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 2016 Vol.32 Issue.3,Published 2016-06-20 article
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 221 Some Recent Advances in Stochastic Simulation WANG C. L. This review article introduces two recent advances in stochastic simulation: the construction of efficient algorithms for estimating rare events and the generation of samples from a stationary distribution that has no closed form. Estimating a very small quantity requires extreme accuracy to form a useful confidence interval. This makes the slowly convergent rare-event simulation a challenge task in both efficiency and accuracy. In this report, we introduce the examples of rare events of interest and the difficulties in estimating them. Various approaches to pursue robust and efficient estimators along the development are discussed and evaluated. Numerical experiments on estimating ruin probability are provided to show the quality of these approaches. In steady-state simulation, how to generate samples from a stationary stochastic process has long been the key subject. The common practice is to discard the data gathered during the initial transient period. However, how long the warm-up period must be raises another problem that has no satisfactory answer. Fortunately, by the development in the past two decades, exact simulation has become possible for certain stochastic models. In this report, we will introduce two important methods and related applications. 2016 Vol. 32 (3): 221-260 [Abstract] ( 239 ) [HTML 1KB] [ PDF 696KB] ( 524 )
 261 Strong Law of Large Numbers of Sequences of Dependent Gaussian and Nonnegative Random Variables YUAN Dailin, ZHAO Lianwen, LIU Cheng Examining the conditions of positively or negatively associated sequences of random variables obeying the strong law of large numbers provided by Alexander, the sequences of Gaussian random variables, nonnegative and uniformly bounded sequences of random variables with general dependent structure were studied, and the sufficient conditions for they obeying the strong law of large numbers were given. At last, an example for Gaussian sequence satisfying the strong law of large numbers was given. 2016 Vol. 32 (3): 261-269 [Abstract] ( 134 ) [HTML 1KB] [ PDF 609KB] ( 535 )
 270 Local Penalized Spline Regression Model Based on Range LI Meng, YANG Lianqiang, JIANG Kun, HE Shengxian Inspired by intuitive meanings of truncated power basis's coefficients, the local penalization based on range's linear decreasing function is given in penalized spline regression model. This method gives less penalization to fitting curve where data is with more volatility, which makes fitted curve controls tradeoff between goodness-of-fit and smoothness better. Simulations show that regression models with local penalized spline obtain lower information rules' scores than global penalized spline when the data is with heteroskedasticity. 2016 Vol. 32 (3): 270-278 [Abstract] ( 167 ) [HTML 1KB] [ PDF 904KB] ( 525 )
 279 The Classification and Properties of States for Markov Chains in Random Environments LI Mingliang, LIU Zaiming In this paper, various concepts of states for Markov chains in random environments are introduced into the research field, and the relationships between these states are discussed. Especially, a partition of the state space is given. Also, the properties of those states are investigated. At last, some examples are given to illustrate the rationality of those states. 2016 Vol. 32 (3): 279-289 [Abstract] ( 127 ) [HTML 1KB] [ PDF 591KB] ( 375 )
 290 On the Stationary Property of a Reflected Cox-Ingersoll-Ross Interest Rate Model Driven by a Levy Process HU Shaoyong, CHEN Shouting Brownian motion and normal distribution have been widely used in Cox-Ingersoll-Ross interest rate framework to model the instantaneous interest rate dynamics. However, empirical studies have also shown that the return distribution of interest rate has a higher peak and two fatter tails than those of the normal distribution. Meanwhile, when the rare catastrophic shocks occur or the regime shifts in the economy and finance, the money market may have jumps. In this paper, we will consider a class of reflected Cox-Ingersoll-Ross interest rate models with $\fn_jvn \100dpi \inline L\'{e}vy$ noise. Furthermore, we shall continue to supply the Laplace transform of the stationary distribution about this reflected diffusion process with jumps. 2016 Vol. 32 (3): 290-300 [Abstract] ( 145 ) [HTML 1KB] [ PDF 464KB] ( 443 )
 301 Testing for Significance in Binary Choice Model with Stochastic Trend Process XU Peng, WANG Lujun, YAN Zichun This paper investigates the test of significance for the binary choice model with stochastic trend process. The results show that when the true parameter vector is zero, the limiting distribution of the t statistic follows standard normal distribution. The joint significance test statistics Wald, LM and LR are asymptotically equivalent and have a Chi-square limiting distribution. 2016 Vol. 32 (3): 301-312 [Abstract] ( 116 ) [HTML 1KB] [ PDF 590KB] ( 470 )
 313 Smothing Spline Estimation for Nonparametric Model of Longitudinal Data ZHANG Xiuzhen, LIAO Jun, LU Kongmin In the last few decades, longitudinal data was deeply research in statistics science and widely used in many field, such as finance, medical science, agriculture and so on. The characteristic of longitudinal data is that the values are independent from different samples but they are correlate from one sample. Many nonparametric estimation methods were applied into longitudinal data models with development of computer technology. Using Cholesky decomposition and Profile least squares estimation, we will propose a effective spline estimation method pointing at nonparametric model of longitudinal data with covariance matrix unknown in this paper. Finally, we point that the new proposed method is more superior than Naive spline estimation in the covariance matrix is unknown case by comparing the simulated results of one example. 2016 Vol. 32 (3): 313-326 [Abstract] ( 134 ) [HTML 1KB] [ PDF 687KB] ( 434 )
 327 2016 Vol. 32 (3): 327-330 [Abstract] ( 79 ) [HTML 1KB] [ PDF 320KB] ( 378 )

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