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Under the mixing random errors, we make the
empirical likelihood (EL) inference for nonparametric regression models with
fixed designs and missing responses. Based on the `complete sample' after
nonparametric regression imputation, we show that the EL ratio statistic of the
nonparametric regression function is asymptotically $\chi^2$-type distributed,
which is used to obtain EL-based confidence intervals for the nonparametric
regression function.
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Let be a correlated random walk in random
environment. For the sub-linear regime, that is, almost surely
but ,
we show that there is $0<s<1$, such that almost surely
, for all s'>s. This result characterizes
the slowdown property of the walk.
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This paper deals with reliability inference results in $R=\pr(Y<X)$
when $X$ and $Y$ are independently generalized half logistic distributed random variables.
The maximum likelihood estimator and Bayesian estimator of $R$ are obtained. Exact and
asymptotic confidence intervals are also discussed. Testing of the reliability based
on exact distribution of the maximum likelihood estimator is discussed. Two different
estimators are compared using simulations and one data analysis has been performed for
illustrative purposes.
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In this paper, we construct a generalized spatial panel data model
with two-way error components where the spatial correlation also exist in the individual
effects. Based on the methods of the generalized moment estimate and the two-step least
square estimate, we look for the best instrumental variable, fit generalized moments and
the weighted matrix to discuss the estimator of the parameters, and prove the consistent
of the estimators. Monte Carlo experiments show that the weighted generalized moment
estimators are better than the unweighted generalized moment estimators, and the estimate
effect of feasible generalized two stages least squares estimators is good.
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For a financial or insurance entity, the problem of finding the
optimal dividend distribution strategy and optimal firm value function is a widely discussed
topic. In the present paper, it is assumed that the firm faces two types of liquidity risks:
a Brownian risk and a Poisson risk. The firm can control the time and amount of dividends
paid out to shareholders. By sufficiently taking into account the safety of the company,
bankruptcy is said to take place at time $t$ if the cash reserve of the firm runs below
the linear barrier b+kt (not zero), see 1. We deal with the problem of maximizing
the expected total discounted dividends paid out until bankruptcy. The optimal dividend
return (or, firm value) function is identified as the classical solution of the associated
Hamilton-Jacobi-Bellman (HJB) equation where a second-order differential-integro equation
is involved. By solving the corresponding HJB equation, the analytical solution of the
optimal firm value function is obtained, the optimal dividend strategy is also characterized,
which is of linear barrier type: at time t the firm keeps cash inside when the cash
reserves level is less than a critical linear barrier and pays cash in excess of
this linear barrier as dividends.
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In this paper, precise large deviations of nonnegative,
non-identical distributions and negatively associated random variables are investigated.
Under certain conditions, the lower bound of the precise large deviations for the
non-random sum is solved and the uniformly asymptotic results for the corresponding
random sum are obtained. At the same time, we deeply discussed the compound renewal
risk model, in which we found that the compound renewal risk model can be equivalent
to renewal risk model under certain conditions. The relative research results of
precise large deviations are applied to the more practical compound renewal risk model,
and the theoretical and practical values are verified. In addition, this paper also
shows that the impact of this dependency relationship between random variables to
precise large deviations of the final result is not significant.
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In survival analysis, most existing approaches for analysing
right-censored failure time data assume that the censoring time is independent of the
failure time. However, investigators often face problems involving dependent censoring,
i.e., failure time and censoring time are possibly dependent and they may be censored
one another, especially in clinical trials. Without accounting for such dependence,
survival distributions cannot be estimated consistently. Numerous attempts to model
this dependence have been made. Among them, copula models are of particular interest
because of their simple structure. Proportional hazard model analysis for informative
right-censored data has been discussed in this paper. An Archimedean copula is assumed
for the joint distribution function of failure time and censoring time variables. Under
the conditions of identifiability of the parameter of the Archimedean copula, the maximum
likelihood estimators of the parameter of Archimedean copula, the parameters and the
cumulative hazard function of PH model are worked out. Extensive simulation studies show
that the feasibility of the proposed method and the consistency of the estimators.
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Kundu and Gupta proposed to use the importance sampling
method to compute the Bayesian estimation of the unknown parameters of the Marshall-Olkin
bivariate Weibull distribution. However, we find that the performance of the importance
sampling method becomes worse as the sample size gets larger. In this paper, we introduce
latent variables to simplify the likelihood function, and use MCMC algorithm to estimate
the unknown parameters. Numerical simulations are carried out to assess the performance
of the proposed method by comparing with the maximum likelihood estimation, and we find
that the Bayesian estimates perform better even for the case of small sample size. A real
data is also analyzed for illustrative purpose.
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For the infinite Jackson network, assume that the net input
rates are greater than the service rates for some nodes. Via solving the new throughput
equation, the stochastic comparable processes are obtained by coupling method, and
furthermore the limits for the queueing length in all nodes are also obtained. Despite
the whole network is non-ergodic, it is possible to get the maximal ergodic subnetwork.
