Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Tests for time series of counts based on the probability-generating function

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability-generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.     

Empirical Non-Parametric Control Charts: Estimation Effects and Corrections

Owing to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and non-normality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a large model is inadequate and nothing remains but to consider non- parametric charts. In principle, these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage that seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyse under what conditions non-parametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes that are markedly less huge (but still larger than the customary range). These corrections serve to control the behaviour during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection will clearly be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.     

理论实证相印语言文化相融--胡正武《训诂阐微集》评议

胡正武新著《训诂阐微集》在训诂方面所展现的,具有理论与实证相得益彰,语言与文化水乳交融,语料丰富内容广博等特点,这是与其深厚扎实的学术功底,别具一格的研究方法相为表里的。胡君甘于寂寞的治学态度,该书朴实无华的语言风格在当今急功近利、充满躁动的商品经济社会里,尤其显示其现实意义。     

BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.     

Semi-parametric estimation of ROC curves based on binomial regression modelling

This paper presents a method of estimating a receiver operating characteristic (ROC) curve when the underlying diagnostic variable X is continuous and fully observed. The new method is based on modelling the probability of response given X , rather than the distribution of X given response. The method offers advantages in modelling flexibility and computational simplicity. The resulting ROC curve estimates are semi-parametric and can, in principle, take an infinite variety of shapes. Moreover, model selection can be based on standard methods within the binomial regression framework. Statistical accuracy of the curve estimate is provided by a simply implemented bootstrap approach.     

中国A、B股市场相关性与协整性的实证研究

运用相关、协整和因果关系检验等计量经济学方法对中国AB股市场之间的相关性与协整性进行了实证研究,以期找出股市间价格波动的运行规律。结果表明,B股市场对境内投资者开放后,沪深两市A股与B股之间开始存在协整关系,并且沪市的A股市场是先于B股市场的,而深市AB股市场之间不存在先导性。研究结果为判断和分析中国股票市场的基本特征和投资者行为,提供了一定的参考依据。     

自然科学的经验基础与实践科学观

经验与陈述的关系并非归纳或演绎的逻辑关系.实际上,所谓经验与陈述之间的鸿沟只是表象主义科学观提出的一个假问题.科学本质上是一种介入性的实践活动,因此,对于新的实践科学观来说,该问题是不存在的.这种新的科学观念产生了一系列新的结果.     

西部经理人激励约束机制现状调查与实证分析--以西安市中小企业为例

运用调查问卷的方法,对西安市中小企业激励约束机制的现状、满意度、现存问题和影响因素等方面进行调研并做出了相关性分析,结果表明(1)西安市中高层管理人员对现有的激励机制不满意;(2)独立董事制度并没有起到相应的监督作用;(3)组织机构层次与信息的变失程度呈强的线性相关性.提出了建立健全信道系统,将激励约机制与市场环境相适应,重视经营者股权激励等方面的建议.