Bayesian variable selection approach to a Bernstein polynomial regression model with stochastic constraints

This paper provides a Bayesian estimation procedure for monotone regression models incorporating the monotone trend constraint subject to uncertainty. For monotone regression modeling with stochastic restrictions, we propose a Bayesian Bernstein polynomial regression model using two-stage hierarchical prior distributions based on a family of rectangle-screened multivariate Gaussian distributions extended from the work of Gurtis and Ghosh [7 S.M. Curtis and S.K. Ghosh, A variable selection approach to monotonic regression with Bernstein polynomials, J. Appl. Stat. 38 (2011), pp. 961–976. doi: 10.1080/02664761003692423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. This approach reflects the uncertainty about the prior constraint, and thus proposes a regression model subject to monotone restriction with uncertainty. Based on the proposed model, we derive the posterior distributions for unknown parameters and present numerical schemes to generate posterior samples. We show the empirical performance of the proposed model based on synthetic data and real data applications and compare the performance to the Bernstein polynomial regression model of Curtis and Ghosh [7 S.M. Curtis and S.K. Ghosh, A variable selection approach to monotonic regression with Bernstein polynomials, J. Appl. Stat. 38 (2011), pp. 961–976. doi: 10.1080/02664761003692423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] for the shape restriction with certainty. We illustrate the effectiveness of our proposed method that incorporates the uncertainty of the monotone trend and automatically adapts the regression function to the monotonicity, through empirical analysis with synthetic data and real data applications.     

交汇契合与并行发展——探寻高等师范教育改革与基础教育改革的共同之路

基础教育与高等师范教育是人才成长的摇篮,而且是教育的两个不同等级的环节.基础教育对中小学生基本素质的形成与知识能力的培养起着不可替代的作用,基础教育质量的提高取决于中小学教师质量的提高;高等师范教育及高等师范院校是学生素质提升与能力提高的关键时期,高等师范教育的目标是为基础教育服务,双方的合作与交流是成功培养人才的需求和必由之路.     

论宪法中的权界式公民义务规范

以义务性规范的形式对宪法权利作出的限制规定,就是宪法中的权界式公民义务规范,它有概括限制型和具体限制型两种类型。宪法权利的法律保留限制式规定,不应视为公民义务规范。权界式义务规范在创设目的、出现位置、表述转换等方面与明示式义务规范有着重大区别。权界式义务规范附属于公民宪法权利规范本身,它可以转换成非义务性的表述,其实质是表示权利应当有所约束。关于宪法权利之限制规定能否被视为公民义务规范的争议,可通过形式与实质的双重视角予以化解。     

Inference on a progressive type I interval-censored truncated normal distribution

In this paper, we consider the problem of making statistical inference for a truncated normal distribution under progressive type I interval censoring. We obtain maximum likelihood estimators of unknown parameters using the expectation-maximization algorithm and in sequel, we also compute corresponding midpoint estimates of parameters. Estimation based on the probability plot method is also considered. Asymptotic confidence intervals of unknown parameters are constructed based on the observed Fisher information matrix. We obtain Bayes estimators of parameters with respect to informative and non-informative prior distributions under squared error and linex loss functions. We compute these estimates using the importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We present a Monte Carlo simulation study to compare the performance of proposed point and interval estimators. Analysis of a real data set is also performed for illustration purposes. Finally, inspection times and optimal censoring plans based on the expected Fisher information matrix are discussed.     

On hysteretic vector autoregressive model with applications

This paper proposes a new hysteretic vector autoregressive (HVAR) model in which the regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. We integrate an adapted multivariate Student-t distribution from amending the scale mixtures of normal distributions. This HVAR model allows for a higher degree of flexibility in the degrees of freedom for each time series. We use the proposed model to test for a causal relationship between any two target time series. Using posterior odds ratios, we overcome the limitations of the classical approach to multiple testing. Both simulated and real examples herein help illustrate the suggested methods. We apply the proposed HVAR model to investigate the causal relationship between the quarterly growth rates of gross domestic product of United Kingdom and United States. Moreover, we check the pairwise lagged dependence of daily PM2.5 levels in three districts of Taipei.     

A new estimator of Kullback–Leibler information and its application in goodness of fit tests*

We propose here a general statistic for the goodness of fit test of statistical distributions. The proposed statistic is constructed based on an estimate of Kullback–Leibler information. The proposed test is consistent and the limiting distribution of the test statistic is derived. Then, the established results are used to introduce goodness of fit tests for the normal, exponential, Laplace and Weibull distributions. A simulation study is carried out for examining the power of the proposed test and to compare it with those of some existing procedures. Finally, some illustrative examples are presented and analysed, and concluding comments are made.     

Parametrizing the Kepler exoplanet period-radius distribution with the bivariate normal inverse Gaussian distribution

This paper presents a simple and robust method for obtaining a comprehensive understanding of the joint period and radius distribution in Kepler exoplanets. The proposed method is based on particle swarm optimization and bivariate Normal Inverse Gaussian distribution. Furthermore, in the construction of the probability density function, this study selects planet-host stars with the GK-type. The injecting approach is also employed to solve the survey completeness of sample. The resulting occurrence rate of Earth analogs is 0.025 with a 95% bootstrap confidence interval between 0.023 and 0.032.     

A semiparametric approach for modelling multivariate nonlinear time series

In this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada     

师范生教学技能培养的实践与探索

为了更好地加强师范生教学技能的培养与训练,采用理论和实践相结合的方法,对师范生教学技能构成要素进行了分析,剖析了师范生教学技能培养实践中存在的问题,提出了加强师范生教学技能培养进一步完善师范类课程设置体系、改革教育技能课教学、加强实践教学环节、加强师范生的学科论文和教学毕业论文的指导等具体措施。     

关于如何培养高等师范学生信息素养的探索

信息技术在师范教育中是现代教育技术内容的重要部分。高等师范院校的毕业生,将在今后各学科教学中运用信息技术,发挥信息技术在教育中的作用,许多毕业生还将直接承担中、小学信息技术课程的教学任务。为此,高等师范生必须加强信息技术学习,形成良好的信息素养。