Triple-goal estimates in two-stage hierarchical models

The beauty of the Bayesian approach is its ability to structure complicated models, inferential goals and analyses. To take full advantage of it, methods should be linked to an inferential goal via a loss function. For example, in the two-stage, compound sampling model the posterior means are optimal under squared error loss. However, they can perform poorly in estimating the histogram of the parameters or in ranking them. 'Triple-goal' estimates are motivated by the desire to have a set of estimates that produce good ranks, a good parameter histogram and good co-ordinate-specific estimates. No set of estimates can simultaneously optimize these three goals and we seek a set that strikes an effective trade-off. We evaluate and compare three candidate approaches: the posterior means, the constrained Bayes estimates of Louis and Ghosh, and a new approach that optimizes estimation of the histogram and the ranks. Mathematical and simulation-based analyses support the superiority of the new approach and document its excellent performance for the three inferential goals.     

Nonparametric estimation of welfare changes

In this article, I propose a simple nonparametric method of estimating welfare measures with no structural assumptions on the demand system. The method is illustrated for both the single good and the multiple good case, using simulated data. Standard errors of the welfare changes are derived using standard bootstrap techniques. The compensating variation and deadweight loss resulting from a housing price increase is evaluated using Canadian mortgage data. The GAUSS coding, which is very short, is included.     

镍磷合金镀层的摩擦磨损特性及其开发前景

本文分析了化学镀镍磷合金层的摩擦磨损试验结果,研究指出这一表面处理技术具有低的摩擦系数和高的耐磨性及硬度,又因沉积处理温度低而不存在变形,亦不影响零件原来的精度及粗糙度,因此宜于作为零件的最终表面处理。若应用于齿轮,凸轮等高副零件,前景十分乐观。最后从试样的磨损失重中估算出磨损系数和磨损减薄量以供作耐磨性设计的参考。     

Classifying Speech Sonority Functional Data using a Projected Kolmogorov-Smirnov Approach

This paper addresses a linguistically motivated question of classification of functional data, namely the statistical classification of languages according to their rhythmic features. This is an important open problem in phonology. The analysis is based on the information provided by the sonority, which is an index of local regularity of the speech signal. Our main tool is the projected Kolmogorov-Smirnov test. This is a new goodness of fit test for functional data. The result obtained supports the linguistic conjecture of the existence of three rhythmic classes.     

Stochastic Loss Reserving in Discrete Time: Individual vs. Aggregate Data Models

In this paper, a stochastic individual data model is considered. It accommodates occurrence times, reporting, and settlement delays and severity of every individual claims. This formulation gives rise to a model for the corresponding aggregate data under which classical chain ladder and Bornhuetter–Ferguson algorithms apply. A claims reserving algorithm is developed under this individual data model and comparisons of its performance with chain ladder and Bornhuetter–Ferguson algorithms are made to reveal the effects of using individual data to instead aggregate data. The research findings indicate a remarkable promotion in accuracy of loss reserving, especially when the claims amounts are not too heavy-tailed.     

正义性可信性与可读性——试论武侠小说的三重制约

武侠小说须要展现侠义精神,这体现为对正义性的追求。为此作品必须具备可信性,否则将直接降低损害侠义精神。从唐传奇到近现代乃至当今的玄幻武侠,不少侠客们口吐飞剑、变化飞腾,但是本领越大,作品越是虚幻苍白,任意虚构本质上违反中国武侠文学的文类规定性。另一方面,绝对追求可信性的态度,会使武侠小说质木无文,缺乏可读性,伤害艺术竞争力。把握好虚实尺度的弹性,显然是武侠小说发展成败的关键。     

An Exact Analysis of the Multi‐class M/M/k Priority Queue with Partial Blocking

Abstract

We consider a multi‐server queuing model with two priority classes that consist of multiple customer types. The customers belonging to one priority class customers are lost if they cannot be served immediately upon arrival. Each customer type has its own Poisson arrival and exponential service rate. We derive an exact method to calculate the steady state probabilities for both preemptive and nonpreemptive priority disciplines. Based on these probabilities, we can derive exact expressions for a wide range of relevant performance characteristics for each customer type, such as the moments of the number of customers in the queue and in the system, the expected postponement time and the blocking probability. We illustrate our method with some numerical examples.     

Letters to the Editor

Although several authors have indicated that the median test has low power in small samples, it continues to be presented in many statistical textbooks, included in a number of popular statistical software packages, and used in a variety of application areas. We present results of a power simulation study that shows that the median test has noticeably lower power, even for the double exponential distribution for which it is asymptotically most powerful, than other readily available rank tests. We suggest that the median test be “retired” from routine use and recommend alternative rank tests that have superior power over a relatively large family of symmetric distributions.     

A Unified Approach to Prior and Loss Robustness

ABSTRACT

We introduce a new statistical framework in order to study Bayesian loss robustness under classes of priors distributions, thus unifying both concepts of robustness. We propose measures that capture variation with respect to both prior selection and selection of loss function and explore general properties of these measures. We illustrate the approach for the continuous exponential family. Robustness in this context is studied first with respect to prior selection where we consider several classes of priors for the parameter of interest, including unimodal and symmetric and unimodal with positive support. After prior variation has been measured we investigate robustness to loss function, using Hellinger and Linex (Linear Exponential) classes of loss functions. The methods are applied to standard examples.     

Bayes Prediction for a Stratified Regression Superpopulation Model Using Balanced Loss Function

We consider the stratified regression superpopulation model and obtain Bayes predictor of the finite population mean under Zellner's two-criterion balanced loss function (BLF). BLF predictor simplifies to a linear combination of the sample and predictive means. Furthermore, it reduces to some of the well-known classical and Bayes predictors. Relative losses and relative savings loss are obtained to investigate loss robustness of the BLF predictor. It is found to perform better than the usual sample mean as well as the predictive mean in the minimal Bayes predictive expected loss sense.