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The model of linear birth and death
processes with killing has been studied by Karlin and Tavar
(1982). This paper is concerned with three problems in connection
with quasi-stationary distributions (QSDs) for linear birth-death
process with killing on a semi-infinite lattice of integers.
The first problem is to determine the decay parameter of
. We have
where
,
,
are the birth, death and killing rates
in state , respectively. The second one is to prove the
uniqueness of the QSD which is a geometric distribution. It is
interesting to find that the unkilled process has a one-parameter
family of QSDs while the killed process has precisely one QSD. The
last one is to solve the domain of attraction problem, that is, we
obtain that any initial distribution is in the domain of attraction
of the unique QSD for . Our study is motivated by the
population genetics problem.
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Global sensitivity indices play important
roles in global sensitivity analysis based on ANOVA high-dimensional
representation, Wang et al. (2012) showed that orthogonal arrays
are A-optimality designs for the estimation of parameter ,
the definition of which can be seen in Section 2. This paper
presented several other optimal properties of orthogonal arrays
under ANOVA high-dimensional representation, including E-optimality
for the estimation of and universal optimality for the
estimation of , where
is the independent
parameters of . Simulation study showed that randomized
orthogonal arrays have less biased and more precise in estimating
the confidence intervals comparing with other methods.
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A multivariate partially linear EV model is
considered in this paper. By correcting the attenuation, a modified
B-spline least squares estimator for both the parametric and the
nonparametric components is proposed. Moreover, we investigate the
asymptotical normality of the modified estimator of the parametric
components and the convergence rate of the estimator of the
nonparametric function.
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In the paper a change-point model of
ca125 longitudinal data for single subject was established. The
formulae of the maximum likelihood estimate for model parameters
were presented. A likelihood ratio test statistic for early
screening of ovarian cancer was proposed. The critical values of
likelihood ratio test statistic was calculated by Monte Carlo method
in some cases. At last the power and robustness of the likelihood
ratio test were discussed.
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In this paper, we research the semiparametric
EV model under NA samples. Some estimators of the parameter,
nonparameter and the variance function are established by the
wavelet smoothing method. Under some general conditions, the strong
consistency and the asymptotic normality of wavelet estimators are
studied.
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This paper studies the strong convergence
of the weighted sums of function for finite state Markov chains in
single infinitely Markovian environments, and obtains some
sufficient conditions for the strong convergence of the weighted
sums.
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In the classic bivariate compound Poisson
models, the numbers of claims are assumed to be correlated through a
common Poisson distribution, while the claim sizes are independent.
In this paper, we assume that both the numbers of claims and claim
sizes are positively dependent through the stochastic ordering.
Through comparing, we find that the condition of positive dependence
through the stochastic ordering is weaker than correlating
through a common Poisson distribution. In fact, the assumption of
positive dependence through the stochastic ordering is weaker than
independence, comonotonicity, conditionally stochastically
increasing et al.. With the positively dependent risks through the
stochastic ordering, we get the optimal reinsurance strategy. In
addition, with the mixed two-dimensional and stochastic-dimensional
dependent risks, we give the explicit expressions of retention
vector under the criterion of minimizing the variance of the total
retained loss and maximizing the quadratic utility, which partially
solves the problem, proposed by Cai and Wei (2012a), of getting such
expressions with multi-dimensional dependent risks.
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In the research it is frequently assumed
that the growth curve is a polynomial in time. In practice,
researchers mainly use higher-order polynomials to obtain more
precise estimates. But this method has many defects, such as the
model can be easily affected by outliers and the polynomial
hypothesis may be much strong in practice. So in this paper we first
proposed nonparametric approach, local polynomial, instead of
parametric method for estimation in growth curve model. We give the
nonparametric growth curve model, and its nonparametric estimation.
Then discuss the large sample character of local polynomial
estimate. The ideal theoretical choice of a local bandwidth is also
discussed in detail in this paper. Finally, through the simulation
study, from the fitting curve and average square error box plot we
can clearly see that the performance of nonparametric approach is
much better than parametric technique.
