An extension of bayesian measure of information to regression

This paper extends Lindley's measure of average information to the linear model, E(Y∣ß) = Xß. An expression which quantifies the average amount of information provided by the nxl vector of observations Y about the pxl vector of coefficient parameters ß will be derived. The effect of the structure of the regressor matrix, X, on the information measure is discussed. An information theoretic optimal design is characterized. Some applications are suggested.     

On a measure of information gain for regression models in survival analysis

Papers dealing with measures of predictive power in survival analysis have seen their independence of censoring, or their estimates being unbiased under censoring, as the most important property. We argue that this property has been wrongly understood. Discussing the so-called measure of information gain, we point out that we cannot have unbiased estimates if all values, greater than a given time τ, are censored. This is due to the fact that censoring before τ has a different effect than censoring after τ. Such τ is often introduced by design of a study. Independence can only be achieved under the assumption of the model being valid after τ, which is impossible to verify. But if one is willing to make such an assumption, we suggest using multiple imputation to obtain a consistent estimate. We further show that censoring has different effects on the estimation of the measure for the Cox model than for parametric models, and we discuss them separately. We also give some warnings about the usage of the measure, especially when it comes to comparing essentially different models.     

Some tests for the power series distibutions in one parameter using the kullback-leibler information measure

The purpose of the article is, in case of one sample, to obtain tests concerning the parameter in the power series distribution in one parameter using Ku11back-Leibier information measure. The class of power series distibutions contains a host of discrete distributions. Ve illustrate the general results obtained in case of the geometric distibution.     

Combining census and registration data to estimate detailed elderly migration flows in England and Wales

Summary.  A log-linear model is developed to estimate detailed elderly migration flows by combining data from the 2001 UK census and National Health Services patient register. After showing that the census and National Health Service migration flows can be reasonably combined, elderly migration flows between groupings of local authority districts by age, sex and health status for the 2000–2001 and 2003–2004 periods are estimated and then analysed to show how the patterns have changed. By combining registration data with census data, we can provide recent estimates of detailed elderly migration flows, which can be used for improvements in social planning or policy.     

An information-theoretic approach to incorporating prior information in binomial sampling

The incorporation of prior information about θ, where θ is the success probability in a binomial sampling model, is an essential feature of Bayesian statistics. Methodology based on information-theoretic concepts is introduced which (a) quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and (b) allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information about θ which is embedded in any prior distribution. In effect, the most conservative prior distribution from a specified class (each member o f which carries the available prior information about θ) is that prior distribution within the class over which the likelihood function has the greatest average domination. The most conservative prior distributions from five different families of prior distributions over the interval (0,1) including the beta distribution are determined and compared for three situations: (1) no prior estimate of θ is available, (2) a prior point estimate or θ is available, and (3) a prior interval estimate of θ is available. The results of the comparisons not only advocate the use of the beta prior distribution in binomial sampling but also indicate which particular one to use in the three aforementioned situations.     

Using pilot study information to increase efficiency in clinical trials

It is often necessary to conduct a pilot study to determine the sample size required for a clinical trial. Due to differences in sampling environments, the pilot data are usually discarded after sample size calculation. This paper tries to use the pilot information to modify the subsequent testing procedure when a two-sided t$t$-test or a regression model is used to compare two treatments. The new test maintains the required significance level regardless of the dissimilarity between the pilot and the target populations, but increases the power when the two are similar. The test is constructed based on the posterior distribution of the parameters given the pilot study information, but its properties are investigated from a frequentist's viewpoint. Due to the small likelihood of an irrelevant pilot population, the new approach is a viable alternative to the current practice.     

A new approach to use multivariate auxiliary information in sample surveys

A new approach to form multivariate difference estimator is suggested which does not require the knowledge of unknown population parameters as such. It gives minimum variance among the class of multivariate difference estimators. The performance of this estimator with respect to Des Raj's (J. Amer. Statist. Assoc. 60 (1965), 270–277) multivariate difference estimator is illustrated. Using the information on two auxiliary variates, the robustness of Des Raj's estimator y_d is studied empirically. Two new estimators to estimate population mean/total are developed on the same lines as that of y_d. The performance of these estimators is studied for a wide variety of populations.     

CVaR-EVT和BMM在极端金融风险管理中的应用研究

随着风险度量一致性原则的提出,研究发现金融机构广泛采用的VaR模型存在严重不足,尤其针对分布具有厚尾特征的极端金融风险无法有效度量。本文采用极值理论（EVT）解决VaR方法的尾部度量不足问题,利用CVaR-EVT和BMM模型分析美国、香港股票市场和我国沪深两市指数18年的日收益数据,研究发现：（1）在95％置信区间及点估计中,分位数为99%的CVaR-EVT所揭示的极端风险优于VaR的估计值;且BMM方法为实施长期极端风险管理提供了有力决策依据,其回报率受分段时区的影响,期间越长,风险估计值越高;（2）模型采用ML和BS方法统计估值显示,我国股票市场极端风险尾部估计值高于香港和美国市场;但是,国内市场逐步稳定,并呈现出跟进国际市场且差距缩小的发展趋势。     

Introduction of a new measure for detecting poor fit due to omitted nonlinear terms in SEM

The model chi-square that is used in linear structural equation modeling compares the fitted covariance matrix of a target model to an unstructured covariance matrix to assess global fit. For models with nonlinear terms, i.e., interaction or quadratic terms, this comparison is very problematic because these models are not nested within the saturated model that is represented by the unstructured covariance matrix. We propose a novel measure that quantifies the heteroscedasticity of residuals in structural equation models. It is based on a comparison of the likelihood for the residuals under the assumption of heteroscedasticity with the likelihood under the assumption of homoscedasticity. The measure is designed to respond to omitted nonlinear terms in the structural part of the model that result in heteroscedastic residual scores. In a small Monte Carlo study, we demonstrate that the measure appears to detect omitted nonlinear terms reliably when falsely a linear model is analyzed and the omitted nonlinear terms account for substantial nonlinear effects. The results also indicate that the measure did not respond when the correct model or an overparameterized model were used.     

Using success to measure quality in British higher education: which subjects attract the best-qualified students?

Summary. A theory is developed to measure the quality of applicants into UK higher education. It is based on the principle that more able applicants will self-select into more difficult subject choices. The advantage is that it gives a unidimensional measure whereby different groups can easily be compared across any dimension of interest, e.g. men, women and the various ethnic groups. Here the relative quality of applicants and acceptances across 170 separate subject groups is calculated and discussed by using a data set with over 2 million observations. It, therefore, offers a way of achieving a more refined measure of the quality of human capital.     

A two-stage procedure to pool information across quantile levels in linear quantile regression

In linear quantile regression, the regression coefficients for different quantiles are typically estimated separately. Efforts to improve the efficiency of estimators are often based on assumptions of commonality among the slope coefficients. We propose instead a two-stage procedure whereby the regression coefficients are first estimated separately and then smoothed over quantile level. Due to the strong correlation between coefficient estimates at nearby quantile levels, existing bandwidth selectors will pick bandwidths that are too small. To remedy this, we use 10-fold cross-validation to determine a common bandwidth inflation factor for smoothing the intercept as well as slope estimates. Simulation results suggest that the proposed method is effective in pooling information across quantile levels, resulting in estimates that are typically more efficient than the separately obtained estimates and the interquantile shrinkage estimates derived using a fused penalty function. The usefulness of the proposed method is demonstrated in a real data example.     

A lower bound to the measure of optimality for main effect plans in the general asymmetric factorial experiments

A design d is called D-optimal if it maximizes det(M _d ) and is called MS-optimal if it maximizes tr(M _d ) and minimizes tr[(M _d )²] among those which maximize tr(M _d ), where M _d stands for the information matrix produced from d under a given model. In this paper, we establish a lower bound for tr[(M _d )²] with respect to a main effects model, where d is an s ₁×s ₂×···×s _m levels asymmetric orthogonal array of strength at least 1. Nonisomorphic asymmetrical MS-optimal orthogonal arrays of strength 1 with N=6, 8 and 12 runs are also presented.     

A predictive approach to the detection of additional information in a multivariate regression model

A predictive approach for the detection of additional information in a multivariate linear regression model is considered for the case of known and unknown error covariance matrices. The predictive density of future Observations on the additional variables under the model that they carry no information has been compared with the predictive density under the model that they do carry information. The Kullback-Leibler measure of divergence is used as a measure of comparison between the models.     

Assessment of the information theory approach to evaluating time-to-event surrogate and true endpoints in a meta-analytic setting

In many disease areas, commonly used long-term clinical endpoints are becoming increasingly difficult to implement due to long follow-up times and/or increased costs. Shorter-term surrogate endpoints are urgently needed to expedite drug development, the evaluation of which requires robust and reliable statistical methodology to drive meaningful clinical conclusions about the strength of relationship with the true long-term endpoint. This paper uses a simulation study to explore one such previously proposed method, based on information theory, for evaluation of time to event surrogate and long-term endpoints, including the first examination within a meta-analytic setting of multiple clinical trials with such endpoints. The performance of the information theory method is examined for various scenarios including different dependence structures, surrogate endpoints, censoring mechanisms, treatment effects, trial and sample sizes, and for surrogate and true endpoints with a natural time-ordering. Results allow us to conclude that, contrary to some findings in the literature, the approach provides estimates of surrogacy that may be substantially lower than the true relationship between surrogate and true endpoints, and rarely reach a level that would enable confidence in the strength of a given surrogate endpoint. As a result, care is needed in the assessment of time to event surrogate and true endpoints based only on this methodology.