Journal ArticleDOI
A longitudinal data analysis interpretation of credibility models
TLDR
The primary contribution to actuarial science is to demonstrate that many additive credibility models can be expressed as special cases of the longitudinal data model, which unify the many existing credibility models with this framework.Abstract:
In this paper, we develop links between credibility theory in actuarial science and longitudinal data models in statistics. Our primary contribution to actuarial science is to demonstrate that many additive credibility models can be expressed as special cases of the longitudinal data model. We, thereby, unify the many existing credibility models with this framework. In addition, a longitudinal data interpretation suggests additional models and techniques that actuaries can use in credibility ratemaking. We also apply standard statistical software, which has been developed to analyze longitudinal data models, to the private passenger automobile data of Hachemeister [Hachemeister, C.A., 1975. Credibility for regression models with applications to trend. In: Kahn, P.M. (Ed.), Credibility: Theory and Applications. Academic Press, New York, pp. 129–163].read more
Citations
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MonographDOI
Longitudinal and Panel Data: Analysis and Applications in the Social Sciences
TL;DR: In this paper, the authors introduce the foundations of longitudinal and panel data analysis at a level suitable for quantitatively oriented graduate social science students as well as individual researchers, emphasizing mathematical and statistical fundamentals but also describing substantive applications from across the social sciences, showing the breadth and scope that these models enjoy.
Journal ArticleDOI
Forecasting with Panel Data
Badi H. Baltagi,Badi H. Baltagi +1 more
TL;DR: The authors give a brief survey of forecasting with panel data, starting with a simple error component regression model and surveying best linear unbiased prediction under various assumptions of the disturbance term, including various ARMA models as well as spatial auto-regressive models.
Journal ArticleDOI
Forecasting with panel data
Badi H. Baltagi,Badi H. Baltagi +1 more
TL;DR: In this paper, a survey of forecasting with panel data is given, which includes various ARMA models as well as spatial autoregressive models, and the best linear unbiased prediction under various assumptions of the disturbance term.
Journal ArticleDOI
Actuarial statistics with generalized linear mixed models
Katrien Antonio,Jan Beirlant +1 more
TL;DR: In this paper, the authors consider statistical techniques for modeling such data within the framework of generalized linear mixed models (GLMMs) which model a transformation of the mean as a linear function of both fixed and random effects.
Journal ArticleDOI
Credibility Using Copulas
Edward W. Frees,Ping Wang +1 more
TL;DR: This paper is the first to propose using a t-copula in the context of generalized linear models, the copula associated with the multivariate t-distribution, and shows that it gives rise to easily computable predictive distributions that are used to generate credibility predictors.
References
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Book
Econometric Analysis of Panel Data
TL;DR: In this article, the authors proposed a two-way error component regression model for estimating the likelihood of a particular item in a set of data points in a single-dimensional graph.
Book
Analysis of longitudinal data
TL;DR: In this paper, a generalized linear model for longitudinal data and transition models for categorical data are presented. But the model is not suitable for categric data and time dependent covariates are not considered.
Book
Analysis of Panel Data
TL;DR: In this paper, the authors propose a homogeneity test for linear regression models (analysis of covariance) and show that linear regression with variable intercepts is more consistent than simple regression with simple intercepts.
Journal ArticleDOI
Generalized linear models. 2nd ed.
Peter McCullagh,John A. Nelder +1 more
TL;DR: A class of statistical models that generalizes classical linear models-extending them to include many other models useful in statistical analysis, of particular interest for statisticians in medicine, biology, agriculture, social science, and engineering.
Journal ArticleDOI
Generalized Linear Models
TL;DR: Generalized linear models, 2nd edn By P McCullagh and J A Nelder as mentioned in this paper, 2nd edition, New York: Manning and Hall, 1989 xx + 512 pp £30