25 October 2010, Volume 26 Issue 5
    

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  • Shi Aiju,Lin Jinguan
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 449-458.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    In this paper, we first extend the
    definitions of matrix $F$ and $t$ distributions to the left
    spherical distribution family, prove the density functions have no
    relation with the one producing them and then show that discuss the
    elliptically contoured distributions are invariant under nonsingular
    matrix transformations. These distributions include the matrix Beta,
    inverse Beta, Dirichlet, inverse Dirichlet, $F$ and $t$ etc. And
    finally it is shown that their distribution density functions not
    only have no relation with the density function generating them but
    also the transformation matrix.

  • Shi Daoji,Guo Hui,Luo Junpeng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 459-468.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    Semiparametric Archimedean copulas, which have a fexible
    dependence structure because of the special way constructed by using
    the existing archimedean generator, can describe the dependence
    structure between the financial data auto-adaptively. The empirical
    results on the exchange rate market suggest that the semiparametric
    Archimedean copula is more flexible than the other three copulas,
    and is suggestive when selecting copulas.

  • Yu Changjun,Wang Yuebao
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 469-476.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    This paper obtains some equivelent conditions
    for a type of convolution closure of local subexponential
    distributions on $[0,\infty)$, which are also valid for
    distributions on $(-\infty,\infty)$ under certain conditions. On the
    basis of these results, the local asymptotics for the distribution
    of symmetrization are given. The results above include the
    corresponding, non-local results of Embrechts and Goldie
    (1980)\ucite{1} and Geluk (2004)\ucite{2}. Some of our proofs are
    more simple than those of Geluk (2004)\ucite{2}.

  • Meng Jiafu,Zhang Riquan,Lv Shiqin
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 477-484.
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    The estimation of semivarying coefficient
    models are studied in this paper. The estimators of the function
    coefficient and the constant coefficient are given by modifying the
    profile least squares. Furthermore, the asymptotical normalities of
    these estimations are investigated. A simulation study is carried
    out to compare the proposed methods.

  • Liu Jing,Yang Shanchao,Yao Yongyuan
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 485-500.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    Expected Shortfall (ES) is one of the most
    popular tools of risk management for financial property, and is an
    ideal coherent risk measure. In this paper, we discuss the two-step
    kernel estimator of ES under polynomial decay of strong mixing
    coefficients of time series. The first step is the kernel estimator
    of VaR (Value at Risk) and the second step is the kernel estimator
    of ES. We obtain Bahadur representation of the kernel estimator of
    ES. Then, we give the mean squares error and the rate of the
    asymptotic normality.

  • Wang Chengyong,Ai Chunrong,Wang Shaoping
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 501-514.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    Combined with semiparametric regression model
    and structural change model with unknown change point, a new
    regression model --- semiparametric regression model with structural
    change --- has been proposed. The weighted least squares estimator
    of parameter $\beta,\beta^\ast,\gamma,k$ and the kernel estimator of
    $f(t)$ are given, and $\sqrt{n}$-consistency properties of
    $\beta,\beta^\ast,\gamma$'s estimator is proved. Also, the
    estimator's strong consistency properties and some test problem
    about the model are discussed. And, at last, we give a simulation
    study to verify the superiority of our new model.

  • Hu Chunhua,Han Dong
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 515-522.
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    This paper study the duality of heterogeneous
    coagulation-fragmentation process (HCFP) which models the
    coagulation, fragmentation and diffusion of clusters of particles on
    lattice. The closed form of stationary distribution for HCFP is
    obtained, and then the integrated form of BBGKY hierarchy of HCFP is
    given.

  • Tan Zhongquan,Peng Zuoxiang
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 523-529.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    Let $\{X_{i}\}^{\infty}_{i=1}$ be a standardized
    non-stationary Gaussian sequence, and the exceedances point process
    $N_{n}$ be the exceedances of level $\mu_{n}(x)$ formed by
    $X_{1},X_{2},\cdots,X_{n}$, $r_{ij}=\ep X_{i}X_{j}$,
    $S_{n}=\tsm_{i=1}^{n}X_{i}$. Under some conditions, the asymptotic
    independence of $N_{n}$ and $S_{n}$ is obtained.

  • Yu Shihang
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 530-536.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    In this paper, the mean-value estimation
    problem with surrogate data and validation sampling is considered. A
    regression calibration kernel function is defined to incorporate the
    information contained in both surrogate variates and validation
    sampling. The proposed estimators are proved to be asymptotically
    normal and convergent rate.

  • Liu Guoqing,Zhang Yinlong,Wang Minhua
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 537-543.
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    We extend the comparison method and present
    a new method to derive sharp closed-form semiparametric bounds on
    small value probability $\pr(X\leq t)$, where $X\in[0,M]$ is a
    random variable with $\ep X=m_1$ and $\ep X^2=m_2$ fixed. The proofs
    of our results are elementary.

  • Yu Zhou,Dong Yuexiao,Fang Yun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2010, 26(5): 544-552.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    We provide marginal coordinate tests based on
    two competing Principal Hessian Directions (PHD) methods. Predictor
    contributions to central mean subspace can be effectively identified
    by our proposed testing procedures. PHD-based tests avoid choosing
    the number of slices, which is a well-known shortcoming of similar
    tests based on Sliced Inverse Regression (SIR) or Sliced Average
    Variance Estimation (SAVE). The asymptotic distributions of our test
    statistics under the null hypothesis are provided and the
    effectiveness of the new tests is illustrated by simulations.}
    \newcommand{\fundinfo}{The first and corresponding authors were supported
    by National Social Science Foundation (08CTJ001).