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In this paper, we prove a new central
limit theorem for nonhomogeneous Markov chain by using the
martingale central limit theorem under the condition of convergence
of transition probability matrices for nonhomogeneous Markov chain
in Cesaro sense, which can not be implied by Dobrushin's work.
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In this paper, we generalize the
semiparametric smooth transition regression model proposed by Wang
(2012a), to adapt for the strictly stationary strong mixing data and
strong mixing data with deterministic trends. The unknown bounded
smooth function embedded in the smooth transition function is
estimated by series estimator, the consistency and asymptotic
normality properties of estimators are proved employing nonlinear
least square regression theory and series estimator approach.
Variance matrix estimation and hypothesis testing problems are also
discussed based on estimated standard errors. The new model is then
used to study the annually inflation rates of China.
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Based on adaptive type-II progressive
hybrid censored data statistical analysis for constant-stress
accelerated life test (CS-ALT) with products' lifetime following
two-parameter generalized exponential (GE) distribution is
investigated. The estimates of the unknown parameters and the
reliability function are obtained through a new method combining the
EM algorithm and the least square method. The observed Fisher
information matrix is achieved with missing information principle,
and the asymptotic unbiased estimate (AUE) of the scale parameter is
also obtained. Confidence intervals (CIs) for the parameters are
derived using asymptotic normality of the estimators and the
percentile bootstrap (Boot-p) method. Finally, Monte Carlo
simulation study is carried out to investigate the precision of the
point estimates and interval estimates, respectively. It is shown
that the AUE of the scale parameter is better than the corresponding
two-step estimation, and the Boot-p CIs are more accurate than the
corresponding asymptotic CIs.
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In many biomedical and engineering
studies, recurrent event data and gap times between successive
events are common and often more than one type of recurrent events
is of interest. It is well known that the proportional hazards model
may not be appropriate for fitting survival times in some settings.
In the paper, we consider an additive hazards model for multiple
type recurrent gap times data to assess the effect of covariates.
For inferences about regression coefficients and baseline cumulative
hazard functions, an estimating equation approach is developed.
Furthermore, we establish asymptotic properties of the proposed
estimators.
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This paper studies the local linear
estimations of the time-varying parameters for time-inhomogeneous
diffusion models. Based on discretely observed sample of
time-inhomogeneous diffusion models, the local linear estimations of
the drift parameters are proposed and their standard errors are
discussed. Considering the volatility parameter being positive, we
obtain the kernel weighted estimation of the diffusion parameter by
using locally log-linear fitting, and discuss asymptotic bias,
asymptotic variance and asymptotic normal distribution of volatility
function. It is shown that the local estimations proposed perform
well through simulation studies.
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This paper deals with asymptotical
stability in probability in the large for stochastic bilinear
systems. Some new criteria for asymptotical stability of such
systems have been established in the inequality of mathematic
expectation. A sufficient condition for bilinear stochastic jump
systems to be asymptotically stable in probability in the large in
Markovian switching laws is derived in a couple of Riccati-like
inequalities by introducing a nonlinear state feedback controller.
An illustrative example shows the effectiveness of the method.
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The paper investigates the problem of
optimal balanced designs in general linear regression models with
mixed effects. The interest lies in estimating fixed effects, random
effects and prediction of the future observation of an individual,
respectively. By using the de la Garaz phenomenon and Loewner order
domination, the dimension of determining the optimal designs are
reduced. The optimal designs are derived by using analytical or
numerical methods, and their optimalities are verified through the
general equivalence theorems.
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The varying-coefficient single-index
models (VCSIM) have been applied in many fields since they combine
the advantages of single-index models and varying-coefficient
models. In this paper, their estimation method is proposed based on
B-spline approximation technique and two calculation methods can be
used. The first one is to directly calculate the parametric and
nonparametric parts simultaneously by Newton-Raphson iteration
algorithm. The second one is to calculate the two parts by profile
method individually. We suggest that the second method is for our
preference when the large amount of parameters are involved,
otherwise the first method will be more convenient. Two simulated
examples are given to illustrate the performances of the proposed
estimation methodologies and calculation procedures.
