Extending the linear model with R , Extending the linear model with R , کتابخانه دیجیتال جندی شاپور اهواز

Extending the Linear Model with R

1. Concepts, models and definitions 2. Nonlinear models in economic theory 3. Parametric nonlinear models 4. The nonparametric approach 5. Parametric linearity tests 6. Testing parameter constancy 7. Nonparametric specification tests 8. Conditional heteroskedasticity 9. State space models 10. Nonparametric models 11. Nonlinear and nonstationary models 12. Estimating parametric models 13. Basic nonparametric estimates 14. Forecasting from nonlinear models 15. Nonlinear impulse responses 16. Building nonlinear models 17. Other topics

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Modelling nonlinear economic time series

Deheuvels (1981a) described a decomposition of the empirical copula process into a finite number of asymptotically mutually independent sub-processes whose joint limiting distribution is tractable under the hypothesis that a multivariate distribution is equal to the product of its margins. It is proved here that this result can be extended to the serial case and that the limiting processes have the same joint distribution as in the non-serial setting. As a consequences, linear rank statistics have the same asymptotic distribution in both contexts. It is also shown how these facts can be exploited to construct simple statistics for detecting dependence graphically and testing it formally. Simulation are used to explore the finite-sample behavior of these statistics, which are found to be powerful against varions types of alternatives.

Tests of Independence and Randomness Based on the Empirical Copula Process

We reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jorgensen and de Souza (Scand Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jorgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit, μ say. They observed that the dependence of the likelihood function on μ is as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.

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Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling

We discuss the estimation and inference problems for the Tweedie compound Poisson process and its application to tarification. For data in the form of the total claim and number of claims for a given time interval and a given exposure, the Tweedie process corresponds to a Poisson process of claims and gamma distributed claim sizes. The model has three parameters, namely the mean claim rate, a dispersion parameter and a shape parameter, and the exposure enters as a weight via the dispersion parameter. The Tweedie process is an exponential dispersion model for fixed value of the shape parameter, and hence regression models for the claim rate may be fitted as in generalized linear models. The shape parameter is estimated by maximum likelihood, and inference is based on the likelihood ratio test, rather than the usual analysis of deviance. A GLIM 4 program for estimation in the model is presented.

Fitting Tweedie's compound poisson model to insurance claims data

In this paper we introduce a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence. The asymptotic normality of the proposed statistics is established, both under the null as well as alternative hypotheses, using LeCam's notion of contiguity. The efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is provided. Finally, we study the asymptotic relative efficiency of the proposed procedures with respect to their normal theory counterparts based on sample autocorrelations.

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Linear Serial Rank Tests for Randomness Against Arma Alternatives

Linear serial rank tests for randomness against ARMA alternatives

 The problem of testing randomness against specified and unspecified contiguous ARMA alternatives is considered In the case of specified alternative, the linear serial rank tests proposed by the authors (Hallin, Ingenbleek and Puri 1985) are shown to be asymptotically most powerful within the class of all possible tests (at the required level) In the case of unspecified alternative, however, any of the above optimal tests is unfortunately completely insensitive against a whole subclass of the alternative Quadratic serial rank statistics, providing tests of the χ2-type are therefore introduced Their asymptotic distributions are derived, under the null hypothesis as well as under contiguous ARMA alternatives The asymptotically maximin most powerful quadratic serial rank tests (for a given density) are then obtained Because of their close similarity with the Box-Pierce parametric test, we call them rank portmanteau tests The asymptotic relative efficiencies (AREs) of the rank portmanteau tests with respect to one another and their AREs with respect to the corresponding Box-Pierce and quadratic Spearman tests are derived

Linear and quadratic serial rank tests for randomness against serial dependence

In a recent paper (Hallin & Ingenbleek, 1981a), the selection procedure proposed in (Hallin, 1977) was applied to the study of the claim probability in the motor third party portfolio of an important Belgian company. The number of observations, however, did not allow for an investigation of the claim amount. The data we study here consist of the entire Swedish portfolio (more than two millions of policies). An adapted version of the selection procedure provides a good insight into the structure of the risk, hence into what the tariff structure should be 1 The rating system used for the Swedish Automobile Insurance Portfolio is based on the factor method. This paper should be looked upon as a critical discussion of the practical application of this method and of its statistical significancy.

The Swedish automobile portfolio in 1977: a statistical study

A nonstationary generalization of the classical Yule-Walker equations, relating the (time-varying) autocorrelations of an autoregressive process to the coefficients of the possible models for this process, is given. The corresponding theoretical model-building (or spectral factorization) problem, i.e. that of expressing the above mentioned models in terms of the autocorrelations, is solved. This paper, as well as several others, is part of a work whose purpose is a systematic study of time-varying ARMA models. © 1983.

Jean-François Ingenbleek

Papers

Linear Serial Rank Tests for Randomness Against Arma Alternatives

Linear serial rank tests for randomness against ARMA alternatives

Linear and quadratic serial rank tests for randomness against serial dependence

The Swedish automobile portfolio in 1977: a statistical study

Nonstationary Yule-Walker equations