14 December 2016, Volume 32 Issue 6
    

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  • SU Zhonggen
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(6): 551-580.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    Tracy and Widom found a new type of probability distribution in
    the study of high dimensional random matrices in the 1990s, which is nowadays normally
    called Tracy-Widom distribution. It is used to described the limiting distribution of the
    extremal eigenvalues in Gaussian Unitary Ensemble. Later on, the study in the past two
    decades indicates that Tracy-Widom distribution is universal like normal distribution and
    can be well used to describe a lot of seemingly distinct random phenomena. As illustrations,
    the paper briefly review nine widely studied random models, each of which is more or
    less related to Tracy-Widom distribution. Compared to normal distribution, Tracy-Widom
    distribution has horribly intricate distribution function, density function and moments.
    people need to use deep mathematical knowledge and advanced computation technology in order
    to extend and to apply Tracy-Widom distribution in practice. But it is absolutely worthy
    further study on account of its importance.

  • YE Xuguo, LIN Jinguan
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(6): 581-591.
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    This paper studies nonparametric estimation of the integrated
    volatility of Poisson jump-diffusion processes with noisy high-frequency data. We
    propose jump-robust two-scale and multi-scale estimators. The estimators are based on
    a combination of the multi-scale method and threshold technique, which serves to remove
    microstructure noise and jumps, respectively. Furthermore, asymptotic properties of the
    proposed estimators, such as consistency, are established.

  • article
  • LIU Haiyan; CHEN Mi
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(6): 592-602.
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    This paper considers the expected penalty functions for a
    discrete semi-Markov risk model, which includes several existing risk models such
    as the compound binomial model (with time-correlated claims) and the compound Markov
    binomial model (with time-correlated claims) as special cases. Recursive formulae
    and the initial values for the discounted free penalty functions are derived in the
    two-state model by an easy method. We also give some applications of our results.

  • ZHANG Xiaoyu, XU Fuxia
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(6): 603-616.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    We study the random variables of radial asymmetry based on
    copulas. We research on the structure of random variables which radial asymmetry
    degree is and get the exact best-possible bounds of random variables which
    radial asymmetry degree is equal to . Then we expand to general case. We propose
    an essential condition of radial asymmetry degree is  and study the structure
    of copula. We provide a broad bounds of copula that the radial asymmetry degree is
    .

  • LIU Bin, SHI Yimin, CAI Jing, WANG Ruibing
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(6): 617-631.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    The linear accelerated model is often used to the statistical
    analysis of constant stress accelerated life test, whereas it does not relate well
    with the facts. By adopting the power functional accelerated model, the relationship
    of sample quantiles among different constant stress levels is obtained, which can
    lead to the estimations of the parameters in accelerated model and the characteristic
    coefficient vectors by virtue of the least square method, then the life-time data
    transformation between different stress levels can be operated. For complete data
    and censoring data, a Dirichlet process prior is introduced to gain the posterior
    distribution and the nonparametric Bayesian estimation of the reliability function,
    meanwhile, the consistency of the posterior estimators is proved. Finally, a real
    life example of Metal-Oxide-Semiconductor capacitors is analyzed to illustrate the
    effect of our model.

  • YANG Xu
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(6): 632-642.
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    A class of backward doubly stochastic differential equations driven by white noises and Poisson random measures are studied in this paper. The definitions of solutions and Yamada-Watanabe type theorem to this equation are established.

  • HE Jie; DUAN Xiaogang; ZHANG Shumei
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(6): 643-654.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    The multivariate response is commonly seen in longitudinal
    and cross-sectional design. The marginal model is an important tool in discovering
    the average influence of the covariates on the response. A main feature of the marginal
    model is that even without specifying the inter-correlation among different components
    of the response, we still get consistent estimation of the regression parameters. This
    paper discusses the GMM estimation of marginal model when the covariates are missing at
    random. Using the inverse probability weighting and different basic working correlation
    matrices, we obtain a series of estimating equations. We estimate the parameters of
    interest by minimizing the corresponding quadratic inference function. Asymptotic
    normality of the proposed estimator is established. Simulation studies are conducted
    to investigate the finite sample performance of the new estimator. We also apply our
    proposal to a real data of mathematical achievement from middle school students.