A semi-parametric approach to robust parameter design

Parameter design or robust parameter design (RPD) is an engineering methodology intended as a cost-effective approach for improving the quality of products and processes. The goal of parameter design is to choose the levels of the control variables that optimize a defined quality characteristic. An essential component of RPD involves the assumption of well estimated models for the process mean and variance. Traditionally, the modeling of the mean and variance has been done parametrically. It is often the case, particularly when modeling the variance, that nonparametric techniques are more appropriate due to the nature of the curvature in the underlying function. Most response surface experiments involve sparse data. In sparse data situations with unusual curvature in the underlying function, nonparametric techniques often result in estimates with problematic variation whereas their parametric counterparts may result in estimates with problematic bias. We propose the use of semi-parametric modeling within the robust design setting, combining parametric and nonparametric functions to improve the quality of both mean and variance model estimation. The proposed method will be illustrated with an example and simulations.     

Inference for quantile measures of kurtosis,peakedness, and tail weight

Insight into measures of peakedness, heavy-tailedness, and kurtosis can be gained by studying Ruppert’s ratios of interquantile ranges. They are not only monotone in Horn’s measure of peakedness when applied to the central portion of the population, but also monotone in the practical tail-index of Morgenthaler and Tukey, when applied to the tails. Non-parametric confidence intervals are found for Ruppert’s ratios, and sample sizes required to obtain such intervals for a pre-specified relative width and level are provided. In addition, the empirical power of distribution-free tests for peakedness and bimodality are found for some symmetric distributions.     

Simulation techniques for generalized Gaussian densities

This contribution deals with the Monte Carlo simulation of generalized Gaussian random variables. Such a parametric family of distributions has been proposed in many applications in science to describe physical phenomena and in engineering, and it seems to be also useful in modelling economic and financial data. For values of the shape parameter α within a certain range, the distribution presents heavy tails. In particular, the cases α=1/3 and α=1/2 are considered. For such values of the shape parameter, different simulation methods are assessed.     

An Examination of the Effect of Continuous Quality Improvements on Optimal Pricing for Durable Goods*

This paper investigates the nature of optimal prices for a durable good in the presence of continuous quality improvements. The analysis of optimal prices is based on a nonlinear dynamic model of sales response that relates price, quality, average life of a product and the persistence of quality perceptions. Numerical solutions to the model are derived by employing the generalized reduced gradient algorithm. The results show that optimal price depends on the persistence of quality perceptions and the average life of a product (an aspect of quality). The analysis of optimal results affirms results based on other models and provides insights on the influence that quality has on optimal pricing. The implications of the results and suggestions for future research are discussed.     

法院如何回应民意:一种法学方法论上的解决方案

围绕司法与民意的讨论,目前各界存在原因认知、概念认知、价值认知上的观点错位,影响民众对司法回应的肯定.作为法律适用机关的法院在回应民意上具有不同于政治机关的特点,必须以一种理性、中立的态度审慎地回应民意,做到有理有节、有所为有所不为.在回应过程中,应当根据民意的特点着重处理法意与民意、社会民意与权力意志之间的矛盾冲突关系,为此,必须在回应民意的时机选择与方法操作上遵循司法活动的基本规律.通过认定疑难案件的程序操作,使得外在的民意得以稳定化,以程序阻隔"舆论暴力";通过法律论证的操作,以普遍化、一致性与融贯性三原则检验与提升民意本身的合理性程度,以方法压缩个人恣意.法院的回应是对成熟且理性的民意的回应,建立在个案基础上的回应能逐步挽回民众对法院的信任.     

政府应急处理中的人权保障——以比例原则为视角

作为我国行政应急管理的基本法,《突发事件应对法》通过构建紧急状态下国家和公民活动规则的基本原则与框架,尊重和保持非常时期下的宪法民主制度和公民权利,从而维系宪法保障人权的基本价值。有效处理突发事件要求政府在紧急状态中享有应急特权,而应急权的行使当然应以比例原则来加以规制。我国的《突发事件应对法》对比例原则进行了明确规定,通过其合理适用,比例原则将有力促进政府应急处置权与公民权利之间的平衡,实现法治国家在紧急状态下的人权保障。     

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model. Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the r$r$th moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin et al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214–223]. The usefulness of these models is illustrated in a simulation study and in applications to three real data sets.     

Bayesian credible intervals for response surface optima

In response surface methodology, one is usually interested in estimating the optimal conditions based on a small number of experimental runs which are designed to optimally sample the experimental space. Typically, regression models are constructed from the experimental data and interrogated in order to provide a point estimate of the independent variable settings predicted to optimize the response. Unfortunately, these point estimates are rarely accompanied with uncertainty intervals. Though classical frequentist confidence intervals can be constructed for unconstrained quadratic models, higher order, constrained or nonlinear models are often encountered in practice. Existing techniques for constructing uncertainty estimates in such situations have not been implemented widely, due in part to the need to set adjustable parameters or because of limited or difficult applicability to constrained or nonlinear problems. To address these limitations a Bayesian method of determining credible intervals for response surface optima was developed. The approach shows good coverage probabilities on two test problems, is straightforward to implement and is readily applicable to the kind of constrained and/or nonlinear problems that frequently appear in practice.