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 2010 Vol.26 Issue.5,Published 2010-10-25 article
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 449 An Invariant Property of the Elliptically Contoured Distribution about the Non-Singular Matrix Transformation Shi Aiju,Lin Jinguan 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. 2010 Vol. 26 (5): 449-458 [Abstract] ( 1384 ) [HTML 1KB] [ PDF 216KB] ( 2005 )
 459 Empirical Research on the Semiparametric Archimedean Copula Shi Daoji,Guo Hui,Luo Junpeng 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. 2010 Vol. 26 (5): 459-468 [Abstract] ( 1978 ) [HTML 1KB] [ PDF 610KB] ( 2589 )
 469 Equivalent Conditions for a Type of Convolution Closure of Local Subexponential Distributions and Applications Yu Changjun,Wang Yuebao 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}. 2010 Vol. 26 (5): 469-476 [Abstract] ( 1494 ) [HTML 1KB] [ PDF 206KB] ( 1911 )
 477 Estimation of Semivarying-Coefficient Models with the Correlated Random Errors Meng Jiafu,Zhang Riquan,Lv Shiqin 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. 2010 Vol. 26 (5): 477-484 [Abstract] ( 1482 ) [HTML 1KB] [ PDF 239KB] ( 1943 )
 485 Two-Step Kernel Estimation of Expected Shortfall for Strong Mixing Time Series Liu Jing,Yang Shanchao,Yao Yongyuan 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. 2010 Vol. 26 (5): 485-500 [Abstract] ( 2510 ) [HTML 1KB] [ PDF 281KB] ( 2030 )
 501 A Semiparametric Regression Model with Structural Change Wang Chengyong,Ai Chunrong,Wang Shaoping 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. 2010 Vol. 26 (5): 501-514 [Abstract] ( 1519 ) [HTML 1KB] [ PDF 506KB] ( 2115 )
 515 The Duality of Heterogeneous Coagulation-Fragmentation Processes Hu Chunhua,Han Dong 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. 2010 Vol. 26 (5): 515-522 [Abstract] ( 1416 ) [HTML 1KB] [ PDF 191KB] ( 2017 )
 523 Joint Asymptotic Distributions of Exceedances Point Process and Partial Sum of Non-Stationary Gaussian Sequence Tan Zhongquan,Peng Zuoxiang 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. 2010 Vol. 26 (5): 523-529 [Abstract] ( 1380 ) [HTML 1KB] [ PDF 210KB] ( 1896 )
 530 Mean-Value Estimation with Validation Data Yu Shihang 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. 2010 Vol. 26 (5): 530-536 [Abstract] ( 1253 ) [HTML 1KB] [ PDF 198KB] ( 1799 )
 537 Some Results on Tail Probabilities with Applications of Generalized Comparison Method Liu Guoqing,Zhang Yinlong,Wang Minhua 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. 2010 Vol. 26 (5): 537-543 [Abstract] ( 1279 ) [HTML 1KB] [ PDF 181KB] ( 2045 )
 544 Marginal Coordinate Tests for Central Mean Subspace with Principal Hessian Directions Yu Zhou,Dong Yuexiao,Fang Yun 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). 2010 Vol. 26 (5): 544-552 [Abstract] ( 1663 ) [HTML 1KB] [ PDF 209KB] ( 2093 )
 553 2010 Vol. 26 (5): 553-558 [Abstract] ( 1174 ) [HTML 1KB] [ PDF 193KB] ( 1984 )
 559 2010 Vol. 26 (5): 559-559 [Abstract] ( 1108 ) [HTML 1KB] [ PDF 92KB] ( 1607 )
 560 2010 Vol. 26 (5): 560-560 [Abstract] ( 1090 ) [HTML 1KB] [ PDF 92KB] ( 1901 )

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