20 May 2007, Volume 23 Issue 2
    

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    学术论文
  • Cui Henjian, Chan Laikow
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 113-122.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    In this paper, a short production run process and some kinds of existed
    control charts for short run process are introduced which includes plotted
    statistics and control limits for subgroup and individual cases respectively.
    Some comparisons are also addressed.
  • Lin Qinquan, Yang Feng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 123-132.
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    For Backward Stochastic Differential Equation with jumps and an increasing
    predictable RCLL process as its penalization term, we have defined
    $g$-supersolution for such a BSDE and obtained the limit theorem. As an application of the limit theorem, the existence and uniqueness of the smallest supersolution for BSDE with jumps and constraints on $(Y,Z,q)$ is proved.
  • Lian Zhibin, Yang Xiangqun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 133-142.
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    The primary objective of this paper is to define the $r$-truncated annuity
    distribution, which is a generalization of the annuity distribution in refs:
    [5], [6]. Conditions for the existence of these distributions are given. It
    is proved that under certain conditions, the $r$-truncated annuity distribution
    is the mixture of an annuity distribution and a special $r$-truncated annuity
    distribution.
  • LI JUNHAI, LIU ZAIMING
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 143-148.
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    In this paper, the expected discounted penalty of mixed exponential renewal risk process was considered. Under some simple conditions, the explicit expression of Laplace transform of the expected discounted penalty is obtained.
  • ZHANG WEIMING,Zong YUNNAN, LIU JIANBIN
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 149-156.
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    This paper extends previous studies for processes that are monitored by the combination of $\wt{x}$ and $R$ charts with variable parameters to include variable control limits based on the Costa method of joint $\ol{x}$ and $R$ charts with variable parameters. Calculating the average time to signal for the combination of $\wt{x}$ and $R$ charts under variable parameters. The proposed charts are compared with the conventional charts, the variable sample size and sampling interval charts.
  • Newfoundland, Canada
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 157-164.
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    The classical B\"{u}hlmann credibility formula estimates the hypothetical mean of
    a particular insured, or risk by square error loss. However, the ratio of the charged premium and the true premium is more appropriate to measure equity of the premium than the absolute value of their difference. Regarding to this case, we propose two alternative loss functions to calculate the credibility premium in this paper. The one combines the squared error loss and the relative loss ratio is called as therelative mean square error loss. The other one mixes the relative entropy loss function instead of the squared error loss is called as the relative entropy loss function. The estimation method of credibility factors and their properties are investigated.
  • WANG LIMING, WABG JINGLONG
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 165-173.
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    The change-point problem about the scale parameter is discussed in this paper.
    Based on two-sample $U$-statistic two tests are proposed, and their approximate distributions, which are $\sup\limits_{0<t<1}|B(t)|$ and extreme valve distribution respectively, where $\{B(t),0\le t\le 1\}$ is a Brownian bridge, are obtained.

  • YUAN YUZE

    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 174-178.
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    In this paper we obtained the precise asymptotics in Davis's law of law numbers and LIL for self-normalized sums, i.e.{\bf Theorem 1}\hy Let $\ep X=0$, and $\ep X^2I_{(|X|\leq x)}$ is slowly varying at $\infty$, then
    $$\lim_{\varepsilon\searrow0}\varepsilon^2\tsm_{n\geq3}\frac{1}{n\log n}
    \pr\Big(\Big|\frac{S_n}{V_n}\Big|\geq\varepsilon\sqrt{\log\log n}\Big)=1.
    $$
    {\bf Theorem 2}\hy Let $\ep X=0$, and $\ep X^2I_{(|X|\leq x)}$ is slowly varying at $\infty$, then for $0\leq\delta\leq1$, we have
    $$ \lim_{\varepsilon\searrow0}\varepsilon^{2\delta+2}\tsm_{n\geq1}
    \frac{(\log n)^{\delta}}{n}\pr\Big(\Big|\frac{S_n}{V_n}\Big|
    \geq\varepsilon\sqrt{\log n}\Big)=\frac{1}{\delta+1}\ep|N|^{2\delta+2},
    $$ where $N$ denote the standard normal random variable.

  • XU WANGLI, LI ZAIXING
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 179-187.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    Partially linear models are assumed to be linearly related to one or more variable,
    but the relation to an additional variable or variables is not assumed to be easily
    parameterized. One primary approach to estimate the parameter and nonparametric part is the method of penalized least squares method, generalized cross-validation (GCV) approach is a popular method for selecting the smoothing parameters. However, the optimality of GCV in the partial linear model with penalized least squares has not been proved. In this article, we provide the support for using GCV through its optimality of the smoothing parameter. Simulation studies are employed to investigate the empirical performance of generalized cross-validation and that of cross-validation for comparison in the context.

  • ZOU BIN,LI LUOQING,WAN CHENGGAO
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 188-196.
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    It has been shown previously by Vapnik, Cucker and Smale that, the empirical risks based on an independent and identically distributed (i.i.d.) sequence must uniformly converge to their expected risks for learning machines as the number of samples approaches infinity. This paper extends the results to the case where the i.i.d. sequence replaced by $\alpha$-mixing sequence. It establishes the rate of uniform convergence for learning machine based on $\alpha$-mixing sequence by applying Markov's inequality.
  • LI GAORONG, XUE LIUGEN
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 197-206.
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    In this paper, we introduce a method of blockwise empirical Cressie-Read likelihood for weakly dependent data. The strong consistency and asymptotic normality of the blockwise empirical Cressie-Read likelihood estimation of the parameters are obtained. It is also shown that the blockwise empirical Cressie-Read likelihood statistic is asymptotically a $chi$-square distribution.
  • 论文
  • QIN GUOYOU, ZHU ZHONGYI
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(2): 207-214.
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    For a partial linear mixed model, we usually focus on the estimation of the
    variance components, and a lot of methods can be applied. However, many of
    these methods, such as maximum likelihood method and restricted maximum
    likelihood method, can be included in the framework of generalized estimating
    equation (GEE). As well known, the GEE method is sensitive to outliers. So,
    an alterative set of robust GEEs for both mean components and correlation
    parameters are proposed for the partial linear mixed model for longitudinal
    data in this paper. Some simulations are conducted to evaluate the performance
    of the proposed estimators. In the end, the method is illustrated with analysis
    of two real data sets.