The Experts below are selected from a list of 15855 Experts worldwide ranked by ideXlab platform
Liang Peng - One of the best experts on this subject based on the ideXlab platform.
-
Uniform interval estimation for an AR(1) process with AR errors
Statistica Sinica, 2017Co-Authors: Jonathan B. Hill, Liang PengAbstract:Jonathan Hill1, Deyuan Li2∗ and Liang Peng3 Abstract. 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.
-
Approximate jackknife Empirical Likelihood Method for estimating equations
Canadian Journal of Statistics, 2012Co-Authors: Liang PengAbstract:It is known that the profile Empirical Likelihood Method based on estimating equations is computationally intensive when the number of nuisance parameters is large. Recently, Li, Peng, & Qi (2011) proposed a jackknife Empirical Likelihood Method for constructing confidence regions for the parameters of interest by estimating the nuisance parameters separately. However, when the estimators for the nuisance parameters have no explicit formula, the computation of the jackknife Empirical Likelihood Method is still intensive. In this paper, an approximate jackknife Empirical Likelihood Method is proposed to reduce the computation in the jackknife Empirical Likelihood Method when the nuisance parameters cannot be estimated explicitly. A simulation study confirms the advantage of the new Method. The Canadian Journal of Statistics 40: 110–123; 2012 © 2012 Statistical Society of Canada Il est bien connu que la Methode du profil de vraisemblance empirique, basee sur les equations destimation, est tres exigeante numeriquement lorsqu'il y a beaucoup de parametres de nuisance. Recemment, Li, Peng et Qi (2011) ont propose une version jack-knife de la Methode de vraisemblance empirique pour construire des regions de confiance pour les parametres d'interet en estimant les parametres de nuisance separement. Cependant, lorsqu'il est impossible dobtenir des estimateurs analytiques pour les parametres de nuisance, le calcul de la version jack-knife de la Methode de vraisemblance empirique demeure ardue a evaluer numeriquement. Dans cet article, nous proposons une approximation afin de reduire le temps de calcul de la version jack-knife de la Methode de vraisemblance empirique lorsque les parametres de nuisance ne peuvent pas etre estimes explicitement. Une etude de simulation confirme l'avantage de cette nouvelle Methode. La revue canadienne de statistique 40: 110–123; 2012 © 2012 Societe statistique du Canada
-
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.
-
Jackknife Empirical Likelihood Method for some risk measures and related quantities
Insurance: Mathematics and Economics, 2012Co-Authors: Liang Peng, Ruodu Wang, Jingping YangAbstract:Quantifying risks is of importance in insurance. In this paper, we employ the jackknife Empirical Likelihood Method to construct confidence intervals for some risk measures and related quantities studied by Jones and Zitikis (2003). A simulation study shows the advantages of the new Method over the normal approximation Method and the naive bootstrap Method.
-
Empirical Likelihood confidence intervals for the endpoint of a distribution function
Test, 2011Co-Authors: Liang PengAbstract:Estimating the endpoint of a distribution function is of interest in product analysis and predicting the maximum lifetime of an item. In this paper, we propose an Empirical Likelihood Method to construct a confidence interval for the endpoint. A simulation study shows the proposed confidence interval has better coverage accuracy than the normal approximation Method, and bootstrap calibration improves the accuracy.
Soumendra N Lahiri - One of the best experts on this subject based on the ideXlab platform.
-
A frequency domain Empirical Likelihood Method for irregularly spaced spatial data
The Annals of Statistics, 2015Co-Authors: Soutir Bandyopadhyay, Soumendra N Lahiri, Daniel J. NordmanAbstract:This paper develops Empirical Likelihood Methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain Empirical Likelihood (FDEL) Methodology for time series (on a regular grid), the formulation of the spatial FDEL needs special care due to lack of the usual orthogonality properties of the discrete Fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic structures. A spatial FDEL is formulated in the paper taking into account the effects of these factors. The main results of the paper show that Wilks' phenomenon holds for a scaled version of the logarithm of the proposed Empirical Likelihood ratio statistic in the sense that it is asymptotically distribution-free and has a chi-squared limit. As a result, the proposed spatial FDEL Method can be used to build nonparametric, asymptotically correct confidence regions and tests for covariance parameters that are defined through spectral estimating equations, for irregularly spaced spatial data. In comparison to the more common studentization approach, a major advantage of our Method is that it does not require explicit estimation of the standard error of an estimator, which is itself a very difficult problem as the asymptotic variances of many common estimators depend on intricate interactions among several population quantities, including the spectral density of the spatial process, the spatial sampling density and the spatial asymptotic structure. Results from a numerical study are also reported to illustrate the Methodology and its finite sample properties.
-
A Progressive Block Empirical Likelihood Method for Time Series
Journal of the American Statistical Association, 2013Co-Authors: Young Min Kim, Soumendra N Lahiri, Daniel J. NordmanAbstract:This article develops a new blockwise Empirical Likelihood (BEL) Method for stationary, weakly dependent time processes, called the progressive block Empirical Likelihood (PBEL). In contrast to the standard version of BEL, which uses data blocks of constant length for a given sample size and whose performance can depend crucially on the block length selection, this new approach involves a data-blocking scheme where blocks increase in length by an arithmetic progression. Consequently, no block length selections are required for the PBEL Method, which implies a certain type of robustness for this version of BEL. For inference of smooth functions of the process mean, theoretical results establish the chi-squared limit of the log-Likelihood ratio based on PBEL, which can be used to calibrate confidence regions. Using the same progressive block scheme, distributional extensions are also provided for other nonparametric Likelihoods with time series in the family of Cressie–Read discrepancies. Simulation evidenc...
-
a penalized Empirical Likelihood Method in high dimensions
Annals of Statistics, 2012Co-Authors: Soumendra N Lahiri, Subhadeep MukhopadhyayAbstract:This paper formulates a penalized Empirical Likelihood (PEL) Method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is derived under different component-wise dependence structures of the observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii) short-range dependence. It follows that the limit distribution of the proposed PEL ratio statistic can vary widely depending on the correlation structure, and it is typically different from the usual chi-squared limit of the Empirical Likelihood ratio statistic in the fixed and finite dimensional case. A unified subsampling based calibration is proposed, and its validity is established in all three cases, (i)-(iii). Finite sample properties of the Method are investigated through a simulation study.
-
a penalized Empirical Likelihood Method in high dimensions
Annals of Statistics, 2012Co-Authors: Soumendra N Lahiri, Subhadeep MukhopadhyayAbstract:We formulate a penalized Empirical Likelihood (PEL) Method for inference on the population mean when the dimension of the observations become unbounded with the sample size. We derive the asymptotic distribution of the PEL ratio statistic. We show that the limit distribution of the proposed PEL ratio statistic can vary widely depending on the correlation structure of the components of the observations that we classify as (i) non-Ergodic, (ii) long range dependent, and (iii) short range dependent. The limit laws differ from the usual chi-squared limit of the Empirical Likelihood ratio statistic in the finite dimensional case. We propose a subsampling approximation for calibrating the PEL ratio test statistic and establish its validity. Finite sample properties of the Method are investigated through a simulation study. ∗Joint work with Deep Mukhopadhyay .
-
On the Mahalanobis-distance based penalized Empirical Likelihood Method in high dimensions
Statistics and Its Interface, 2012Co-Authors: Soumendra N Lahiri, Subhadeep MukhopadhyayAbstract:In this paper, we consider the penalized Empirical Likelihood (PEL) Method of Bartolucci (2007) for inference on the population mean which is a modification of the standard Empirical Likelihood and employs a penalty based on the Mahalanobis-distance. We derive the asymptotic distributions of the PEL ratio statistic when the dimension of the observations increases with the sample size. Finite sample properties of the Method are investigated through a small simulation study.
Bing-yi Jing - One of the best experts on this subject based on the ideXlab platform.
-
Jackknife Empirical Likelihood Method for case-control studies with gene-environment independence on controls
Statistics and Its Interface, 2012Co-Authors: Bing-yi Jing, Jing Qin, Wang ZhouAbstract:In this paper, we propose a jackknife Empirical Likelihood Method to do inference for the interested parameters of the multiplicative-intercept risk models by taking into account the gene-environment independence on controls in case-control studies. It is shown that the proposed statistic is asymptotically chi-squared distributed. Simulation studies investigate the small-sample properties. A real example is also given.
-
Empirical Likelihood for partial linear models
Annals of the Institute of Statistical Mathematics, 2003Co-Authors: Qihua Wang, Bing-yi JingAbstract:In this paper the Empirical Likelihood Method due to Owen (1988,Biometrika,75, 237–249) is applied to partial linear random models. A nonparametric version of Wilks' theorem is derived. The theorem is then used to construct confidence regions of the parameter vector in the partial linear models, which has correct asymptotic coverage. A simulation study is conducted to compare the Empirical Likelihood and normal approximation based Method.
-
Adjusted Empirical Likelihood Method for quantiles
Annals of the Institute of Statistical Mathematics, 2003Co-Authors: Wang Zhou, Bing-yi JingAbstract:Empirical Likelihood (EL) was first applied to quantiles by Chen and Hall (1993,Ann. Statist.,21, 1166–1181). In this paper, we shall propose an alternative EL approach which is also some kind of the kernel Method. It not only eliminates the need to solve nonlinear equations, but also is extremely easy to implement. Confidence intervals derived from the proposed approach are shown, by an nonparametric version of Wilks' theorem, to have the same order of coverage accuracy (order 1/n) as those of Chen and Hall. Numerical results are presented to compare our Method with other Methods.
-
Empirical Likelihood FOR COX REGRESSION MODEL UNDER RANDOM CENSORSHIP
Communications in Statistics - Simulation and Computation, 2001Co-Authors: Gengsheng Qin, Bing-yi JingAbstract:In this paper we investigate the Empirical Likelihood Method for Cox regression model when the failure times are subject to random censoring. An Empirical Likelihood ratio for the vector of regression coefficients is defined and it is shown that its limiting distribution is a chi-square distributions with p degrees of freedom. Some simulation studies are presented to compare the Empirical Likelihood Method with the normal approximation Method.
-
Empirical Likelihood for Censored Linear Regression
Scandinavian Journal of Statistics, 2001Co-Authors: Gengsheng Qin, Bing-yi JingAbstract:In this paper we investigate the Empirical Likelihood Method in a linear regression model when the observations are subject to random censoring. An Empirical Likelihood ratio for the slope parameter vector is defined and it is shown that its limiting distribution is a weighted sum of independent chi-square distributions. This reduces to the Empirical Likelihood to the linear regression model first studied by Owen (1991) if there is no censoring present. Some simulation studies are presented to compare the Empirical Likelihood Method with the normal approximation based Method proposed in Lai et al. (1995). It was found that the Empirical Likelihood Method performs much better than the normal approximation Method.
Daniel J. Nordman - One of the best experts on this subject based on the ideXlab platform.
-
A frequency domain Empirical Likelihood Method for irregularly spaced spatial data
The Annals of Statistics, 2015Co-Authors: Soutir Bandyopadhyay, Soumendra N Lahiri, Daniel J. NordmanAbstract:This paper develops Empirical Likelihood Methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain Empirical Likelihood (FDEL) Methodology for time series (on a regular grid), the formulation of the spatial FDEL needs special care due to lack of the usual orthogonality properties of the discrete Fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic structures. A spatial FDEL is formulated in the paper taking into account the effects of these factors. The main results of the paper show that Wilks' phenomenon holds for a scaled version of the logarithm of the proposed Empirical Likelihood ratio statistic in the sense that it is asymptotically distribution-free and has a chi-squared limit. As a result, the proposed spatial FDEL Method can be used to build nonparametric, asymptotically correct confidence regions and tests for covariance parameters that are defined through spectral estimating equations, for irregularly spaced spatial data. In comparison to the more common studentization approach, a major advantage of our Method is that it does not require explicit estimation of the standard error of an estimator, which is itself a very difficult problem as the asymptotic variances of many common estimators depend on intricate interactions among several population quantities, including the spectral density of the spatial process, the spatial sampling density and the spatial asymptotic structure. Results from a numerical study are also reported to illustrate the Methodology and its finite sample properties.
-
A Progressive Block Empirical Likelihood Method for Time Series
Journal of the American Statistical Association, 2013Co-Authors: Young Min Kim, Soumendra N Lahiri, Daniel J. NordmanAbstract:This article develops a new blockwise Empirical Likelihood (BEL) Method for stationary, weakly dependent time processes, called the progressive block Empirical Likelihood (PBEL). In contrast to the standard version of BEL, which uses data blocks of constant length for a given sample size and whose performance can depend crucially on the block length selection, this new approach involves a data-blocking scheme where blocks increase in length by an arithmetic progression. Consequently, no block length selections are required for the PBEL Method, which implies a certain type of robustness for this version of BEL. For inference of smooth functions of the process mean, theoretical results establish the chi-squared limit of the log-Likelihood ratio based on PBEL, which can be used to calibrate confidence regions. Using the same progressive block scheme, distributional extensions are also provided for other nonparametric Likelihoods with time series in the family of Cressie–Read discrepancies. Simulation evidenc...
-
An Empirical Likelihood Method for spatial regression
Metrika, 2008Co-Authors: Daniel J. NordmanAbstract:Properties of a “blockwise”Empirical Likelihood for spatial regression with non-stochastic regressors are investigated for spatial data on a lattice. The Method enables nonparametric confidence regions for spatial trend parameters to be calibrated, even though non-random regressors introduce non-stationary forms of spatial dependence into the “blockwise” construction. Additionally, the regression results are valid in a general framework allowing for a variety of behavior in regressor variables as well as the underlying spatial error process. The same regression Method also applies when the regressors are stochastic.
-
A BLOCKWISE Empirical Likelihood FOR SPATIAL LATTICE DATA
2008Co-Authors: Daniel J. NordmanAbstract:This article considers an Empirical Likelihood Method for data located on a spatial grid. The Method allows inference on spatial parameters, such as means and variograms, without knowledge of the underlying spatial dependence structure. Log-Likelihood ratios are shown to have chi-square limits under spatial dependence for calibrating tests and confidence regions, and maximum Empirical Likelihood estimators permit parameter estimation and testing of spatial moment conditions. A practical Bartlett correction is proposed to improve the coverage accuracy of confidence regions. The spatial Empirical Likelihood Method is investigated through a simulation study and illustrated with a data example.
Subhadeep Mukhopadhyay - One of the best experts on this subject based on the ideXlab platform.
-
a penalized Empirical Likelihood Method in high dimensions
Annals of Statistics, 2012Co-Authors: Soumendra N Lahiri, Subhadeep MukhopadhyayAbstract:This paper formulates a penalized Empirical Likelihood (PEL) Method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is derived under different component-wise dependence structures of the observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii) short-range dependence. It follows that the limit distribution of the proposed PEL ratio statistic can vary widely depending on the correlation structure, and it is typically different from the usual chi-squared limit of the Empirical Likelihood ratio statistic in the fixed and finite dimensional case. A unified subsampling based calibration is proposed, and its validity is established in all three cases, (i)-(iii). Finite sample properties of the Method are investigated through a simulation study.
-
a penalized Empirical Likelihood Method in high dimensions
Annals of Statistics, 2012Co-Authors: Soumendra N Lahiri, Subhadeep MukhopadhyayAbstract:We formulate a penalized Empirical Likelihood (PEL) Method for inference on the population mean when the dimension of the observations become unbounded with the sample size. We derive the asymptotic distribution of the PEL ratio statistic. We show that the limit distribution of the proposed PEL ratio statistic can vary widely depending on the correlation structure of the components of the observations that we classify as (i) non-Ergodic, (ii) long range dependent, and (iii) short range dependent. The limit laws differ from the usual chi-squared limit of the Empirical Likelihood ratio statistic in the finite dimensional case. We propose a subsampling approximation for calibrating the PEL ratio test statistic and establish its validity. Finite sample properties of the Method are investigated through a simulation study. ∗Joint work with Deep Mukhopadhyay .
-
On the Mahalanobis-distance based penalized Empirical Likelihood Method in high dimensions
Statistics and Its Interface, 2012Co-Authors: Soumendra N Lahiri, Subhadeep MukhopadhyayAbstract:In this paper, we consider the penalized Empirical Likelihood (PEL) Method of Bartolucci (2007) for inference on the population mean which is a modification of the standard Empirical Likelihood and employs a penalty based on the Mahalanobis-distance. We derive the asymptotic distributions of the PEL ratio statistic when the dimension of the observations increases with the sample size. Finite sample properties of the Method are investigated through a small simulation study.