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.     

中国黄金期货市场价格发现功能研究

黄金期货在国内上市三年有余,其价格发现功能发挥如何?本文利用上市以来的972个黄金期货和黄金现货样本数据对黄金期货市场功能发挥情况进行了量化研究。分别采用了协整理论、误差修正模型、格兰杰因果分析和脉冲响应函数进行分析。结果显示黄金期货市场已经渐渐发挥其价格发现功能,但并不十分显著,究其原因,与交易制度密切相关。     

我国统一货币政策调控的区域效应非对称性分析

由于人民币升值的压力和我国国际收支的双顺差,外国资产迅速扩张,外汇占款成了我国基础货币的主要投放渠道。由于各区域的经济对外开放程度存在差异,统一的货币政策在不同区域的效应可能存在差异。通过对我国2004年第1季度至2011年第2季度央行统一的货币政策操作在不同区域的政策效应的非对称性进行了理论分析和实证检验,认为对东中西部应分别采用不同的货币政策。     

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.     

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.