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2018 Vol.34 Issue.6,Published 2018-12-26

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551 The Bayes Posterior Estimator of the Variance Parameter of the Normal Distribution with a Normal-Inverse-Gamma Prior under Stein's Loss
XIE Yuhan; SONG Wenhe; ZHOU Mingqin; ZHANG Yingying

or the variance parameter of the normal distribution with a normal-inverse-gamma prior, we analytically calculate the Bayes posterior estimator with respect to a conjugate normal-inverse-gamma prior distribution under Stein's loss function. This estimator minimizes the Posterior Expected Stein's Loss (PESL). We also analytically calculate the Bayes posterior estimator and the PESL under the squared error loss function. The numerical simulations exemplify our theoretical studies that the PESLs do not depend on the sample, and that the Bayes posterior estimator and the PESL under the squared error loss function are unanimously larger than those under Stein's loss function. Finally, we calculate the Bayes posterior estimators and the PESLs of the monthly simple returns of the SSE Composite Index.

2018 Vol. 34 (6): 551-564 [Abstract] ( 176 ) [HTML 1KB] [ PDF 728KB] ( 425 )
565 The Infinitesimal Generator of Markov Semigroup Associated with Multivalued Stochastic Differential Equation
XU Siyan; ZHENG Mengqi

Under the condition that the coefficients are Lipschitz continuous, we study the infinitesimal generator of Markov semigroup corresponding to the multivalued stochastic equation. In order to provide a core of the infinitesimal generator, we investigate the associated multivalued elliptic equation and its viscosity solutions.

2018 Vol. 34 (6): 565-576 [Abstract] ( 136 ) [HTML 1KB] [ PDF 483KB] ( 426 )
article
577 A Note on Uniform Integrability of Random Variables in a Probability Space and Sublinear Expectation Space
HU Zechun; ZHOU Qianqian

In this note we discuss uniform integrability of random variables. In a probability space, we introduce two new notions on uniform integrability of random variables, and prove that they are equivalent to the classic one. In a sublinear expectation space, we give de La Vall\'{e}e Poussin criterion for the uniform integrability of random variables and do some other discussions.

2018 Vol. 34 (6): 577-586 [Abstract] ( 131 ) [HTML 1KB] [ PDF 447KB] ( 389 )
587 Research on Performance of Multivariate FT VSI Bayesian Control Chart for Complex Electromechanical Products
ZHENG Hui; LIU Chunming; WANG Dongfei

Aiming at the complex mechanical and electrical products quality control and early warning problems, a performance analysis model of control chart, which combines the multivariate Bayesian statistical method with the economic performance analysis is constructed. In the solution model, a FT VSI strategy is used in the multivariate Bayesian control chart. If a small probability of random failure occurs, then a loose sampling scheme is selected. Otherwise, a strict sampling program is applied. To quantify the correlation between the economic and the statistical performance of the multivariate Bayesian control chart, a quality control model based on Monte Carlo simulation is used and the ANOSE (Average Number of Observations to Signals or End of the production run) is taken under different economic parameters, which performs the degree of influence of the statistical performance of the control chart. In addition, the relationship between the quality control cost and the false alarm rate of the multi-Bayesian control chart is explained. Finally, for instance, a multiple quality control process of the automatic transmission of the automobile is used to verify the performance evaluation and optimization of the multivariate FT VSI Bayesian control chart. The results show that the method has a better application.

2018 Vol. 34 (6): 587-597 [Abstract] ( 121 ) [HTML 1KB] [ PDF 1044KB] ( 334 )
598 Efficient Robust Estimation of Mean and Covariance for Longitudinal Data
FAN Yali; XU Xiaolin

In this article, we develop efficient robust method for estimation of mean and covariance simultaneously for longitudinal data in regression model. Based on Cholesky decomposition for the covariance matrix and rewriting the regression model, we propose a weighted least square estimator, in which the weights are estimated under generalized empirical likelihood framework. The proposed estimator obtains high efficiency from the close connection to empirical likelihood
method, and achieves robustness by bounding the weighted sum of squared residuals. Simulation study shows that, compared to existing robust estimation methods for longitudinal data, the proposed estimator has relatively high efficiency and comparable robustness. In the end, the proposed method is used to analyse a real data set.

2018 Vol. 34 (6): 598-612 [Abstract] ( 130 ) [HTML 1KB] [ PDF 490KB] ( 353 )
613 Objective Bayesian Analysis for Step-Stress Accelerated Degradation Test Based on Wiener Process Models
GUAN Qiang; TANG Yincai

Step-stress accelerated degradation test (SSADT) is a useful tool for assessing the lifetime distribution of highly reliable products when the available test items are very few. In this paper, we discuss multiple-steps step-stress accelerated degradation models based on Wiener process, and we apply the objective Bayesian method for such analytically intractable models to obtain the noninformative priors (Jefferys prior and two Reference priors). Moreover, we show that their posterior distributions are proper, and we propose Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two Reference
priors. Finally, we present some simulation studies to compare the objective Bayesian estimates with the other Bayesian estimate and the maximum likelihood estimates (MLEs). Simulation results demonstrate the superiority of objective Bayesian analysis method.

2018 Vol. 34 (6): 613-629 [Abstract] ( 137 ) [HTML 1KB] [ PDF 866KB] ( 347 )
630 Review of Regression Analysis for Functional Data
DING Hui; XU Wenchao; ZHU Hanbing; WANG Guochang; ZHANG Tao; ZHANG Riquan

With the advance of computer storage capacity and online observation technique, more and more data are collected with curves and images. The most two important feature of curve and image data are high-dimension and high correlation between adjacent data. Functional data analysis has more advantage in deal with these data, which can not be treated by traditional multivariate statistics methods. Recently, a variety of functional data methods have been developed, including curve alignment, principal component analysis, regression, classification and clustering. In this paper, we mainly introduce the origins,development and recent process of functional data. Specifically, we firstly introduce the notion of functional data. Secondly, functional principal component analysis has been presented. Then, this paper is devoted to introduce estimation, variable selection and hypothesis testing of functional regression models. Lastly, the paper concludes with a brief discussion of future directions.

2018 Vol. 34 (6): 630-654 [Abstract] ( 251 ) [HTML 1KB] [ PDF 858KB] ( 462 )
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