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Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample
properties of the proposed method are studied by a simulation study, and a real example is analyzed.
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An absorbing Markov chain is an important statistic model and widely used in algorithm modeling for many disciplines, such as digital image processing, network analysis and so on. In order to get the stationary distribution for such model, the inverse of the transition matrix usually needs to be calculated. However, it is still difficult and costly for large matrices. In this paper, for absorbing Markov chains with two absorbing states, we propose a simple method to compute the stationary distribution for models with diagonalizable transition matrices. With this approach, only an eigenvector with eigenvalue 1 needs to be calculated. We
also use this method to derive probabilities of the gambler's ruin problem from a matrix perspective. And, it is able to handle expansions of this problem. In fact, this approach is a variant of the general method for absorbing Markov chains. Similar techniques can be used to avoid calculating the inverse matrix in the general method.
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For \rho-mixing samples, we discuss thestrong consistency of the nonparametric kernel regression estimator proposed by Gasser and Muller. Under more weaker conditions, its strong consistency and uniformly strong consistency are proved.
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Coherent systems are very important in reliability,survival analysis and other life sciences. In this paper, we consider the number of working components in an $(n-k+1)$-out-of-$n$ system, given that at least $(n-m+1)$ components are working at time $t$, and the system has failed at time $t$. In this condition, we compute the probability that there are exactly $i$ working components. First the reliability and several stochastic properties are obtained. Furthermore, we extend the results to general coherent systems with absolutely continuous and exchangeable components.
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Hidden Markov model is widely used in statistical modeling of time, space and state transition data. The definition of hidden Markov multivariate normal distribution is given. The principle of using cluster analysis to determine the hidden state of observed variables is introduced. The maximum likelihood estimator of the unknown parameters in the model is derived. The simulated observation data set is used to test the estimation effect and stability of the method. The characteristic is simple classical statistical inference such as cluster analysis and maximum likelihood estimation. The method solves the parameter estimation problem of complex statistical models.
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In this paper, we study a class of stochastic Volterra equations, which include the stochastic differential equation driven by fractional Brownian motion. By using a maximal inequality due to It\^o (1979), we establish the central limit theorem for stochastic Volterra equation on the continuous path space, with respect to the uniform norm.
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In this paper, we consider the optimal investment strategy which maximizes the utility of the terminal wealth of an insurer with SAHARA utility functions. This class of utility functions has non-monotone absolute risk aversion, which is more flexible than the CARA and CRRA utility functions. In the case that the risk process is modeled as a Brownian motion and the stock process is modeled as a geometric Brownian motion, we get the closed-form solutions for our problem by the martingale method for both the constant threshold and when the threshold evolves dynamically according to a specific process. Finally, we show that the optimal strategy is state-dependent.
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This paper studies the distribution of finite-time ruin quantities. It gives the probability mass function of finite time number of claims, and find the distribution function of aggregate claims by using discretise method and compared with exact distribution function, which shows that the approximation works very well. In addition, by applying decomposition for density function, it gives the explicit expression for joint density of ruin time and deficit at ruin.
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The reliability of gas fire-extinguishing system is difficult to calculate because of the small sample size, so this paper uses Bayesian method to calculate reliability of the gaseous fire-extinguishing system. The method process includes conversion of multi-source prior information, information fusion, information check, weight calculation and reliability calculation of unit and system. The method properly solves the problem of reliability calculation by combining the field sample information with multi-source prior information.
