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When the run size of experiment is relative
small, it is possible to use the method of exhaustion to select its
possible existing orthogonal balanced block designs. In this way, we
can find out both orthogonal balanced block designs as more as
possible and some information on how to construct orthogonal
balanced block designs for some experiment of big run size. Some
result of experiment run size of no more than 9 is given out.
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The estimation of regression parameters
and the contamination coefficient of a linear model are studied when
its response variables are contaminated and interval censored. Under
some suitable conditions it is proved that the estimators which are
established in this paper are strongly consistent. Some simulation
results indicate that our method performs very well even though the
data both contaminated and interval censored.
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In this paper, we first study strong limit
theorems for even-odd Markov chain fields on a Cayley tree by using
the method of constructing martingale. Then, we give strong laws of
large numbers on the frequencies of states for even-odd Markov chain
fields on a Cayley tree, which we extend a known result.
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In the regression analysis, it is common to
assume the independence and homogeneous of the observation
responses. In generalized parametric and nonparametric models, there
does not exist the homoscedasticity of the model. However, in many
exponential models, random effect is another main cause for over or
under-dispersion of variance. So in this paper, the testing of
random effect in discrete generalized single index model with random
effects for longitudinal data is studied. Simulation for the Score
testing statistics is also illustrated.
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In contrast with the classical
Cramer-Lundberg model where the premium process is a linear
function of time, we consider the constant barrier strategy under
the risk model where the aggregate premium process is modeled as a
compound Poisson process. Dickson and Waters (2004) pointed out that
the shareholders should be liable to cover the deficit at ruin.
Thus, the optimization criteria considered in this paper is
maximizing the expectation of the difference between discounted
dividends until ruin and the deficit at ruin. As an illustration,
the condition of the optimal barrier is calculated in the case where
the individual stochastic premium amount and claim amount are
exponential distributed.
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We first establish a criterion for the minimal
$Q$-function to be a Feller transition function when $Q$ is a
quasi-monotone q-matrix. We then apply this result to generalized
branching q-matrices and obtain the corresponding Feller criteria
for generalized branching processes. In particular, it is shown that
there always exists a separating point $\theta_0$ with
$1\leq\theta_0\leq2$ or $\theta_0<+\infty$ such that whether the
generalized branching processes (with resurrection) are Feller
processes or not according to $\theta<\theta_0$ or
$\theta>\theta_0$, where $\theta$ is the nonlinear number given in
the branching q-matrix
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The conditional mean, variance and higher-conditional
moment functions are often of special interest in regression. In
this paper,we generalize central mean subspace and focus especial
attention on the k th-conditional moment function. For this, we
first borrow the new concept --- the central k th-conditional
moment subspace, and study its basic properties. To avoid computing
the inverse of the covariance of predictors with large
dimensionality and highly collinearity, we develop a method called
the $k$th-moment weighted partial least squares to handle with the
estimation of the central k th-conditional moment subspace.
Finally, we obtain strong consistency
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In this paper, we propose a local linear
estimator for conditional third central moment. The asymptotic bias
and variance are derived. General cross validation (GCV) is
recommended for bandwidth selection. A simple simulation study is
carried out to illustrate the usefulness of the proposed method.}
\newcommand{\fundinfo}{This work was supported by National
Social Science Foundation (08CTJ001)
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Exponential stabilization in mean square is investigated
for a class of stochastic systems, where Markovian switching and
time-varying delay is introduced. In order to guarantee the
exponential stability in mean square for the system, a sufficient
condition is derived using the method of Liapunov function and LMI.
Furthermore, a kind of desirable gain matrix is designed to make the
system the exponential stability in mean square by the state
feedback. Finally, when the Markov chain goes around all its modes,
a mode-independent gain matrix is presented to guarantee the
exponential stability in mean square for this system
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The empirical likelihood method has been
extensively applied to many models of statistical inference. This
paper is based on empirical likelihood for partial linear models for
statistical diagnosis. First, the estimating equations of the model
are given and the maximum empirical likelihood estimates of the
parameters are obtained; then, based on empirical likelihood method,
the three different measures of influence curvatures are studied;
last, stochastic simulation and data analysis are given to
illustrate the validity of statistical diagnostic measures
