Generalized linear models with random effects in the two-parameter exponential family

In this paper, we develop a new class of double generalized linear models, introducing a random-effect component in the link function describing the linear predictor related to the precision parameter. This is a useful procedure to take into account extra variability and also to make the model more robust. The Bayesian paradigm is adopted to make inference in this class of models. Samples of the joint posterior distribution are drawn using standard Monte Carlo Markov Chain procedures. Finally, we illustrate this algorithm by considering simulated and real data sets.     

Identification of multiple influential observations in logistic regression

The identification of influential observations in logistic regression has drawn a great deal of attention in recent years. Most of the available techniques like Cook's distance and difference of fits (DFFITS) are based on single-case deletion. But there is evidence that these techniques suffer from masking and swamping problems and consequently fail to detect multiple influential observations. In this paper, we have developed a new measure for the identification of multiple influential observations in logistic regression based on a generalized version of DFFITS. The advantage of the proposed method is then investigated through several well-referred data sets and a simulation study.     

广义线性模型在非寿险精算中的应用及其研究进展

广义线性模型在精算中的应用始于20世纪80年代，其应用涉及到精算学的各个领域，如生命表的修匀、损失分布、信度理论、风险分类、准备金和费率估计等方面。在对广义线性模型适用于非寿险精算的典型特征进行分析的基础上，对广义线性模型在非寿险精算中的应用及其研究进展进行分析和总结的同时，重点分析利率厘定和准备金估计中广义线性模型的建模思想，并结合实际提出了今后研究的方向。     

Prediction Error Estimation Under Bregman Divergence for Non-Parametric Regression and Classification

Abstract.  Prediction error is critical to assess model fit and evaluate model prediction. We propose the cross-validation (CV) and approximated CV methods for estimating prediction error under the Bregman divergence (BD), which embeds nearly all of the commonly used loss functions in the regression, classification procedures and machine learning literature. The approximated CV formulas are analytically derived, which facilitate fast estimation of prediction error under BD. We then study a data-driven optimal bandwidth selector for local-likelihood estimation that minimizes the overall prediction error or equivalently the covariance penalty. It is shown that the covariance penalty and CV methods converge to the same mean-prediction-error-criterion. We also propose a lower-bound scheme for computing the local logistic regression estimates and demonstrate that the algorithm monotonically enhances the target local likelihood and converges. The idea and methods are extended to the generalized varying-coefficient models and additive models.     

Identification and classification of multiple outliers,high leverage points and influential observations in linear regression

Detection of multiple unusual observations such as outliers, high leverage points and influential observations (IOs) in regression is still a challenging task for statisticians due to the well-known masking and swamping effects. In this paper we introduce a robust influence distance that can identify multiple IOs, and propose a sixfold plotting technique based on the well-known group deletion approach to classify regular observations, outliers, high leverage points and IOs simultaneously in linear regression. Experiments through several well-referred data sets and simulation studies demonstrate that the proposed algorithm performs successfully in the presence of multiple unusual observations and can avoid masking and/or swamping effects.