On Infinitely Divisible Exponential Dispersion Model Related to Poisson-Exponential Distribution

We construct a univariate exponential dispersion model comprised of discrete infinitely divisible distributions. This model emerges in the theory of branching processes. We obtain a representation for the Lévy measure of relevant distributions and characterize their laws as Poisson mixtures and/or compound Poisson distributions. The regularity of the unit variance function of this model is employed for the derivation of approximations by the Poisson-exponential model. We emphasize the role of the latter class. We construct local approximations relating them to properties of special functions and branching diffusions.     

Power Loss for Inhomogeneous Poisson Processes

In this work, based on a realization of an inhomogeneous Poisson process whose intensity function depends on a real parameter, we consider a simple null hypothesis against the composite one sided alternative. Under certain regularity conditions we will obtain the power loss of the score test which measures its performance with respect to the Neyman-Pearson test. We present the second-order approximation of the power of the score test under the close alternatives by specifying the explicit form of the next term after the Gaussian term.     

Cointegration: Bayesian Significance Test

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926 Yule , G. U. ( 1926 ). Why we do sometimes get nonsense-correlations between time-series? A study in sampling and the nature of time-series (with discussion) . J. Roy. Statist. Soc. 89 : 1 – 64 .[Crossref] , [Google Scholar]). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999 Bauwens , L. , Lubrano , M. , Richard , J.-F. ( 1999 ). Bayesian Inference in Dynamic Econometric Models . Oxford : Oxford University Press . [Google Scholar]) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful and convincing results”.

The present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used.     

Evaluation of a Frequentist Hierarchical Model to Estimate Prevalence When Sampling from a Large Geographic Area Using Pool Screening

We present a frequentist Bernoulli-Beta hierarchical model to relax the constant prevalence assumption underlying the traditional prevalence estimation approach based on pooled data. This assumption is called into question when sampling from a large geographic area. Pool screening is a method that combines individual items into pools. Each pool will either test positive (at least one of the items is positive) or negative (all items are negative). Pool screening is commonly applied to the study of tropical diseases where pools consist of vectors (e.g., black flies) that can transmit the disease. The goal is to estimate the proportion of infected vectors.

Intermediate estimators (model parameters) and estimators of ultimate interest (pertaining to prevalence) are evaluated by standard measures of merit, such as bias, variance, and mean squared error making extensive use of expansions. Using the hierarchical model an investigator can determine the probability of the prevalence being below a pre-specified threshold value, a value at which no reemergence of the disease is expected. An investigation into the least biased choice of the α parameter in the Beta (α, β) prevalence distribution leads to the choice of α = 1.     

A Positive False Discovery Rate Convergence Result

The positive false discovery rate (pFDR) is the average proportion of false rejections given that the overall number of rejections is greater than zero. Assuming that the proportion of true null hypotheses, proportion of false positives, and proportion of true positives all converge pointwise, the pFDR converges to a continuous limit uniformly over all significance levels. We are showing that the uniform convergence still holds given a weaker assumption that the proportion of true positives converges in L ¹.     

A Practical Procedure to Find Matching Priors for Frequentist Inference

We present a practical way to find matching priors via the use of saddlepoint approximations and obtain p-values of tests of an interest parameter in the presence of nuisance parameters. The advantages of our procedure are the flexibility in choosing different initial conditions so that one may adjust the performance of a test, and the less intensive computational efforts compared to a Markov Chain Monto Carlo method.     

《现代联绵字理论负面影响研究》序

序文先简要介绍本书的内容及研究意义,界定本书中的常用术语,说明开展本课题研究的原因,概括现代联绵字理论流行以来所造成的诸多危害。接下来说明本课题研究是在严格区分中国传统语文学与中国现代语言学的前提下进行的,并肯定了中国传统语文学的求实致用,同时也指出现代语言学研究的悲哀。     

Input Variable Selection in Neural Network Models

One of the most important issues in using neural networks for the analysis of real-world problems is the input variable selection problem. This article connects input variable selection with multiple testing in the neural network regression models. In the proposed procedure, the number and the type of input neurons are selected by means of a testing scheme, based on appropriate measures of relevance of a given input variable to the model. In order to avoid the data snooping problem, family-wise error rate is controlled by using the StepM method proposed by Romano and Wolf (2005 Romano , J. P. , Wolf , M. ( 2005 ). Exact and approximate stepdown methods for multiple hypothesis testing . J. Amer. Statist. Assoc. 100 : 94 – 108 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The testing procedure is calibrated by using the subsampling, which is shown to deliver consistent results under weak assumptions on the data generating process and on the structure of the neural network model.     

趋势平稳过程与单位根过程的趋势特征研究

为了深入研究具有高次趋势特征序列的单位根(平稳性)检验问题,研究了高次趋势平稳过程和带高次趋势的单位根过程的概念及其时间趋势特征。结果表明,带漂移的单位根过程实际具有线性趋势,带k(k≥1)次趋势的单位根过程实际具有k+1次趋势;而k(k≥0)次(趋势)平稳过程则具有k次趋势。无论是趋势平稳过程,还是单位根过程,都可以通过差分变换确定其时间趋势特征。