Liang Peng

Georgia State University, Atlanta, Georgia, United States

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Publications (102)91.88 Total impact

  • Liang Peng, Yongcheng Qi, Fang Wang
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    ABSTRACT: It has been a long history in testing whether a mean vector with a fixed dimension has a specified value. Some well-known tests include the Hotelling $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988) 237-249; Ann. Statist. 18 (1990) 90-120]. Recently, Hotelling $T^2$-test has been modified to work for a high-dimensional mean, and the empirical likelihood method for a mean has been shown to be valid when the dimension of the mean vector goes to infinity. However, the asymptotic distributions of these tests depend on whether the dimension of the mean vector is fixed or goes to infinity. In this paper, we propose to split the sample into two parts and then to apply the empirical likelihood method to two equations instead of d equations, where d is the dimension of the underlying random vector. The asymptotic distribution of the new test is independent of the dimension of the mean vector. A simulation study shows that the new test has a very stable size with respect to the dimension of the mean vector, and is much more powerful than the modified Hotelling $T^2$-test.
    05/2014;
  • Shiqing Ling, Liang Peng, Fukang Zhu
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    ABSTRACT: It is well known that estimating bilinear models is quite challenging. Many different ideas have been proposed to solve this problem. However, there is not a simple way to do inference even for its simple cases. This paper studies the special bilinear model $$Y_t=\mu+\phi Y_{t-2}+ bY_{t-2}\varepsilon_{t-1}+ \varepsilon_t,$$ where $\{\varepsilon_t\}$ is a sequence of i.i.d. random variables with mean zero. We first give a sufficient condition for the existence of a unique stationary solution for the model and then propose a GARCH-type maximum likelihood estimator for estimating the unknown parameters. It is shown that the GMLE is consistent and asymptotically normal under only finite fourth moment of errors. Also a simple consistent estimator for the asymptotic covariance is provided. A simulation study confirms the good finite sample performance. Our estimation approach is novel and nonstandard and it may provide a new insight for future research in this direction.
    05/2014;
  • Shiqing Ling, Liang Peng, Fukang Zhu
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    ABSTRACT: It is well known that estimating bilinear models is quite challenging. Many different ideas have been proposed to solve this problem. However, there is not a simple way to do inference even for its simple cases. This article proposes a generalized autoregressive conditional heteroskedasticity-type maximum likelihood estimator for estimating the unknown parameters for a special bilinear model. It is shown that the proposed estimator is consistent and asymptotically normal under only finite fourth moment of errors. Copyright © 2014 Wiley Publishing Ltd
    Journal of Time Series Analysis 04/2014; · 0.79 Impact Factor
  • Fukang Zhu, Zongwu Cai, Liang Peng
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    ABSTRACT: Researchers have constantly asked whether stock returns can be predicted by some macroeconomic data. However, it is known that macroeconomic data may exhibit nonstationarity and/or heavy tails, which complicates existing testing procedures for predictability. In this paper we propose novel empirical likelihood methods based on some weighted score equations to test whether the monthly CRSP value-weighted index can be predicted by the log dividend-price ratio or the log earnings-price ratio. The new methods work well both theoretically and empirically regardless of the predicting variables being stationary or nonstationary or having an infinite variance.
    The Annals of Applied Statistics 04/2014; 8(1). · 2.24 Impact Factor
  • Fukang Zhu, Zongwu Cai, Liang Peng
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    ABSTRACT: Researchers have constantly asked whether stock returns can be predicted by some macroeconomic data. However, it is known that macroeconomic data may exhibit nonstationarity and/or heavy tails, which complicates existing testing procedures for predictability. In this paper we propose novel empirical likelihood methods based on some weighted score equations to test whether the monthly CRSP value-weighted index can be predicted by the log dividend-price ratio or the log earnings-price ratio. The new methods work well both theoretically and empirically regardless of the predicting variables being stationary or nonstationary or having an infinite variance.
    03/2014;
  • 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 03/2014; · 0.53 Impact Factor
  • Jonathan Hill, Liang Peng
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    ABSTRACT: The consistency of the quasi-maximum likelihood estimator for random coefficient autoregressive models requires that the coefficient be a non-degenerate random variable. In this article, we propose empirical likelihood methods based on weighted-score equations to construct a confidence interval for the coefficient. We do not need to distinguish whether the coefficient is random or deterministic and whether the process is stationary or non-stationary, and we present two classes of equations depending on whether a constant trend is included in the model. A simulation study confirms the good finite-sample behaviour of our resulting empirical likelihood-based confidence intervals. We also apply our methods to study US macroeconomic data.
    Journal of Time Series Analysis 01/2014; · 0.79 Impact Factor
  • Source
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    ABSTRACT: We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the underlying distribution admits an approximate parametric form, and, furthermore, our estimation makes use of the full observed data. The proposed method is semiparametric as no parametric forms are assumed on all the marginal distributions. But we select appropriate bivariate copulas to model the joint dependence structure by taking the advantage of the recent development in constructing large dimensional vine copulas. Consequently a sample quantile resulted from a large bootstrap sample drawn from the fitted joint distribution is taken as the estimator for the extreme quantile. This estimator is proved to be consistent. The reliable and robust performance of the proposed method is further illustrated by simulation.
    11/2013;
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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.
    The Annals of Statistics 10/2013; 41(4). · 2.53 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
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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
  • 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.
    Canadian Journal of Statistics 04/2013; · 0.59 Impact Factor
  • Ruodu Wang, Liang Peng, Jingping Yang
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    ABSTRACT: In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependence structure. These bounds are directly related to the problem of obtaining the worst Value-at-Risk of the total risk. Using the idea of complete mixability, we provide a new lower bound for any given marginal distributions and give a necessary and sufficient condition for the sharpness of this new bound. For the sum of dependent risks with an identical distribution, which has either a monotone density or a tail-monotone density, the explicit values of the worst Value-at-Risk and bounds on the distribution of the total risk are obtained. Some examples are given to illustrate the new results.
    Finance and Stochastics 04/2013; 17(2). · 1.21 Impact Factor
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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
  • Source
    Ruodu Wang, Liang Peng, Yongcheng Qi
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    ABSTRACT: It has been a long history to test the equality of two multivariate means. One popular test is the so-called Hotelling T 2 test. However, as the dimension diverges, the Hotelling T 2 test performs poorly due to the possible inconsistency of the sample covariance estimation. To overcome this issue and allow the dimension to diverge as far as possible, Bai and Saranada (1996) and Chen and Qin (2010) proposed tests without the sample covariance involved, and derived the asymptotic limits which depend on whether the dimension is fixed or diverges under a specific multivariate model. In this paper, we propose a jackknife empirical likelihood test which has a chi-square limit independent of the dimension, and the conditions are much weaker than those in the existing methods. A simulation study shows that the proposed new test has a very robust size with respect to the dimension, and is powerful too.
    Statistica Sinica 01/2013; 23(2). · 1.44 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). · 1.10 Impact Factor
  • 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
  • Liang Peng
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    ABSTRACT: 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 CanadaIl est bien connu que la méthode du profil de vraisemblance empirique, basée sur les équations destimation, est très exigeante numériquement lorsqu'il y a beaucoup de paramètres de nuisance. Récemment, Li, Peng et Qi (2011) ont proposé une version jack-knife de la méthode de vraisemblance empirique pour construire des régions de confiance pour les paramètres d'intérêt en estimant les paramètres de nuisance séparément. Cependant, lorsqu'il est impossible dobtenir des estimateurs analytiques pour les paramètres de nuisance, le calcul de la version jack-knife de la méthode de vraisemblance empirique demeure ardue à évaluer numériquement. Dans cet article, nous proposons une approximation afin de réduire le temps de calcul de la version jack-knife de la méthode de vraisemblance empirique lorsque les paramètres de nuisance ne peuvent pas être estimés explicitement. Une étude de simulation confirme l'avantage de cette nouvelle méthode. La revue canadienne de statistique 40: 110–123; 2012 © 2012 Société statistique du Canada
    Canadian Journal of Statistics 03/2012; 40(1). · 0.59 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.
    Journal of Multivariate Analysis 02/2012; 104:56-72. · 1.06 Impact Factor

Publication Stats

538 Citations
91.88 Total Impact Points

Institutions

  • 2014
    • Georgia State University
      • Department of Risk Management and Insurance
      Atlanta, Georgia, United States
  • 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