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.     

Local influence in multilevel models

The authors study the local influence of observations in multilevel regression models. To this end, they perturb simultaneously the variances, responses and design matrix. To measure the local change caused by these perturbations, they use generalized Cook statistics for the fixed and random parameter estimates. Closed form local influence measures also allow them to assess the joint influence of various observations. They suggest a simple computation method and illustrate their results using two examples.     

Adaptive tests of regression functions via multiscale generalized likelihood ratios

Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data.     

BURR CRITICAL VALUE APPROXIMATIONS FOR TESTS OF AUTOCORRELATION AND HETEROSCEDASTICITY

The paper evaluates the accuracy of Burr approximations of critical values and p-values for test a of autocorrelation and heteroscedasticity in the linear regression model.     

Creating a reference to a complex emergency situation using time series methods: war in Guinea-Bissau 1998-1999

Impacts of complex emergencies or relief interventions have often been evaluated by absolute mortality compared to international standardized mortality rates. A better evaluation would be to compare with local baseline mortality of the affected populations. A projection of population-based survival data into time of emergency or intervention based on information from before the emergency may create a local baseline reference. We find a log-transformed Gaussian time series model where standard errors of the estimated rates are included in the variance to have the best forecasting capacity. However, if time-at-risk during the forecasted period is known then forecasting might be done using a Poisson time series model with overdispersion. Whatever, the standard error of the estimated rates must be included in the variance of the model either in an additive form in a Gaussian model or in a multiplicative form by overdispersion in a Poisson model. Data on which the forecasting is based must be modelled carefully concerning not only calendar-time trends but also periods with excessive frequency of events (epidemics) and seasonal variations to eliminate residual autocorrelation and to make a proper reference for comparison, reflecting changes over time during the emergency. Hence, when modelled properly it is possible to predict a reference to an emergency-affected population based on local conditions. We predicted childhood mortality during the war in Guinea-Bissau 1998-1999. We found an increased mortality in the first half-year of the war and a mortality corresponding to the expected one in the last half-year of the war.     

BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.     

基于因果关系的教育研究方法思考

探索、检验因果关系是教育科学研究的重要目标之一,相关分析、回归分析、路径分析等常用统计方法存在许多不足。结构方程模型是针对这些不足提出来的,从统计思路上,它具有优点,但还不够完善,应引起我国教育学界的注意。     

Geometric Method and Generalized Linear Models. Two Opposite Multiparametric Approaches Illustrated on a Sample of Pituitary Adenomas

We used two statistical methods to identify prognostic factors: a log-linear model (logistic and COX regression, based on the notions of linearity and multiplicative relative risk), and the CORICO method (ICOnography of CORrelations) based on the geometric significance of the correlation coefficient. We applied the methods to two different situations (a "case-control study' and a "historical cohort'). We show that the geometric exploratory tool is particularly suited to the analysis of small samples with a large number of variables. It could save time when setting up new study protocols. In this instance, the geometric approach highlighted, without preconceived ideas, the potential role of multihormonality in the course of pituitary adenoma and the unexpected influence of the date of tumour excision on the risk attached to haemorrhage.     

核准制IPO定价实证分析

本文用信息经济学的理论和计量经济学的实证分析方法研究了我国核准制下的新股定价问题 ,指出市场主体决策时的信息差异是造成新股发行价和上市价相背离的主要原因 ,并构建多元回归模型对这一假设进行了检验。     

Psychological taxing in Flemish municipalities

We analyse whether the psychological pricing in the private sector has a public sector counterpart in tax policy. Analysing the main theoretical arguments for the existence of price points, and applying them to the public sector, suggests that psychological taxing reveals itself by the use of non-0 ending tax rates. The tax rate endings of the local income taxes, which are set by 308 Flemish municipalities in the fiscal year 1998, suggests the presence of psychological taxing. Non-0 endings occur more frequently in municipalities where demand for public policy is more elastic (and where, therefore, the benefits to the politicians from setting a tax just below a tax point is higher). The pre-tax income inequality and the level of the tax rate positively affect psychological taxing. The latter effect is reinforced in those municipalities where the existing tax rate is above the average tax rate in neighbouring municipalities and below their neighbours’ minimum, although this effect has a limited effect and is offset the further below the minimum the tax is set.