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.     

改进灰色预测在油田多目标规划决策中的应用

建立了S油田勘探、开发、炼化、机械、公用工程等多个部门和全局的非线性多级目标优化规划模型,应用关联分析、改进灰色预测、回归分析求取规划模型的约束方程并线性化;编制了相应的计算软件,使之快速预测和优化油田各部门“九五”各年的投资和产值;并将优化结果与油田过去或计划值加以对比,给油田规划决策带来一定的参考。     

Generalized additive models for location, scale and shape

Summary.  A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y , as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton–Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.     

Seemingly unrelated regression on the autoregressive (Ar(p)) singular equation system

This paper studies the estimation of seemingly unrelated regressions (SUR) of singular equation systems with an autoregressive error process (AR(p)) for each equation.Parameter estimates of the autoregressive singular equation system are not generally invariant to the equation deleted. Under the model specification restriction on the autoregressive parameters, the invariance property is preserved, and this paper shows that a single equation generalized least squares (GLS) estimation for a general autoregressive error process is equivalent to the SURGLS estimation of the AR(p) singular equation system.     

On Rao score and PearsonX 2 statistics in generalized linear models

The identity of the Rao score and PearsonX ² statistics is well known in the areas where the latter was first introduced: goodness-of-fit in contingency tables and binary responses. We show in this paper that the same identity holds when the two statistics are used for testing goodness-of-fit of Generalized Linear Models. We also highlight the connections that exist between the two statistics when they are used for the comparison of nested models. Finally, we discuss some merits of these unifying results. Work financially supported by cofin. MIUR grants 2000 and 2002.     

计算中国男性人体环节体积的二元回归方程的研究

采用CT—图像分析法,在尸体研究的基础上,对50例中国男性样本(18～23岁)进行了全身CT横断层扫描、影像分析和测算,获得了样本各环节的长度和体积等惯性数据。进而确定了中国男性青年人体体积的分布,并据此建立了以身高、体重为自变量的直接计算中国青年人体各环节体积的二元回归方程。     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

A regression-based smoothing spline Monte Carlo algorithm for pricing American options in discrete time

American options in discrete time can be priced by solving optimal stopping problems. This can be done by computing so-called continuation values, which we represent as regression functions defined recursively by using the continuation values of the next time step. We use Monte Carlo to generate data, and then we apply smoothing spline regression estimates to estimate the continuation values from these data. All parameters of the estimate are chosen data dependent. We present results concerning consistency and the estimates’ rate of convergence.     

Finite Sample Performance of tests for Symmetry of the Errors in a Linear Model

The finite sample performance of a number of tests for symmetry of the distribution of the errors of a linear model is considered. The first family of tests is based on the discrepancy between two regression fits. The first fit is appropriate under symmetric errors while the second is appropriate for skewed as well as symmetric error distributions. The second family of procedures consists of tests for the univariate symmetry problem. Thus, in the linear model setting these tests are based on residuals. An extensive empirical study of the finite sample, null behavior of the tests is presented. The results of a power comparison among the tests is also discussed.