem. There have been a few recent proposals to alleviate or resolve the mismatch problem; see, for example adjusted EL (Chen et al, 2008;Emerson and Owen, 2009;Liu and Chen, 2010;Chen and Huang, 2012), penalized EL (Bartolucci, 2007;Lahiri and Mukhopadhyay, 2012) and the domain expansion approach (Tsao andWu, 2013, 2014). However, all these works deal with independent estimation equations, and their direct applicability to the important time series case is not clear.…”

Section: Introductionmentioning

confidence: 99%

On the Coverage Bound Problem of Empirical Likelihood Methods for Time Series

Zhang

Shao

2015

Journal of the Royal Statistical Society Series B: Statistical Methodology

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The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood and non-standard expansive empirical likelihood methods for time series data are investigated via studying the probability of violating the convex hull constraint. The large sample bounds are derived on the basis of the pivotal limit of the blockwise empirical log-likelihood ratio obtained under fixed b asymptotics, which has recently been shown to provide a more accurate approximation to the finite sample distribution than the conventional χ 2 -approximation. Our theoretical and numerical findings suggest that both the finite sample and the large sample upper bounds for coverage probabilities are strictly less than 1 and the blockwise empirical likelihood confidence region can exhibit serious undercoverage when the dimension of moment conditions is moderate or large, the time series dependence is positively strong or the block size is large relative to the sample size. A similar finite sample coverage problem occurs for non-standard expansive empirical likelihood.To alleviate the coverage bound problem, we propose to penalize both empirical likelihood methods by relaxing the convex hull constraint. Numerical simulations and data illustrations demonstrate the effectiveness of our proposed remedies in terms of delivering confidence sets with more accurate coverage. Some technical details and additional simulation results are included in on-line supplemental material.

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“…Qin & Lawless (1994) developed the EL inference procedure for general estimating equations for complete data, and Owen (2001) makes an excellent summary about the theory and applications of the EL methods. Recent progress in the EL method includes linear transformation models with right censoring ), Yang & Zhao (2012), the jackknife EL procedure (Jing et al (2009), Gong et al (2010, Zhang & Zhao (2013), ), high dimensional EL method (Chen et al (2009), Hjort et al (2009), Tang & Leng (2010, Lahiri et al (2012)), and the signedrank regression (Bindele & Zhao, 2016). More recently, in the context of missing response under the MNAR assumption, empirical likelihood approaches have been proposed by Niu et al (2014) and Tang et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

Bindele¹,

Zhao²

2018

STAT SINICA

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In this paper, a general regression model with responses missing not at random is considered. From a rankbased estimating equation, a rank-based estimator of the regression parameter is derived. Based on this estimator's asymptotic normality property, a consistent sandwich estimator of its corresponding asymptotic covariance matrix is obtained. In order to overcome the over-coverage issue of the normal approximation procedure, the empirical likelihood based on the rank-based gradient function is defined, and its asymptotic distribution is established. Extensive simulation experiments under different settings of error distributions with different response probabilities are considered, and the simulation results show that the proposed empirical likelihood approach has better performance in terms of coverage probability and average length of confidence intervals for the regression parameters compared with the normal approximation approach and its least-squares counterpart. A real data example is provided to illustrate the proposed methods.

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A penalized empirical likelihood method in high dimensions

Cited by 41 publications

References 33 publications

Peter Hall's Contribution to Empirical Likelihood

Peter Hall's Contribution to Empirical Likelihood

On the Coverage Bound Problem of Empirical Likelihood Methods for Time Series

Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

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