Liang Peng

Georgia State University, Atlanta, Georgia, United States

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Publications (110)95.95 Total impact

  • Aiai Liu, Yanxi Hou, Liang Peng
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    ABSTRACT: Systemic risk concerns extreme co-movement of several financial variables, which involves characterizing tail dependence. The coefficient of tail dependence was proposed by Ledford and Tawn (1996, 1997) to distinguish asymptotic independence and asymptotic dependence. Recently a new measure based on the conditional Kendall’s tau was proposed by Asimit et al. (2015) to measure the tail dependence and to distinguish asymptotic independence and asymptotic dependence. For effectively constructing a confidence interval for this new measure, this paper proposes a smooth jackknife empirical likelihood method, which does not need to estimate any additional quantities such as asymptotic variance. A simulation study shows that the proposed method has a good finite sample performance.
    Insurance Mathematics and Economics 06/2015; DOI:10.1016/j.insmatheco.2015.05.014 · 1.10 Impact Factor
  • Chenxue Li, Deyuan Li, Liang Peng
    Journal of Business and Economic Statistics 06/2015; DOI:10.1080/07350015.2015.1052460 · 2.32 Impact Factor
  • Ruodu Wang, Liang Peng, Jingping Yang
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    ABSTRACT: The CreditRisk+ model is widely used in industry for computing the loss of a credit portfolio. The standard CreditRisk+ model assumes independence among a set of common risk factors, a simplified assumption that leads to computational ease. In this article, we propose to model the common risk factors by a class of multivariate extreme copulas as a generalization of bivariate Fréchet copulas. Further we present a conditional compound Poisson model to approximate the credit portfolio and provide a cost-efficient recursive algorithm to calculate the loss distribution. The new model is more flexible than the standard model, with computational advantages compared to other dependence models of risk factors.
    North American Actuarial Journal 12/2014; 19(1):24-40. DOI:10.1080/10920277.2014.976311
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    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.
    Statistical Science 05/2014; 29(1). DOI:10.1214/13-STS425 · 1.69 Impact Factor
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    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.
  • 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 05/2014; 35(3). DOI:10.1111/jtsa.12064 · 0.81 Impact Factor
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    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). DOI:10.1214/13-AOAS708 · 1.69 Impact Factor
  • 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; 36(1). DOI:10.1111/jtsa.12092 · 0.81 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.
  • 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; 86. DOI:10.1016/j.spl.2013.12.019 · 0.53 Impact Factor
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    ABSTRACT: It is known that the normalized maxima of a sequence of independent and identically distributed bivariate normal random vectors with correlation coefficient $\rho \in (-1,1)$ is asymptotically independent, which may seriously underestimate extreme probabilities in practice. By letting $\rho$ depend on the sample size and go to one with certain rate, H\"usler and Reiss (1989) showed that the normalized maxima can become asymptotically dependent. In this paper, we extend such a study to a triangular array of multivariate Gaussian sequence, which further generalizes the results in Hsing, H\"usler and Reiss (1996) and Hashorva and Weng (2013).
    Statistics [?] Probability Letters 02/2014; 103. DOI:10.1016/j.spl.2015.04.007 · 0.53 Impact Factor
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    ABSTRACT: Modeling and forecasting extreme co-movements in financial market is important for conducting any stress tests in risk management. Asymptotic independence and asymptotic dependence behave drastically different in characterizing such co-movements. For example, the impact of extreme events is usually overestimated whenever asymptotic dependence is wrongly assumed. On the other hand, the impact is seriously underestimated whenever the data is misspecifed as asymptotic independent. Therefore, distinguishing between asymptotic independence/dependence scenarios is very informative for any decision maker and especially in risk management. Motivated by the popular Kendall's tau dependence measure, we investigate the properties of the limiting conditional Kendall's tau in order to detect the presence of asymptotic independence/dependence.We also propose nonparametric estimation for this new measure and derive its asymptotic limit. A simulation study shows the good performance of the new measure and its combination with the coefficient of tail dependence proposed by Ledford and Tawn (1996, 1997). Finally, applications to financial and insurance data are provided as well.
    SSRN Electronic Journal 01/2014; DOI:10.2139/ssrn.2376288
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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.
    Journal Of The Royal Statistical Society 11/2013; DOI:10.1111/rssb.12103
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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). DOI:10.1214/13-AOS1136 · 2.44 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. DOI:10.1016/j.spl.2013.05.037 · 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). DOI:10.1017/S0266466612000801 · 1.15 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). DOI:10.3150/11-BEJ409 · 1.30 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; DOI:10.2139/ssrn.2256653 · 0.70 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). DOI:10.1007/s00780-012-0200-5 · 1.09 Impact Factor
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    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 04/2013; 23(2). DOI:10.5705/ss.2011.261 · 1.23 Impact Factor

Publication Stats

878 Citations
95.95 Total Impact Points

Institutions

  • 2014–2015
    • Georgia State University
      • Department of Risk Management and Insurance
      Atlanta, Georgia, United States
    • Xiamen University
      Amoy, Fujian, China
  • 2001–2014
    • Georgia Institute of Technology
      • • School of Mathematics
      • • School of Electrical & Computer Engineering
      Atlanta, Georgia, United States
  • 2009
    • The Chinese University of Hong Kong
      Hong Kong, Hong Kong
  • 2006
    • University of Minnesota Duluth
      • Department of Mathematics & Statistics
      Duluth, MN, United States
  • 2001–2002
    • Australian National University
      • Centre for Mathematics & its Applications
      Canberra, Australian Capital Territory, Australia