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.     

Modified cross-validation in density estimation

We propose a new modified (biased) cross-validation method for adaptively determining the bandwidth in a nonparametric density estimation setup. It is shown that the method provides consistent minimizers. Some simulation results are reported on which compare the small sample behavior of the new and the classical cross-validation selectors.     

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.     

Uncertainty Analysis for Computer Model Projections of Hurricane Losses

Projecting losses associated with hurricanes is a complex and difficult undertaking that is wrought with uncertainties. Hurricane Charley, which struck southwest Florida on August 13, 2004, illustrates the uncertainty of forecasting damages from these storms. Due to shifts in the track and the rapid intensification of the storm, real-time estimates grew from 2 to 3 billion dollars in losses late on August 12 to a peak of 50 billion dollars for a brief time as the storm appeared to be headed for the Tampa Bay area. The storm hit the resort areas of Charlotte Harbor near Punta Gorda and then went on to Orlando in the central part of the state, with early poststorm estimates converging on a damage estimate in the 28 to 31 billion dollars range. Comparable damage to central Florida had not been seen since Hurricane Donna in 1960. The Florida Commission on Hurricane Loss Projection Methodology (FCHLPM) has recognized the role of computer models in projecting losses from hurricanes. The FCHLPM established a professional team to perform onsite (confidential) audits of computer models developed by several different companies in the United States that seek to have their models approved for use in insurance rate filings in Florida. The team's members represent the fields of actuarial science, computer science, meteorology, statistics, and wind and structural engineering. An important part of the auditing process requires uncertainty and sensitivity analyses to be performed with the applicant's proprietary model. To influence future such analyses, an uncertainty and sensitivity analysis has been completed for loss projections arising from use of a Holland B parameter hurricane wind field model. Uncertainty analysis quantifies the expected percentage reduction in the uncertainty of wind speed and loss that is attributable to each of the input variables.     

Influence diagnostics and outlier tests for semiparametric mixed models

Summary. Semiparametric mixed models are useful in biometric and econometric applications, especially for longitudinal data. Maximum penalized likelihood estimators (MPLEs) have been shown to work well by Zhang and co-workers for both linear coefficients and nonparametric functions. This paper considers the role of influence diagnostics in the MPLE by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component. We focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the MPLE algorithm. We also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers. The influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example.     

多元线性回归方程及其应用

通过建立多元线性回归的数学模型,利用最小二乘估计得到正规方程组并进行相关性检验,从而解决相关实际问题。     

Model Diagnostics for Remote Access Regression Servers

To protect public-use microdata, one approach is not to allow users access to the microdata. Instead, users submit analyses to a remote computer that reports back basic output from the fitted model, such as coefficients and standard errors. To be most useful, this remote server also should provide some way for users to check the fit of their models, without disclosing actual data values. This paper discusses regression diagnostics for remote servers. The proposal is to release synthetic diagnostics—i.e. simulated values of residuals and dependent and independent variables–constructed to mimic the relationships among the real-data residuals and independent variables. Using simulations, it is shown that the proposed synthetic diagnostics can reveal model inadequacies without substantial increase in the risk of disclosures. This approach also can be used to develop remote server diagnostics for generalized linear models.     

Nonresponse weighting adjustment using estimated response probability

To reduce nonresponse bias in sample surveys, a method of nonresponse weighting adjustment is often used which consists of multiplying the sampling weight of the respondent by the inverse of the estimated response probability. The authors examine the asymptotic properties of this estimator. They prove that it is generally more efficient than an estimator which uses the true response probability, provided that the parameters which govern this probability are estimated by maximum likelihood. The authors discuss variance estimation methods that account for the effect of using the estimated response probability; they compare their performances in a small simulation study. They also discuss extensions to the regression estimator.     

Goodness‐of‐fit methods for matched case‐control studies

The authors propose graphical and numerical methods for checking the adequacy of the logistic regression model for matched case‐control data. Their approach is based on the cumulative sum of residuals over the covariate or linear predictor. Under the assumed model, the cumulative residual process converges weakly to a centered Gaussian limit whose distribution can be approximated via computer simulation. The observed cumulative residual pattern can then be compared both visually and analytically to a certain number of simulated realizations of the approximate limiting process under the null hypothesis. The proposed techniques allow one to check the functional form of each covariate, the logistic link function as well as the overall model adequacy. The authors assess the performance of the proposed methods through simulation studies and illustrate them using data from a cardiovascular study.