非寿险费率厘定的索赔频率预测模型及其应用

在非寿险分类费率厘定中,泊松回归模型是最常使用的索赔频率预测模型,但实际的索赔频率数据往往存在过离散特征,使泊松回归模型的结果缺乏可靠性.因此,讨论处理过离散问题的各种回归模型,包括负二项回归模型、泊松-逆高斯回归模型、泊松-对数正态回归模型、广义泊松回归模型、双泊松回归模型、混合负二项回归模型、混合二项回归模型、Delaporte回归模型和Sichel回归模型,并对其进行系统比较研究认为:这些模型都可以看做是对泊松回归模型的推广,可以用于处理各种不同过离散程度的索赔频率数据,从而改善费率厘定的效果;同时应用一组实际的汽车保险数据,讨论这些模型的具体应用.     

Comparisons of some bivariate regression models

The bivariate negative binomial regression (BNBR) and the bivariate Poisson log-normal regression (BPLR) models have been used to describe count data that are over-dispersed. In this paper, a new bivariate generalized Poisson regression (BGPR) model is defined. An advantage of the new regression model over the BNBR and BPLR models is that the BGPR can be used to model bivariate count data with either over-dispersion or under-dispersion. In this paper, we carry out a simulation study to compare the three regression models when the true data-generating process exhibits over-dispersion. In the simulation experiment, we observe that the bivariate generalized Poisson regression model performs better than the bivariate negative binomial regression model and the BPLR model.     

Semiparametric zero-inflated Bernoulli regression with applications

When the observed proportion of zeros in a data set consisting of binary outcome data is larger than expected under a regular logistic regression model, it is frequently suggested to use a zero-inflated Bernoulli (ZIB) regression model. A spline-based ZIB regression model is proposed to describe the potentially nonlinear effect of a continuous covariate. A spline is used to approximate the unknown smooth function. Under the smoothness condition, the spline estimator of the unknown smooth function is uniformly consistent, and the regression parameter estimators are asymptotically normally distributed. We propose an easily implemented and consistent estimation method for the variances of the regression parameter estimators. Extensive simulations are conducted to investigate the finite-sample performance of the proposed method. A real-life data set is used to illustrate the practical use of the proposed methodology. The real-life data analysis indicates that the prediction performance of the proposed semiparametric ZIB regression model is better compared to the parametric ZIB regression model.     

D-optimal Designs for a Combined Simple Linear and Haar-Wavelet Regression Model

A combined simple linear and Haar-wavelet regression model is the combination of a simple linear model and a Haar-wavelet regression model. In this article we show how to construct D-optimal designs for a combined simple linear and Haar-wavelet regression model. An example is also given.     

Semi-non parametric smooth isotonic regression

We propose a new method for smooth isotonic regression analysis. Unlike most existing methods for isotonic regression, the proposed method is akin to parametric regression without order restriction. To account for smoothness and isotonicity simultaneously, we exploit the flexible class of semi-non parametric densities to model isotonic regression functions. Under this framework, the full range of inference techniques for parametric regression models become applicable for model estimation and model validation in isotonic regression.     

On the Restricted Liu Estimator in the Logistic Regression Model

The logistic regression model is used when the response variables are dichotomous. In the presence of multicollinearity, the variance of the maximum likelihood estimator (MLE) becomes inflated. The Liu estimator for the linear regression model is proposed by Liu to remedy this problem. Urgan and Tez and Mansson et al. examined the Liu estimator (LE) for the logistic regression model. We introduced the restricted Liu estimator (RLE) for the logistic regression model. Moreover, a Monte Carlo simulation study is conducted for comparing the performances of the MLE, restricted maximum likelihood estimator (RMLE), LE, and RLE for the logistic regression model.     

A Bayesian Approach for Zero-Inflated Count Regression Models by Using the Reversible Jump Markov Chain Monte Carlo Method and an Application

In this study, estimation of the parameters of the zero-inflated count regression models and computations of posterior model probabilities of the log-linear models defined for each zero-inflated count regression models are investigated from the Bayesian point of view. In addition, determinations of the most suitable log-linear and regression models are investigated. It is known that zero-inflated count regression models cover zero-inflated Poisson, zero-inflated negative binomial, and zero-inflated generalized Poisson regression models. The classical approach has some problematic points but the Bayesian approach does not have similar flaws. This work points out the reasons for using the Bayesian approach. It also lists advantages and disadvantages of the classical and Bayesian approaches. As an application, a zoological data set, including structural and sampling zeros, is used in the presence of extra zeros. In this work, it is observed that fitting a zero-inflated negative binomial regression model creates no problems at all, even though it is known that fitting a zero-inflated negative binomial regression model is the most problematic procedure in the classical approach. Additionally, it is found that the best fitting model is the log-linear model under the negative binomial regression model, which does not include three-way interactions of factors.     

On Semiparametric Mode Regression Estimation

It has been found that, for a variety of probability distributions, there is a surprising linear relation between mode, mean, and median. In this article, the relation between mode, mean, and median regression functions is assumed to follow a simple parametric model. We propose a semiparametric conditional mode (mode regression) estimation for an unknown (unimodal) conditional distribution function in the context of regression model, so that any m-step-ahead mean and median forecasts can then be substituted into the resultant model to deliver m-step-ahead mode prediction. In the semiparametric model, Least Squared Estimator (LSEs) for the model parameters and the simultaneous estimation of the unknown mean and median regression functions by the local linear kernel method are combined to infer about the parametric and nonparametric components of the proposed model. The asymptotic normality of these estimators is derived, and the asymptotic distribution of the parameter estimates is also given and is shown to follow usual parametric rates in spite of the presence of the nonparametric component in the model. These results are applied to obtain a data-based test for the dependence of mode regression over mean and median regression under a regression model.     

Exponentiated-exponential geometric regression model

A regression model, based on the exponentiated-exponential geometric distribution, is defined and studied. The regression model can be applied to count data with under-dispersion or over-dispersion. Some forms of its modifications to truncated or inflated data are mentioned. Some tests to discriminate between the regression model and its competitors are discussed. Real numerical data sets are used to illustrate the applications of the regression model.     

Regression Kink With an Unknown Threshold

This article explores estimation and inference in a regression kink model with an unknown threshold. A regression kink model (or continuous threshold model) is a threshold regression constrained to be everywhere continuous with a kink at an unknown threshold. We present methods for estimation, to test for the presence of the threshold, for inference on the regression parameters, and for inference on the regression function. A novel finding is that inference on the regression function is nonstandard since the regression function is a nondifferentiable function of the parameters. We apply recently developed methods for inference on nondifferentiable functions. The theory is illustrated by an application to the growth and debt problem introduced by Reinhart and Rogoff, using their long-span time-series for the United States.     

A Multivariate Generalized Poisson Regression Model

A multivariate generalized Poisson regression model based on the multivariate generalized Poisson distribution is defined and studied. The regression model can be used to describe a count data with any type of dispersion. The model allows for both positive and negative correlation between any pair of the response variables. The parameters of the regression model are estimated by using the maximum likelihood method. Some test statistics are discussed, and two numerical data sets are used to illustrate the applications of the multivariate count data regression model.     

Ridge Regression Estimation for Survey Samples

This paper describes procedure for constructing a vector of regression weights. Under the regression superpopulation model, the ridge regression estimator that has minimum model mean squared error is derived. Through a simulation study, we compare the ridge regression weights, regression weights, quadratic programming weights, and raking ratio weights. The ridge regression procedure with weights bounded by zero performed very well.     

The heteroscedastic odd log-logistic generalized gamma regression model for censored data

We propose a four-parameter extended generalized gamma model, which includes as special cases some important distributions and it is very useful for modeling lifetime data. A advantage is that it can represent the error distribution for a new heteroscedastic log-odd log-logistic generalized gamma regression model. The proposed heteroscedastic regression model can be used more effectively in the analysis of survival data since it includes as special models several widely-known regression models. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. Overall, the new regression model is very useful to the analysis of real data.     

计量经济学和统计学视角下的线性回归模型——再议线性回归模型的设定

从属性、构建方法及意义等方面,分析研究线性回归模型在计量经济学和统计学两学科视角下的差异,并根据这种差异进一步提出回归模型的基本设定思路。研究表明:识别这种差异是完成模型设定工作的基础性和必要性举措,有助于实现线性回归模型的正确设定。以经典例证对计量经济学和统计学回归模型在应用中的区别以及模型设定问题进行进一步展示和分析。     

A Partially Linear Model Using a Gaussian Process Prior

A partially linear model is a semiparametric regression model that consists of parametric and nonparametric regression components in an additive form. In this article, we propose a partially linear model using a Gaussian process regression approach and consider statistical inference of the proposed model. Based on the proposed model, the estimation procedure is described by posterior distributions of the unknown parameters and model comparisons between parametric representation and semi- and nonparametric representation are explored. Empirical analysis of the proposed model is performed with synthetic data and real data applications.     

Influence analysis in skew-Birnbaum–Saunders regression models and applications

In this paper, we propose a method to assess influence in skew-Birnbaum–Saunders regression models, which are an extension based on the skew-normal distribution of the usual Birnbaum–Saunders (BS) regression model. An interesting characteristic that the new regression model has is the capacity of predicting extreme percentiles, which is not possible with the BS model. In addition, since the observed likelihood function associated with the new regression model is more complex than that from the usual model, we facilitate the parameter estimation using a type-EM algorithm. Moreover, we employ influence diagnostic tools that considers this algorithm. Finally, a numerical illustration includes a brief simulation study and an analysis of real data in order to show the proposed methodology.     

Marginalized zero-inflated generalized Poisson regression

The generalized Poisson (GP) regression model has been used to model count data that exhibit over-dispersion or under-dispersion. The zero-inflated GP (ZIGP) regression model can additionally handle count data characterized by many zeros. However, the parameters of ZIGP model cannot easily be used for inference on overall exposure effects. In order to address this problem, a marginalized ZIGP is proposed to directly model the population marginal mean count. The parameters of the marginalized zero-inflated GP model are estimated by the method of maximum likelihood. The regression model is illustrated by three real-life data sets.     

Regression analysis of autocorrelated poisson-distribution) data

A regression model assuming Poisson-dia distributed data. with autocorrelated errors falls into the class of regression models that; have the error structure which is both heteroscedastic and autocorrelated. In general, this class of regression models are not estimable. However, due to the properties of the Poisson distribution that the variance is equal to the mean, this regression model on Poisson-distributed data with autocorrelated. errors is estimable. In this note the special structure of the covarlance matrix of the model with the first order auto-correlated error Is derived utilizing this property, A method based on the least squares method of Frome, Kutner, and Beauchamp (1973), supplemented by steps for handling autocorrelation in studies of time series analysis, nonlinear regression, and econometrics is presented for obtaining generalized least squares estimates for the parameters of the model.     

A dependent Dirichlet process model for survival data with competing risks

In this paper, we first propose a dependent Dirichlet process (DDP) model using a mixture of Weibull models with each mixture component resembling a Cox model for survival data. We then build a Dirichlet process mixture model for competing risks data without regression covariates. Next we extend this model to a DDP model for competing risks regression data by using a multiplicative covariate effect on subdistribution hazards in the mixture components. Though built on proportional hazards (or subdistribution hazards) models, the proposed nonparametric Bayesian regression models do not require the assumption of constant hazard (or subdistribution hazard) ratio. An external time-dependent covariate is also considered in the survival model. After describing the model, we discuss how both cause-specific and subdistribution hazard ratios can be estimated from the same nonparametric Bayesian model for competing risks regression. For use with the regression models proposed, we introduce an omnibus prior that is suitable when little external information is available about covariate effects. Finally we compare the models’ performance with existing methods through simulations. We also illustrate the proposed competing risks regression model with data from a breast cancer study. An R package “DPWeibull” implementing all of the proposed methods is available at CRAN.

     

Heteroscedastic log-exponentiated Weibull regression model

We introduce a new class of heteroscedastic log-exponentiated Weibull (LEW) regression models. The class of regression models can be applied to censored data and be used more effectively in survival analysis. Maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model is investigated. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the heteroscedastic LEW regression model. The normal curvatures for studying local influence are derived under various perturbation schemes. An empirical application to a real data set is provided to illustrate the usefulness of the new class of heteroscedastic regression models.