Liang Peng

Georgia Institute of Technology, Atlanta, Georgia, United States

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Publications (87)57.79 Total impact

  • Liang Peng, Yongcheng Qi, Ruodu Wang
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    ABSTRACT: We propose an empirical likelihood method to test whether the coefficients in a possibly high-dimensional linear model are equal to given values. The asymptotic distribution of the test statistic is independent of the number of covariates in the linear model.
    Statistics [?] Probability Letters 01/2014; · 0.53 Impact Factor
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    Rongmao Zhang, Liang Peng, Ruodu Wang
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    ABSTRACT: Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded structure. The asymptotic distributions of the new tests are independent of the dimension.
    10/2013;
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    ABSTRACT: Relevant sample quantities such as the sample autocorrelation function and extremes contain useful information about autoregressive time series with heteroskedastic errors. As these quantities usually depend on the tail index of the underlying heteroskedastic time series, estimating the tail index becomes an important task. Since the tail index of such a model is determined by a moment equation, one can estimate the underlying tail index by solving the sample moment equation with the unknown parameters being replaced by their quasi-maximum likelihood estimates. To construct a confidence interval for the tail index, one needs to estimate the complicated asymptotic variance of the tail index estimator, however. In this paper the asymptotic normality of the tail index estimator is first derived, and a profile empirical likelihood method to construct a confidence interval for the tail index is then proposed. A simulation study shows that the proposed empirical likelihood method works better than the bootstrap method in terms of coverage accuracy, especially when the process is nearly nonstationary.
    Econometric Theory 10/2013; 29(05). · 1.48 Impact Factor
  • Huijun Feng, Liang Peng, Fukang Zhu
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    ABSTRACT: Empirical likelihood methods based on some weighted score equations are proposed for constructing confidence intervals for the coefficient in the simple bilinear model without assuming normality for the errors and without estimating the asymptotic variance explicitly. A simulation study confirms the good finite sample behavior of the proposed methods.
    Statistics [?] Probability Letters 10/2013; 83(10):2152–2159. · 0.53 Impact Factor
  • Liang Peng, Linyi Qian, Jingping Yang
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    ABSTRACT: Bivariate extreme-value distributions have been used in modeling extremes in environmental sciences and risk management. An important issue is estimating the dependence function, such as the Pickands dependence function. Some estimators for the Pickands dependence function have been studied by assuming that the marginals are known. Recently, Genest and Segers [Ann. Statist. 37 (2009) 2990–3022] derived the asymptotic distributions of those proposed estimators with marginal distributions replaced by the empirical distributions. In this article, we propose a class of weighted estimators including those of Genest and Segers (2009) as special cases. We propose a jackknife empirical likelihood method for constructing confidence intervals for the Pickands dependence function, which avoids estimating the complicated asymptotic variance. A simulation study demonstrates the effectiveness of our proposed jackknife empirical likelihood method.
    Bernoulli 05/2013; 19(2). · 0.94 Impact Factor
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    Minqiang Li, Liang Peng, Yongcheng Qi
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    ABSTRACT: Since its introduction by Owen in [29, 30], the empirical likeli-hood 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 esti-mating 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 empiri-cal likelihood method to overcome this computational burden. This proposed method is easy to implement and works well in practice.
    04/2013;
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    Song Xi Chen, Liang Peng, Cindy L Yu
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    ABSTRACT: Markov processes are used in a wide range of disciplines including finance. The transitional densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available especially for Lévy driven processes. We propose an empirical likelihood approach for estimation and model specification test based on the conditional characteristic function for processes whose sample paths can be either continuous or discontinuous with jumps. An empirical likelihood estimator for the parameter of a parametric process, and a smoothed empirical likelihood ratio test for the parametric specification of the process are proposed, which are shown to have good theoretical properties and empirical performance. Simulations and empirical case study are carried out to confirm the effectiveness of the estimator and the test.
    Bernoulli 02/2013; 19(1). · 0.94 Impact Factor
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    ABSTRACT: 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.
    Insurance: Mathematics and Economics. 07/2012; 51(1).
  • Huijun Feng, Liang Peng
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    ABSTRACT: It has been a long history for testing whether the underlying distribution belongs to a particular family. In this paper, we propose some jackknife empirical likelihood tests via estimating equations. The proposed new tests allow one to add more relevant constraints so as to improve the powers. A simulation study shows the effectiveness of the new tests.
    Journal of Statistical Planning and Inference 06/2012; 142(6):1571–1585. · 0.71 Impact Factor
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    ABSTRACT: 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. KeywordsCopulas–Empirical likelihood method–Jackknife
    Test 01/2012; 21(1):74-92. · 1.27 Impact Factor
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    Ngai Hang Chan, Deyuan Li, Liang Peng
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    ABSTRACT: An empirical likelihood–based confidence interval is proposed for interval esti-mations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its asymptotic limit is always normal with-out assuming stationarity of the process. Unlike the bootstrap method or the least squares procedure, the proposed empirical likelihood–based confidence interval is applicable regardless of whether the underlying autoregressive process is stationary, unit root, near-integrated, or even explosive, thereby providing a unified approach for interval estimation of an AR(1) model to encompass all situations. Finite-sample simulation studies confirm the effectiveness of the proposed method.
    Econometric Theory 01/2012; 28:705-717. · 1.48 Impact Factor
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    ABSTRACT: 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.
    J. Multivariate Analysis. 01/2012; 104:56-72.
  • Minqiang Li, Liang Peng, Yongcheng Qi
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    ABSTRACT: Since its introduction by Owen (1988, 1990), 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 and Lawless (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 article the authors propose a jackknife empirical likelihood method to overcome this computational burden. This proposed method is easy to implement and works well in practice. The Canadian Journal of Statistics 39: 370–384; 2011 © 2011 Statistical Society of CanadaDepuis leur introduction par Owen (1988, 1990), la méthode de vraisemblance empirique a été étudiée de façon exhaustive et elle est beaucoup utilisée dans la littérature pour construire des régions de confiance et confronter des hypothèses. Pour une grande classe de statistiques obtenues en résolvant des équations d'estimation, la fonction de vraisemblance empirique peut être formulée à partir de ces équations d'estimation telles que proposées par Qin et Lawless (1994). Lorsqu'uniquement une petite partie des paramètres sont d'intérêt, une méthode de vraisemblance empirique de profil doit être utilisée pour construire une région de confiance ce qui peut s'avérer très coûteux à évaluer numériquement. Dans cet article, les auteurs proposent une version jackknife de la méthode de vraisemblance empirique pour surmonter les coûts de calculs. Cette méthode est facile à implanter et elle fonctionne bien en pratique. La revue canadienne de statistique 39: 370–384; 2011 © 2011 Société statistique du Canada
    Canadian Journal of Statistics 05/2011; 39(2):370 - 384. · 0.59 Impact Factor
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    Deyuan Li, Liang Peng, Xinping Xu
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    ABSTRACT: Recently, Li and Peng (J Stat Plan Inference 139:1937–1952, 2009) proposed a bias reduction method for estimating the endpoint of a distribution function via an external estimator for the so-called second order parameter. Unlike the same study for the tail index of a heavy tailed distribution, the above procedure requires a certain rate of convergence of the external estimator rather than consistence. This makes the choice of such an external estimator impractical especially when the optimal rate of sample fraction is employed in the bias reduction estimation. In this paper, we propose a new bias reduction method which estimates all parameters by using the same number of upper order statistics.
    Extremes 01/2011; 13(2). · 1.40 Impact Factor
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    ABSTRACT: Copulas are becoming a quite flexible tool in modeling dependence among the components of a multivariate vector. In order to predict extreme losses in insurance and finance, extreme value copulas and tail copulas play a more important role than copulas. In this paper, we review some estimation and testing procedures for both, extreme value copulas and tail copulas, which received much less attention in the literature than corresponding studies of copulas.
    Journal of the Korean Statistical Society 01/2011; · 0.51 Impact Factor
  • ZHOUPING LI, YUN GONG, LIANG PENG
    01/2011;
  • Journal of The Korean Statistical Society - J KOREAN STAT SOC. 01/2011; 40(2):159-160.
  • Minqiang Li, Liang Peng
    [show abstract] [hide abstract]
    ABSTRACT: It has been a long history for testing whether the underlying distribution belongs to a particular one or a parametric class of distributions. In this paper, we propose some empirical likelihood ratio tests via estimating equations. The proposed new tests allow one to add more relevant constraints so as to improve the powers. A simulation study shows the effectiveness of the new tests. The new method is then used to test employer size and market value distributions of US firms.
    Journal of Statistical Planning and Inference 01/2011; 141(7):2428-2439. · 0.71 Impact Factor
  • Ruodu Wang, Liang Peng, Jingping Yang
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    ABSTRACT: For fitting a parametric copula to multivariate data, a popular way is to employ the so-called pseudo maximum likelihood estimation proposed by Genest, Ghoudi, and Rivest. Although interval estimation can be obtained via estimating the asymptotic covariance of the pseudo maximum likelihood estimation, we propose a jackknife empirical likelihood method to construct confidence regions for the parameters without estimating any additional quantities such as the asymptotic covariance. A simulation study shows the advantages of the new method in case of strong dependence or having more than one parameter involved.
    Scandinavian Actuarial Journal - SCAND ACTUAR J. 01/2011;
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    ABSTRACT: By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the extrapolation is quite limited generally in comparison with a heavy tailed distribution. In view of this drawback, a Weibull tailed distribution has been studied recently. Some methods for choosing the sample fraction in estimating the Weibull tail coefficient and some bias reduction estimators have been proposed in the literature. In this paper, we show that the theoretical optimal sample fraction does not exist and a bias reduction estimator does not always produce a smaller mean squared error than a biased estimator. These are different from using a heavy tailed distribution. Further we propose a refined class of Weibull tailed distributions which are more useful in estimating high quantiles and extreme tail probabilities.
    Journal of Statistical Planning and Inference. 01/2010;

Publication Stats

418 Citations
412 Downloads
57.79 Total Impact Points

Institutions

  • 2001–2014
    • Georgia Institute of Technology
      • • School of Mathematics
      • • School of Electrical & Computer Engineering
      Atlanta, Georgia, United States
  • 2006–2013
    • University of Minnesota Duluth
      • Department of Mathematics & Statistics
      Duluth, MN, United States
  • 2010
    • Tongji University
      • Department of Mathematics
      Shanghai, Shanghai Shi, China
  • 2009–2010
    • The Chinese University of Hong Kong
      • Department of Statistics
      Hong Kong, Hong Kong
    • Fudan University
      • Department of Statistics
      Shanghai, Shanghai Shi, China
    • Peking University
      Peping, Beijing, China
  • 2002–2008
    • Erasmus Universiteit Rotterdam
      • Department of Economics
      Rotterdam, South Holland, Netherlands
  • 2001–2002
    • Australian National University
      • Centre for Mathematics & its Applications
      Canberra, Australian Capital Territory, Australia