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2010 Vol.26 Issue.5,Published 2010-10-25

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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 )
应用概率统计
 

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