Noninformative priors for linear combinations of normal means with unequal variances

For normal populations with unequal variances, we develop matching priors and reference priors for a linear combination of the means. Here, we find three second-order matching priors: a highest posterior density (HPD) matching prior, a cumulative distribution function (CDF) matching prior, and a likelihood ratio (LR) matching prior. Furthermore, we show that the reference priors are all first-order matching priors, but that they do not satisfy the second-order matching criterion that establishes the symmetry and the unimodality of the posterior under the developed priors. The results of a simulation indicate that the second-order matching prior outperforms the reference priors in terms of matching the target coverage probabilities, in a frequentist sense. Finally, we compare the Bayesian credible intervals based on the developed priors with the confidence intervals derived from real data.     

On inference for Kendall's τ within a longitudinal data setting

Kendall's τ is a non-parametric measure of correlation based on ranks and is used in a wide range of research disciplines. Although methods are available for making inference about Kendall's τ, none has been extended to modeling multiple Kendall's τs arising in longitudinal data analysis. Compounding this problem is the pervasive issue of missing data in such study designs. In this article, we develop a novel approach to provide inference about Kendall's τ within a longitudinal study setting under both complete and missing data. The proposed approach is illustrated with simulated data and applied to an HIV prevention study.     

Efficient Bayesian sampling plans for exponential distributions with type-I-censored samples

The aim of this paper is to introduce an efficient Bayesian sampling procedure for exponential distribution with type-I censoring. An online inspection method is suggested to reach a Bayes decision prior the termination time of life test. Bayesian sampling plans (BSPs) with quadratic loss function are established to illustrate the use of the proposed method. Some BSPs are tabulated, and the performance of the proposed BSPs is compared with two existing competitive methods. Numerical results indicate that a significant reduction in the experimental time over the conventional BSP can be achieved when the online inspection method is applied.     

Evaluating Probabilistic Forecasts with Bayesian Signal Detection Models

We propose the use of signal detection theory (SDT) to evaluate the performance of both probabilistic forecasting systems and individual forecasters. The main advantage of SDT is that it provides a principled way to distinguish the response from system diagnosticity, which is defined as the ability to distinguish events that occur from those that do not. There are two challenges in applying SDT to probabilistic forecasts. First, the SDT model must handle judged probabilities rather than the conventional binary decisions. Second, the model must be able to operate in the presence of sparse data generated within the context of human forecasting systems. Our approach is to specify a model of how individual forecasts are generated from underlying representations and use Bayesian inference to estimate the underlying latent parameters. Given our estimate of the underlying representations, features of the classic SDT model, such as the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC), follow immediately. We show how our approach allows ROC curves and AUCs to be applied to individuals within a group of forecasters, estimated as a function of time, and extended to measure differences in forecastability across different domains. Among the advantages of this method is that it depends only on the ordinal properties of the probabilistic forecasts. We conclude with a brief discussion of how this approach might facilitate decision making.     

Uniform Convergence of Compactly Supported Wavelet Expansions of Gaussian Random Processes

New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of non stationary processes. An application of the obtained results to stationary processes is also presented. It is shown that the convergence rate of the expansions is exponential.     

Protection of privacy in efficient application of randomized response techniques

In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response (RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion, testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976), Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994) among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika 57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants before they agree to use the randomization device. The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported by CSIR Grant No. 21(0539)/02/EMR-II.     

Buffon's needle and the estimation of migration distances

A procedure is suggested for estimating migration distances from data on the proportion of migrants crossing regional boundaries. The method makes use of Buffon's needle, a problem in geometrical probability from the eighteenth century that was originally used as an empirical means of estimating π. The procedure is described for various scenarios that differ in their assumptions about region shape, the spatial distribution of population, and the distribution of migration distances. An application to migration distances in the United States is given, and additional attention is given to the estimation of intraregional migration distances.     

An additive subdistribution hazard model for competing risks data

The cumulative incidence function plays an important role in assessing its treatment and covariate effects with competing risks data. In this article, we consider an additive hazard model allowing the time-varying covariate effects for the subdistribution and propose the weighted estimating equation under the covariate-dependent censoring by fitting the Cox-type hazard model for the censoring distribution. When there exists some association between the censoring time and the covariates, the proposed coefficients’ estimations are unbiased and the large-sample properties are established. The finite-sample properties of the proposed estimators are examined in the simulation study. The proposed Cox-weighted method is applied to a competing risks dataset from a Hodgkin's disease study.     

高校大学生行为缺失的表现与对策

近些年,大学生行为缺失现象日益突出,本文对当前大学生行为缺失现象加以分析,对当代大学生存在的各种行为缺失现象进行归纳,找出这些现象产生的根源,并为防止这些现象的发生提出相应对策。     

Assessing and Improving the Performance of Nearly Efficient Unit Root Tests in Small Samples

Abstract

The development of unit root tests continues unabated, with many recent contributions using techniques such as generalized least squares (GLS) detrending and recursive detrending to improve the power of the test. In this article, the relation between the seemingly disparate tests is demonstrated by algebraically nesting all of them as ratios of quadratic forms in normal variables. By doing so, and using the exact sampling distribution of the ratio, it is straightforward to compute, examine, and compare the test' critical values and power functions. It is shown that use of GLS detrending parameters other than those recommended in the literature can lead to substantial power improvements. The open and important question regarding the nature of the first observation is addressed. Tests with high power are proposed irrespective of the distribution of the initial observation, which should be of great use in practical applications.