Second order asymptotic and non-asymptotic optimality properties of combined tests

Let p independent test statistics be available to test a null hypothesis concerned with the same parameter. The p are assumed to be similar tests. Asymptotic and non-asymptotic optimality properties of combined tests are studied. The asymptotic study centers around two notions. The first is Bahadur efficiency. The second is based on a notion of second order comparisons. The non-asymptotic study is concerned with admissibility questions. Most of the popular combining methods are considered along with a method not studied in the past. Among the results are the following: Assume each of the p statistics has the same Bahadur slope. Then the combined test based on the sum of normal transforms, is asymptotically best among all tests studied, by virtue of second order considerations. Most of the popular combined tests are inadmissible for testing the noncentrality parameter of chi-square, t, and F distributions. For chi-square a combined test is offered which is admissible, asymptotically optimal (first order), asymptotically optimal (second order) among all tests studied, and for which critical values are obtainable in special cases. Extensions of the basic model are given.     

从产业发展演进探索上海产业转型

"创新驱动发展、经济转型升级"是上海产业发展应遵循的总方针。行业比重处于扩张期的、对国民经济拉动作用大于社会平均水平的行业属于未来需要重点关注和发展的行业。上海未来产业发展要关注:提高新一代信息技术产业、新能源产业的能级;进一步做强上海高端制造业品牌;提升金融、贸易、航运、信息等服务业水平;发挥旅游业对上海经济的带动作用;调整、转型,发挥重化工业在上海经济中的作用;不可忽视建筑业、房地产业在经济发展中的作用。     

Fiducial and Posterior Sampling

The fiducial coincides with the posterior in a group model equipped with the right Haar prior. This result is generalized here. For this the underlying probability space of Kolmogorov is replaced by a σ-finite measure space and fiducial theory is presented within this frame. Examples are presented that demonstrate that this also gives good alternatives to existing Bayesian sampling methods. It is proved that the results provided here for fiducial models imply that the theory of invariant measures for groups cannot be generalized directly to loops: there exist a smooth one-dimensional loop where an invariant measure does not exist.     

乡镇改革的理论探索和思路创新

乡镇机构改革是当前农村综合改革的关键环节。本文在理论上分析了乡镇改革的不同路径,结合各地改革的实践,提出新一轮的乡镇机构改革必须以创新的理论为指导,以政府职能转变为核心,以各项配套措施协调推进,并确立以人为本的价值取向。     

适当变换问题是解数学题的一个关键

数学问题是千变万化的 ,解决数学问题的方法也是多种多样的。如何选择正确的解题方法是数学教学法研究的中心课题之一。对数学问题 ,学生总是采用从原问题入手推出原问题结论的方法 ,但有些数学问题 ,采用这种方法难以解决 ,笔者认为适当变换问题是解题的关键 ,本文就变换问题时应遵循的几点原则予以浅述     

Variance Estimation in Heteroscedastic Models by Undecimated Haar Transform

We propose a method in order to maximize the accuracy in the estimation of piecewise constant and piecewise smooth variance functions in a nonparametric heteroscedastic fixed design regression model. The difference-based initial estimates are obtained from the given observations. Then an estimator is constructed by using iterative regularization method with the analysis-prior undecimated three-level Haar transform as regularizer term. We notice that this method shows better results in the mean square sense over an existing adaptive estimation procedure considering all the standard test functions used in addition to the functions that we target. Some simulations and comparisons with other methods are conducted to assess the performance of the proposed method.     

Prequential omnibus goodness-of-fit tests for stochastic processes: A numerical study

This article is a contribution to the study of an omnibus goodness-of-fit (Gof) test based on Rosenblatt Probability Integral Transform (RPIT) within Dawid's prequential framework. This Gof test is easy to use since it has a common test statistic (with apparently the same asymptotic distribution) for a wide range of stochastic models. Intensive Monte-Carlo simulations are presented to investigate the behavior of this test for several stochastic models: renewal, autoregressive (AR, ARMA, ARCH, GARCH) and Poisson processes, generalized linear models... These simulations suggest that the RPIT test could be used to test the fit of a wide range of stochastic models but it may be not powerful when compared to Gof tests specifically designed for the tested processes. It is also conjectured that this test is still appropriate for testing the Gof of any discrete-time stochastic process provided that efficient estimators are used.     

On characteristic function-based bootstrap tests

Summary A two-step method is proposed for evaluating the bootstrap null distribution function of some useful test statistics appropriate for two-sample and multi-sample comparisons. In the first step, the characteristic function of the bootstrap null distribution function is determined by recursive equations; in the second a numerical inversion by the Fast Fourier Transform is performed to evaluate this null distribution function. A simulation experiment is performed to show how computer timings increase with the pooled sample size.     

A Bayesian wavelet approach to estimation of a change-point in a nonlinear multivariate time series

ABSTRACT

We propose a semiparametric approach to estimate the existence and location of a statistical change-point to a nonlinear multivariate time series contaminated with an additive noise component. In particular, we consider a p-dimensional stochastic process of independent multivariate normal observations where the mean function varies smoothly except at a single change-point. Our approach involves conducting a Bayesian analysis on the empirical detail coefficients of the original time series after a wavelet transform. If the mean function of our time series can be expressed as a multivariate step function, we find our Bayesian-wavelet method performs comparably with classical parametric methods such as maximum likelihood estimation. The advantage of our multivariate change-point method is seen in how it applies to a much larger class of mean functions that require only general smoothness conditions.     

现代汉语标志型被动句的句法分析

在现代汉语标志型被动句中,名词性成分（NP）可作主语,也可作标志词“叫”、“被”、“让”、“受”、“遭受”等的宾语以及谓语动词的宾语。介词标志型被动句中的动词性成分前后一般都有附加成分,它有五种基本句型。动词标志型被动句则有两种基本句型。被动句和主动句之间存在一定的变换关系。