Probability Generating Function Based Jeffrey's Divergence for Statistical Inference

Statistical inference procedures based on transforms such as characteristic function and probability generating function have been examined by many researchers because they are much simpler than probability density functions. Here, a probability generating function based Jeffrey's divergence measure is proposed for parameter estimation and goodness-of-fit test. Being a member of the M-estimators, the proposed estimator is consistent. Also, the proposed goodness-of-fit test has good statistical power. The proposed divergence measure shows improved performance over existing probability generating function based measures. Real data examples are given to illustrate the proposed parameter estimation method and goodness-of-fit test.     

Methods to assess measurement error in questionnaires of sedentary behavior

Sedentary behavior has already been associated with mortality, cardiovascular disease, and cancer. Questionnaires are an affordable tool for measuring sedentary behavior in large epidemiological studies. Here, we introduce and evaluate two statistical methods for quantifying measurement error in questionnaires. Accurate estimates are needed for assessing questionnaire quality. The two methods would be applied to validation studies that measure a sedentary behavior by both questionnaire and accelerometer on multiple days. The first method fits a reduced model by assuming the accelerometer is without error, while the second method fits a more complete model that allows both measures to have error. Because accelerometers tend to be highly accurate, we show that ignoring the accelerometer's measurement error, can result in more accurate estimates of measurement error in some scenarios. In this article, we derive asymptotic approximations for the mean-squared error of the estimated parameters from both methods, evaluate their dependence on study design and behavior characteristics, and offer an R package so investigators can make an informed choice between the two methods. We demonstrate the difference between the two methods in a recent validation study comparing previous day recalls to an accelerometer-based ActivPal.     

如何恰当地界定中国高技术制造业的统计范围

在简要考察美国商务部和OECD等国际组织对高技术产业的界定方法及其合理性的基础上,对中国官方界定的高技术产业统计范围及其演变过程进行了梳理,对能否从高附加值、高成长性和高效益等特征出发筛选高技术产业以及如何恰当地界定中国高技术产业的统计范围做了进一步的讨论。研究结果认为,应从中国所处的经济发展阶段和整体的技术水平出发,以"R&D经费强度"和"科技人员比重"二者之一高于中国制造业的平均水平为标准,确定中国高技术制造业的统计范围。     

Bayesian t-tests for correlations and partial correlations

In this paper, we develop Bayes factor based testing procedures for the presence of a correlation or a partial correlation. The proposed Bayesian tests are obtained by restricting the class of the alternative hypotheses to maximize the probability of rejecting the null hypothesis when the Bayes factor is larger than a specified threshold. It turns out that they depend simply on the frequentist t-statistics with the associated critical values and can thus be easily calculated by using a spreadsheet in Excel and in fact by just adding one more step after one has performed the frequentist correlation tests. In addition, they are able to yield an identical decision with the frequentist paradigm, provided that the evidence threshold of the Bayesian tests is determined by the significance level of the frequentist paradigm. We illustrate the performance of the proposed procedures through simulated and real-data examples.     

Multivariate process dispersion monitoring without subgrouping

The memory-type adaptive and non-adaptive control charts are among the best control charts for detecting small-to-moderate changes in the process parameter(s). In this paper, we propose the Crosier CUSUM (CCUSUM), EWMA, adaptive CCUSUM (ACCUSUM) and adaptive EWMA (AEWMA) charts for efficiently monitoring the changes in the covariance matrix of a multivariate normal process without subgrouping. Using extensive Monte Carlo simulations, the length characteristics of these control charts are computed. It turns out that the ACCUSUM and AEWMA charts perform uniformly and substantially better than the CCUSUM and EWMA charts when detecting a range of shift sizes in the covariance matrix. Moreover, the AEWMA chart outperforms the ACCUSUM chart. A real dataset is used to explain the implementation of the proposed control charts.     

武汉市固定资产投资与经济增长关系的实证分析

固定资产投资是经济增长的一个重要因素,对经济增长具有直接的拉动作用,同时对投资的调节也成为国家宏观调控的一个重要手段。以武汉市为例,选取了年固定资产投资与国内生产总值的数据进行协整分析,并建立了误差修正模型,得出了二者之间存在长期均衡关系。     

Generalized Expected Utility, Heteroscedastic Error, and Path Dependence in Risky Choice

We evaluate the fit of several generalized expected utility models under homoscedasticity and three different heteroscedastic error structures for the data set first reported in Hey and Orme (1994). Standard chi-squared tests are used for nested tests, and both the Akaike (1973) information criterion and its consistent version (Hurvich and Tsai, 1989) are used for non-nested ranking of these models. A testing framework is developed that explicitly accounts for the path-dependent nature of the model selection problem. Not only does the selection of preference models depend on the error structure assumed, but the reverse is also true: the selection of the error structure depends on the preference structure assumed. An erratum to this article is available at .     

On the Critical Value Behaviour of Multiple Decision Procedures

In this paper we investigate the asymptotic critical value behaviour of certain multiple decision procedures as e.g. simultaneous confidence intervals and simultaneous as well as stepwise multiple test procedures. Supposing that n hypotheses or parameters of interest are under consideration we investigate the critical value behaviour when n increases. More specifically, we answer e.g. the question by which amount the lengths of confidence intervals increase when an additional parameter is added to the statistical analysis. Furthermore, critical values of different multiple decision procedures as for instance step-down and step-up procedures will be compared. Some general theoretic results are derived and applied for various distributions.     

Correlation in a Bayesian framework

The authors consider the correlation between two arbitrary functions of the data and a parameter when the parameter is regarded as a random variable with given prior distribution. They show how to compute such a correlation and use closed form expressions to assess the dependence between parameters and various classical or robust estimators thereof, as well as between p‐values and posterior probabilities of the null hypothesis in the one‐sided testing problem. Other applications involve the Dirichlet process and stationary Gaussian processes. Using this approach, the authors also derive a general nonparametric upper bound on Bayes risks.     

Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics

This paper concerns the geometric treatment of graphical models using Bayes linear methods. We introduce Bayes linear separation as a second order generalised conditional independence relation, and Bayes linear graphical models are constructed using this property. A system of interpretive and diagnostic shadings are given, which summarise the analysis over the associated moral graph. Principles of local computation are outlined for the graphical models, and an algorithm for implementing such computation over the junction tree is described. The approach is illustrated with two examples. The first concerns sales forecasting using a multivariate dynamic linear model. The second concerns inference for the error variance matrices of the model for sales, and illustrates the generality of our geometric approach by treating the matrices directly as random objects. The examples are implemented using a freely available set of object-oriented programming tools for Bayes linear local computation and graphical diagnostic display.