An Introduction to Ranking and Selection

This expository paper explains the philosophy of the indifference-zone approach and the subset-selection approach to ranking and selection procedures. It includes examples of operating characteristic curves and data applications for selection problems based on the binomial and normal distributions. A variety of different models and goals are provided with a list of references.     

Frequency of Selecting Noise Variables in Subset Regression Analysis: A Simulation Study

This article presents the results of a simulation study of variable selection in a multiple regression context that evaluates the frequency of selecting noise variables and the bias of the adjusted R ² of the selected variables when some of the candidate variables are authentic. It is demonstrated that for most samples a large percentage of the selected variables is noise, particularly when the number of candidate variables is large relative to the number of observations. The adjusted R ² of the selected variables is highly inflated.     

农民工的社会网络能提升返乡创业企业经营绩效吗？——基于全国返乡创业企业的调查数据

乡村振兴离不开返乡创业,社会网络已成为农民工返乡创业成功的关键。基于2019年全国2139家返乡创业企业调查数据,将社会网络分为强、弱关系网络两个维度,研究了农民工的社会网络对其返乡创业企业经营绩效的影响。研究表明：（1）整体上看,农民工的强、弱关系网络均能显著提升其返乡创业企业的经营绩效,但两者对企业经营绩效的影响强度存在差异。（2）异质性分析发现,农民工的强关系网络对生存型返乡创业企业经营绩效的提升更为显著,弱关系网络对发展型和价值型返乡创业企业经营绩效的提升更为显著;在东中西部地区,农民工的弱关系网络对返乡创业企业的经营绩效均具有显著正向影响,而强关系网络对中部地区返乡创业企业经营绩效的正向影响明显;农民工的弱关系网络对第二、三产业的返乡创业企业经营绩效的提升作用更显著。（3）机制分析发现,创新精神是农民工社会网络促进返乡创业企业经营绩效提升的作用机制。因此,建议地方政府搭建促进返乡创业者相互交流的平台,努力实现返乡创业者强弱关系的双重嵌入,积极扩大返乡农民工的社会网络,同时要注重培养返乡创业者的创新精神,进而提升返乡创业企业的经营绩效,实现高质量发展。     

Model averaging for M-estimation

M-estimation is a widely used technique for robust statistical inference. In this paper, we study model selection and model averaging for M-estimation to simultaneously improve the coverage probability of confidence intervals of the parameters of interest and reduce the impact of heavy-tailed errors or outliers in the response. Under general conditions, we develop robust versions of the focused information criterion and a frequentist model average estimator for M-estimation, and we examine their theoretical properties. In addition, we carry out extensive simulation studies as well as two real examples to assess the performance of our new procedure, and find that the proposed method produces satisfactory results.     

Bayesian factor models in characterizing molecular adaptation

Assessing the selective influence of amino acid properties is important in understanding evolution at the molecular level. A collection of methods and models has been developed in recent years to determine if amino acid sites in a given DNA sequence alignment display substitutions that are altering or conserving a prespecified set of amino acid properties. Residues showing an elevated number of substitutions that favorably alter a physicochemical property are considered targets of positive natural selection. Such approaches usually perform independent analyses for each amino acid property under consideration, without taking into account the fact that some of the properties may be highly correlated. We propose a Bayesian hierarchical regression model with latent factor structure that allows us to determine which sites display substitutions that conserve or radically change a set of amino acid properties, while accounting for the correlation structure that may be present across such properties. We illustrate our approach by analyzing simulated data sets and an alignment of lysin sperm DNA.     

Discriminating between the Weibull and log-normal distributions for Type-II censored data

Log-normal and Weibull distributions are the two most popular distributions for analysing lifetime data. In this paper, we consider the problem of discriminating between the two distribution functions. It is assumed that the data are coming either from log-normal or Weibull distributions and that they are Type-II censored. We use the difference of the maximized log-likelihood functions, in discriminating between the two distribution functions. We obtain the asymptotic distribution of the discrimination statistic. It is used to determine the probability of correct selection in this discrimination process. We perform some simulation studies to observe how the asymptotic results work for different sample sizes and for different censoring proportions. It is observed that the asymptotic results work quite well even for small sizes if the censoring proportions are not very low. We further suggest a modified discrimination procedure. Two real data sets are analysed for illustrative purposes.     

Bayesian model comparison for compartmental models with applications in positron emission tomography

We develop strategies for Bayesian modelling as well as model comparison, averaging and selection for compartmental models with particular emphasis on those that occur in the analysis of positron emission tomography (PET) data. Both modelling and computational issues are considered. Biophysically inspired informative priors are developed for the problem at hand, and by comparison with default vague priors it is shown that the proposed modelling is not overly sensitive to prior specification. It is also shown that an additive normal error structure does not describe measured PET data well, despite being very widely used, and that within a simple Bayesian framework simultaneous parameter estimation and model comparison can be performed with a more general noise model. The proposed approach is compared with standard techniques using both simulated and real data. In addition to good, robust estimation performance, the proposed technique provides, automatically, a characterisation of the uncertainty in the resulting estimates which can be considerable in applications such as PET.     

Cointegration Detection Using Dynamic Factor Models

A method of information-criterion-based cointegration detection using dynamic factor models is proposed. The results of the data-based and non data-based Monte Carlo simulations suggest that this method is as effective as conventional hypothesis-testing methods. In the proposed method, an observed multivariate time series is described in terms of common stochastic trends plus stationary autoregressive cycles. Then the best model is selected from among alternative models obtained by changing the number of common stochastic trends, on the basis of information criteria. Consequently, the cointegration rank is determined on the basis of the selected model. Two advantages of the proposed method are also discussed.     

Positive False Discovery Rate Estimate in Step-Wise Variable Selection

Selecting predictors to optimize the outcome prediction is an important statistical method. However, it usually ignores the false positives in the selected predictors. In this article, we advocate a conventional stepwise forward variable selection method based on the predicted residual sum of squares, and develop a positive false discovery rate (pFDR) estimate for the selected predictor subset, and a local pFDR estimate to prioritize the selected predictors. This pFDR estimate takes account of the existence of non null predictors, and is proved to be asymptotically conservative. In addition, we propose two views of a variable selection process: an overall and an individual test. An interesting feature of the overall test is that its power of selecting non null predictors increases with the proportion of non null predictors among all candidate predictors. Data analysis is illustrated with an example, in which genetic and clinical predictors were selected to predict the cholesterol level change after four months of tamoxifen treatment, and pFDR was estimated. Our method's performance is evaluated through statistical simulations.     

宋代閤职的内外演变与磨勘叙迁探析

宋代共设有三等閤职，最初供职于閤门，后閤职官员出外任职情况变得普遍，直接推动了外任武官兼带閤职制度的发展，此后閤职作为武官兼带的一种职名，成为奖励军功以及控制武官的一种有效手段。而閤职制度的发展也使閤职作为武臣清选的地位逐渐确立，表现之一就是在磨勘叙迁上较一般武官而言具有一定的优越性。同时，内外不同的閤职在磨勘制度上也有一定的差异，这些差异的产生也加深了閤职作为武臣清选的内涵。