AN APPROACH TO OPTIMIZATION IN RESPONSE SURFACE METHODOLOGY

We consider the optimization of a response surface given by a polynomial model. In this article the problem is stated as a stochastic optimization problem. For the first-order model, the E-Model technique is used to find the maximum and stationary points; the exact distributions are derived under the linearity assumption.

     

沉淀硬化不锈钢PH15—7Mo的组织结构与强化相

本文用定量金相法和膨胀法研究了 PH15～7Mo 钢中,δ铁素体含量,马氏体转变温度和转变量,板条状马氏体和ε马氏体的生成与热处理制度的关系。用射透电子显微镜和x射线相分析法观察和鉴定了析出相的形貌和晶体结构类型。从而阐明该钢的热处理原理和合理使用的温度范围。认为钢材的强化来源于马氏体组织形态和强化相的沉淀硬化效应,强化相为富 Al 相和 Mo 的碳化物。     

品牌需求价格弹性与市场份额的关系——对国内彩电行业的实证研究

本文运用log-log市场反应函数,对国内彩电行业中品牌市场份额对品牌价格弹性的影响进行了实证研究。研究结果发现,彩电品牌市场份额对其需求价格弹性绝对值有正向显著影响,这一结论明显区别于国外实证研究的结果,其原由反映了转型过程中国内彩电市场的基本特征。本文的结果及原因分析,对中国彩电企业的营销实践具有重要指导意义。     

非线性协整的秩检验方法及其响应面函数研究

 本文对非线性协整关系的秩检验方法进行了系统的梳理,运用Monte Carlo模拟给出了不同样本容量的各个秩检验统计量的临界值,并进一步探讨了其响应面函数,给出了各个秩检验统计量临界值的近似计算公式。对中国上证综指与主要发达国家股指关系的秩协整检验表明,与传统线性协整Johansen检验相比,秩协整检验能够检测到更多的线性和非线性协整关系。     

Testing for linearity in simple regression models

In this paper a new test is introduced which checks the linearity assumption in bivariate regression models. It is based on the idea that the slope through the data points (x_i,y_i) and (x_j,y_j) should be approximately equal to the slope through the data points (x_j,y_j) and (x_k,y_k) for x_i<x_j<x_k under the assumption that the random variable Y is a linear function of the independent variable x. This idea is formalized in a U-statistic on which the test for linearity is based. The test performs well for the considered case of power transformations, which is of high practical relevance.     

REDUCED DISTANCE MEASURES AND TRANSFORMATIONS IN PROCESSING MULTIVARIATE OUTLIERS

The study of multivariate outliers raises many problems of definition, principle and manipulation. Well-authenticated tests of discordancy exist only for the multivariate normal distribution. Detection of outliers in non-normal distributions involves the adoption of appropriate criteria to represent 'extremeness' of observations in a sample; corresponding tests of discordancy usually require tedious, or even intractable, distributional and computational manipulations. A class of transformations of the data is considered with a view of transferring some of the familiar and desirable features of discordancy tests for normal samples to non-normal situations.     

Demographic comparison between self-response and personal visit interview in Census 2000

During Census 2000, over 95 percent of the housing units were in mailback areas. In these areas either the United States Postal Service or Census Bureau staff delivered the census questionnaire. In urban and suburban areas of the country, the United States Postal Service delivered the census questionnaires between March 13 and 15 of 2000. The addresses in these areas are predominately city style; house number and street name. In more rural areas of the country with predominately non-city style addresses, Census Bureau staff delivered the questionnaire during March of 2000. Respondents completed their census questionnaires and returned them through the mail. Returns from these housing units are classified as self-response. Respondents which did not complete and return their census questionnaire by April 18, 2000 were interviewed during the nonresponse followup operation (personal visit interview). This paper will examine the demographic characteristics of persons enumerated on the mail return questionnaire (self-response) and the persons enumerated during the nonresponse followup operation (personal visit interview).     

A Note on the Derivation of Fisher's Transformation of the Correlation Coefficient

Fisher's transformation of the bivariate-normal correlation coefficient is usually derived as a variance-stabilizing transformation and its normalizing property is then demonstrated by the reduced skewness of the distribution resulting from the transformation. In this note the transformation is derived as a normalizing transformation that incorporates variance stabilization. Some additional remarks are made on the transformation and its uses.     

Rotatability is a Sufficient Condition for A- and D-Rotatability

Designs for estimating axial slopes of a response surface are considered. A design is said to be A- (D-) rotatable if the trace (determinant) of variance–covariance matrix of the estimated slopes at a point in the factor space is a function of the distance of the point from the center of the design. It is shown that for any order d and any dimension k, a design which is rotatable in the Box and Hunter (1957 Box , G. E. P. , Hunter , J. S. ( 1957 ). Multifactor experimental designs for exploring response surfaces . Annals of Mathematical Statistics 28 : 195 – 241 .[Crossref] , [Google Scholar]) sense is automatically A- and D-rotatable. Some specific examples illustrating the validity of this general result are provided.     

Statistical Comparison of the Goodness of Fit Delivered by Five Families of Distributions Used in Distribution Fitting

A basic assumption in distribution fitting is that a single family of distributions may deliver useful representation to the universe of available distributions. To date, little study has been conducted to compare the relative effectiveness of these families. In this article, five families are compared by fitting them to a sample of 20 distributions, using 2 fitting objectives: minimization of the L ₂ norm and four-moment matching. Values of L ₂ norm associated with the fitted families are used as input data to test for significant differences. The Pearson family and the RMM (Response Modeling Methodology) family significantly outperforms all other families.