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Liang Peng - One of the best experts on this subject based on the ideXlab platform.
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Jackknife-blockwise Empirical Likelihood methods under dependence
Journal of Multivariate Analysis, 2012Co-Authors: Rongmao Zhang, Liang PengAbstract:Empirical Likelihood for general estimating equations is a method for testing hypothesis or constructing confidence regions on parameters of interest. If the number of parameters of interest is smaller than that of estimating equations, a profile Empirical Likelihood has to be employed. In case of dependent data, a profile blockwise Empirical Likelihood method can be used. However, if too many nuisance parameters are involved, a computational difficulty in optimizing the profile Empirical Likelihood arises. Recently, Li et al. (2011) [9] proposed a jackknife Empirical Likelihood method to reduce the computation in the profile Empirical Likelihood methods for independent data. In this paper, we propose a jackknife-blockwise Empirical Likelihood method to overcome the computational burden in the profile blockwise Empirical Likelihood method for weakly dependent data.
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Empirical Likelihood METHODS FOR THE GINI INDEX
Australian & New Zealand Journal of Statistics, 2011Co-Authors: Liang PengAbstract:Summary The Gini index and its generalizations have been used extensively for measuring inequality and poverty in the social sciences. Recently, interval estimation based on nonparametric statistics has been proposed in the literature, for example the naive bootstrap method, the iterated bootstrap method and the bootstrap method via a pivotal statistic. In this paper, we propose Empirical Likelihood methods to construct confidence intervals for the Gini index or the difference of two Gini indices. Simulation studies show that the proposed Empirical Likelihood method performs slightly worse than the bootstrap method based on a pivotal statistic in terms of coverage accuracy, but it requires less computation. However, the bootstrap calibration of the Empirical Likelihood method performs better than the bootstrap method based on a pivotal statistic.
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Reduce Computation in Profile Empirical Likelihood Method
Canadian Journal of Statistics, 2011Co-Authors: Liang PengAbstract:Since its introduction by Owen, the Empirical Likelihood method has been extensively investigated and widely used to construct confidence regions and to test hypotheses in the literature. For a large class of statistics that can be obtained via solving estimating equations, the Empirical Likelihood function can be formulated from these estimating equations as proposed by Qin, J. and Lawless, J.F. (1994). If only a small part of parameters is of interest, a profile Empirical Likelihood method has to be employed to construct confidence regions, which could be computationally costly. In this paper we propose a jackknife Empirical Likelihood method to overcome this computational burden. This proposed method is easy to implement and works well in practice.
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Jackknife Empirical Likelihood method for copulas
TEST, 2011Co-Authors: Liang Peng, Ingrid Van KeilegomAbstract:Copulas are used to depict dependence among several random variables. Both parametric and non-parametric estimation methods have been studied in the literature. Moreover, profile Empirical Likelihood methods based on either Empirical copula estimation or smoothed copula estimation have been proposed to construct confidence intervals of a copula. In this paper, a jackknife Empirical Likelihood method is proposed to reduce the computation with respect to the existing profile Empirical Likelihood methods.
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Reduce computation in profile Empirical Likelihood method
2011Co-Authors: Liang PengAbstract:Since its introduction by Owen in [29, 30], the Empirical Likelihood method has been extensively investigated and widely used to construct confidence regions and to test hypotheses in the literature. For a large class of statistics that can be obtained via solving estimating equations, the Empirical Likelihood function can be formulated from these estimating equations as proposed by [35]. If only a small part of parameters is of interest, a profile Empirical Likelihood method has to be employed to construct confidence regions, which could be computationally costly. In this paper we propose a jackknife Empirical Likelihood method to overcome this computational burden. This proposed method is easy to implement and works well in practice.
Min Tsao - One of the best experts on this subject based on the ideXlab platform.
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Transforming the Empirical Likelihood towards better accuracy
Canadian Journal of Statistics, 2017Co-Authors: Bing-yi Jing, Min Tsao, Wang ZhouAbstract:Under-coverage has been a long-standing issue with the Empirical Likelihood confidence region. Several methods can be used to address this issue, but they all add complexity to the Empirical Likelihood inference requiring extra computation and/or extra theoretical investigation. The objective of this article is to find a method that does not add complexity. To this end we look for a simple transformation of the Empirical Likelihood to alleviate the under-coverage. Using several criteria concerning the accuracy, consistency, and preservation of the geometric appeal of the original Empirical Likelihood we obtain a transformed version of the Empirical Likelihood that is extremely simple in theory and computation. Its confidence regions are surprisingly accurate, even in small sample and multidimensional situations. It can be easily used to alleviate the under-coverage problem of Empirical Likelihood confidence regions. The Canadian Journal of Statistics xx: 1–13; 2017 © 2017 Statistical Society of Canada
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Two-sample extended Empirical Likelihood for estimating equations
Journal of Multivariate Analysis, 2015Co-Authors: Min TsaoAbstract:We propose a two-sample extended Empirical Likelihood for inference on the difference between two p-dimensional parameters defined by estimating equations. The standard two-sample Empirical Likelihood for the difference is Bartlett correctable but its domain is a bounded subset of the parameter space. We expand its domain through a composite similarity transformation to derive the two-sample extended Empirical Likelihood which is defined on the full parameter space. The extended Empirical Likelihood has the same asymptotic distribution as the standard one and can also achieve the second-order accuracy of the Bartlett correction. We include two applications to illustrate the use of two-sample Empirical Likelihood methods and to demonstrate the superior coverage accuracy of the extended Empirical Likelihood confidence regions.
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Extended Empirical Likelihood for estimating equations
Biometrika, 2014Co-Authors: Min TsaoAbstract:We derive an extended Empirical Likelihood for parameters defined by estimating equations which generalizes the original Empirical Likelihood to the full parameter space. Under mild conditions, the extended Empirical Likelihood has all the asymptotic properties of the original Empirical Likelihood. The first-order extended Empirical Likelihood is easy to use and substantially more accurate than the original Empirical Likelihood.
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Two-sample extended Empirical Likelihood
Statistics & Probability Letters, 2014Co-Authors: Min TsaoAbstract:Jing (1995) and Liu et al. (2008) studied the two-sample Empirical Likelihood and showed that it is Bartlett correctable for the univariate and multivariate cases, respectively. We expand its domain to the full parameter space, and obtain a two-sample extended Empirical Likelihood which is more accurate and can also achieve the second-order accuracy of the Bartlett correction.
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Extended Empirical Likelihood for general estimating equations
arXiv: Statistics Theory, 2013Co-Authors: Min TsaoAbstract:We derive an extended Empirical Likelihood for parameters defined by estimating equations which generalizes the original Empirical Likelihood for such parameters to the full parameter space. Under mild conditions, the extended Empirical Likelihood has all asymptotic properties of the original Empirical Likelihood. Its contours retain the data-driven shape of the latter. It can also attain the second order accuracy. The first order extended Empirical Likelihood is easy-to-use yet it is substantially more accurate than other Empirical Likelihoods, including second order ones. We recommend it for practical applications of the Empirical Likelihood method.
Nicole A. Lazar - One of the best experts on this subject based on the ideXlab platform.
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Split sample Empirical Likelihood
Computational Statistics & Data Analysis, 2020Co-Authors: Adam Jaeger, Nicole A. LazarAbstract:Abstract Empirical Likelihood offers a nonparametric approach to estimation and inference, which replaces the probability density-based Likelihood function with a function defined by estimating equations. While this eliminates the need for a parametric specification, the restriction of numerical optimization greatly decreases the applicability of Empirical Likelihood for large data problems. A solution to this problem is the split sample Empirical Likelihood; this variant utilizes a divide and conquer approach, allowing for parallel computation of the Empirical Likelihood function. The results show the asymptotic distribution of the estimators and test statistics derived from the split sample Empirical Likelihood are the same seen in standard Empirical Likelihood yet have significantly decreased computational times.
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Split Sample Empirical Likelihood
arXiv: Methodology, 2017Co-Authors: Adam Jaeger, Nicole A. LazarAbstract:We propose a new approach that combines multiple non-parametric Likelihood-type components to build a data-driven approximation of the true Likelihood function. Our approach is built on Empirical Likelihood, a non-parametric approximation of the Likelihood function. We show the asymptotic behaviors of our approach are identical to those seen in Empirical Likelihood. We demonstrate that our method performs comparably to Empirical Likelihood while significantly decreasing computational time.
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Piecewise Empirical Likelihood
arXiv: Computation, 2016Co-Authors: Adam Jaeger, Nicole A. LazarAbstract:Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical Likelihood, a non-parametric approach to the Likelihood function, is also limited in application due to the computational demands necessary. We propose a new approach that combines multiple non-parametric Likelihood-type components to build a data-driven approximation of the true function. We will examine the theoretical properties of this piecewise Empirical Likelihood and demonstrate the computational gains of this methodology.
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Bayesian Empirical Likelihood
Biometrika, 2003Co-Authors: Nicole A. LazarAbstract:Research has shown that Empirical Likelihood tests have many of the same asymptotic properties as those derived from parametric Likelihoods. This leads naturally to the possibility of using Empirical Likelihood as the basis for Bayesian inference. Different ways in which this goal might be accomplished are considered. The validity of the resultant posterior inferences is examined, as are frequentist properties of the Bayesian Empirical Likelihood intervals. Copyright Biometrika Trust 2003, Oxford University Press.
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Empirical Likelihood in the presence of nuisance parameters
Biometrika, 1999Co-Authors: Nicole A. Lazar, Per A. MyklandAbstract:SUMMARY Empirical Likelihood was introduced as a nonparametric analogue of ordinary parametric Likelihood. It is well known that the Empirical Likelihood ratio statistic inherits a number of properties of the parametric Likelihood ratio statistic, such as the asymptotic chi-squared distribution and Bartlett correctability. This raises the question of whether or not the same is true in the presence of nuisance parameters. Recent work by Qin & Lawless (1994) indicates that the chi-squared distribution is still valid to first order. We show that, when nuisance parameters are present, as introduced via a system of estimating equations, the asymptotic expansion for the signed square root of the Empirical Likelihood ratio statistic has a nonstandard form. This implies that the Empirical Likelihood ratio statistic itself does not permit a Bartlett correction.
J. N. K. Rao - One of the best experts on this subject based on the ideXlab platform.
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pseudo Empirical Likelihood inference for multiple frame surveys
Journal of the American Statistical Association, 2010Co-Authors: J. N. K. RaoAbstract:This article presents a pseudo–Empirical Likelihood approach to inference for multiple-frame surveys. We establish a unified framework for point and interval estimation of finite population parameters, and show that inferences on the parameters of interest making effective use of different types of auxiliary population information can be conveniently carried out through the constrained maximization of the pseudo–Empirical Likelihood function. Confidence intervals are constructed using either the asymptotic χ2 distribution of an adjusted pseudo–Empirical Likelihood ratio statistic or a bootstrap calibration method. Simulation results based on Statistics Canada’s Family Expenditure Survey data show that the proposed methods perform well in finite samples for both point and interval estimation. In particular, a multiplicity-based pseudo–Empirical Likelihood method is proposed. This method is easily used for multiple-frame surveys with more than two frames and does not require complete frame membership inform...
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Empirical Likelihood based inference under imputation for missing response data
Annals of Statistics, 2002Co-Authors: Qihua Wang, J. N. K. RaoAbstract:Inference under kernel regression imputation for missing response data is considered. An adjusted Empirical Likelihood approach to inference for the mean of the response variable is developed. A nonparametric version of Wilks' theorem is proved for the adjusted Empirical log-Likelihood ratio by showing that it has an asymptotic standard chi-squared distribution, and the corresponding Empirical Likelihood confidence interval for the mean is constructed. With auxiliary information, an Empirical Likelihood-based estimator is defined and an adjusted Empirical log-Likelihood ratio is derived. Asymptotic normality of the estimator is proved. Also, it is shown that the adjusted Empirical log-Likelihood ratio obeys Wilks' theorem. A simulation study is conducted to compare the adjusted Empirical Likelihood and the normal approximation methods in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparision is also made by simulation between the Empirical Likelihood-based estimator and related estimators. Our simulation indicates that the adjusted Empirical Likelihood method performs competitively and that the use of auxiliary information provides improved inferences.
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Empirical Likelihood-based Inference in Linear Models with Missing Data
Scandinavian Journal of Statistics, 2002Co-Authors: Qihua Wang, J. N. K. RaoAbstract:The missing response problem in linear regression is studied. An adjusted Empirical Likelihood approach to inference on the mean of the response variable is developed. A non‐parametric version of Wilks's theorem for the adjusted Empirical Likelihood is proved, and the corresponding Empirical Likelihood confidence interval for the mean is constructed. With auxiliary information, an Empirical Likelihood‐based estimator with asymptotic normality is defined and an adjusted Empirical log‐Likelihood function with asymptotic χ2 is derived. A simulation study is conducted to compare the adjusted Empirical Likelihood methods and the normal approximation methods in terms of coverage accuracies and average lengths of the confidence intervals. Based on biases and standard errors, a comparison is also made between the Empirical Likelihood‐based estimator and related estimators by simulation. Our simulation indicates that the adjusted Empirical Likelihood methods perform competitively and the use of auxiliary information provides improved inferences.
Cheng Yong Tang - One of the best experts on this subject based on the ideXlab platform.
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High-dimensional Empirical Likelihood inference
Biometrika, 2020Co-Authors: Jinyuan Chang, Song Xi Chen, Cheng Yong TangAbstract:Summary High-dimensional statistical inference with general estimating equations is challenging and remains little explored. We study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications tests. First, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by Empirical Likelihood ratio. Second, we propose a test statistic as the maximum of the marginal Empirical Likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed Empirical Likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. Numerical studies demonstrate promising performance and potential practical benefits of the new methods.
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High-dimensional Empirical Likelihood inference
arXiv: Methodology, 2018Co-Authors: Jinyuan Chang, Song Xi Chen, Cheng Yong TangAbstract:High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications test. For the first one, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by Empirical Likelihood ratio. For the second one, we propose a test statistic as the maximum of the marginal Empirical Likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed Empirical Likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. The numerical studies demonstrate promising performance and potential practical benefits of the new methods.
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marginal Empirical Likelihood and sure independence feature screening
Annals of Statistics, 2013Co-Authors: Jinyuan Chang, Cheng Yong TangAbstract:We study a marginal Empirical Likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal Empirical Likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal Empirical Likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening procedure for linear models and the generalized linear models. Different from most existing feature screening approaches that rely on the magnitudes of some marginal estimators to identify true signals, the proposed screening approach is capable of further incorporating the level of uncertainties of such estimators. Such a merit inherits the self-studentization property of the Empirical Likelihood approach, and extends the insights of existing feature screening methods. Moreover, we show that our screening approach is less restrictive to distributional assumptions, and can be conveniently adapted to be applied in a broad range of scenarios such as models specified using general moment conditions. Our theoretical results and extensive numerical examples by simulations and data analysis demonstrate the merits of the marginal Empirical Likelihood approach.
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Penalized Empirical Likelihood and growing dimensional general estimating equations
Biometrika, 2012Co-Authors: Chenlei Leng, Cheng Yong TangAbstract:When a parametric Likelihood function is not specified for a model, estimating equations may provide an instrument for statistical inference. Qin and Lawless (1994) illustrated that Empirical Likelihood makes optimal use of these equations in inferences for fixed low-dimensional unknown parameters. In this paper, we study Empirical Likelihood for general estimating equations with growing high dimensionality and propose a penalized Empirical Likelihood approach for parameter estimation and variable selection. We quantify the asymptotic properties of Empirical Likelihood and its penalized version, and show that penalized Empirical Likelihood has the oracle property. The performance of the proposed method is illustrated via simulated applications and a data analysis. Copyright 2012, Oxford University Press.
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Penalized high-dimensional Empirical Likelihood
Biometrika, 2010Co-Authors: Cheng Yong Tang, Chenlei LengAbstract:We propose penalized Empirical Likelihood for parameter estimation and variable selection for problems with diverging numbers of parameters. Our results are demonstrated for estimating the mean vector in multivariate analysis and regression coefficients in linear models. By using an appropriate penalty function, we showthat penalized Empirical Likelihood has the oracle property. That is, with probability tending to 1, penalized Empirical Likelihood identifies the true model and estimates the nonzero coefficients as efficiently as if the sparsity of the true model was known in advance. The advantage of penalized Empirical Likelihood as a nonparametric Likelihood approach is illustrated by testing hypotheses and constructing confidence regions. Numerical simulations confirm our theoretical findings. Copyright 2010, Oxford University Press.