Selected Papers from the 10th Tartu Conference on Multivariate Statistics

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (31 January 2017) | Viewed by 13103

Special Issue Editor


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Institute of Mathematics and Statistics, University of Tartu, Narva mnt 18, 51009 Tartu, Estonia
Interests: premium estimation and reserving in non-life insurance; approximation of distributions; skewed distributions

Special Issue Information

Dear Colleagues,

The 10th Tartu Conference on Multivariate Statistics will be held in Tartu, Estonia, from 28 June to 1 July, 2016. The conference series has a long tradition starting from 1977, and the anniversary conference covers a wide range of problems in modern multivariate statistics, including statistical learning, estimation and testing problems, multivariate mixed models, multivariate distributions, survey statistics, stochastic models in finance and insurance, experimental design and applications in different areas.

This Special Issue selects excellent insurance and finance related papers from the conference, including both theoretical development of methods and practical application of statistical tools to solve specific problems. We invite investigators to contribute original research articles, as well as review articles, to this Special Issue.

Assoc. Prof. Dr. Meelis Käärik
Guest Editor

Manuscript Submission Information

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Published Papers (3 papers)

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Research

399 KiB  
Article
On Comparison of Stochastic Reserving Methods with Bootstrapping
by Liivika Tee, Meelis Käärik and Rauno Viin
Risks 2017, 5(1), 2; https://doi.org/10.3390/risks5010002 - 04 Jan 2017
Cited by 3 | Viewed by 5260
Abstract
We consider the well-known stochastic reserve estimation methods on the basis of generalized linear models, such as the (over-dispersed) Poisson model, the gamma model and the log-normal model. For the likely variability of the claims reserve, bootstrap method is considered. In the bootstrapping [...] Read more.
We consider the well-known stochastic reserve estimation methods on the basis of generalized linear models, such as the (over-dispersed) Poisson model, the gamma model and the log-normal model. For the likely variability of the claims reserve, bootstrap method is considered. In the bootstrapping framework, we discuss the choice of residuals, namely the Pearson residuals, the deviance residuals and the Anscombe residuals. In addition, several possible residual adjustments are discussed and compared in a case study. We carry out a practical implementation and comparison of methods using real-life insurance data to estimate reserves and their prediction errors. We propose to consider proper scoring rules for model validation, and the assessments will be drawn from an extensive case study. Full article
662 KiB  
Article
Estimation of Star-Shaped Distributions
by Eckhard Liebscher and Wolf-Dieter Richter
Risks 2016, 4(4), 44; https://doi.org/10.3390/risks4040044 - 30 Nov 2016
Cited by 3 | Viewed by 3967
Abstract
Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density in a star-shaped distribution model. For the generator function and the [...] Read more.
Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density in a star-shaped distribution model. For the generator function and the star-generalized radius density, we consider a non-parametric kernel-type estimator. This estimator is combined with a parametric estimator for the contours which are assumed to follow a parametric model. Therefore, the semiparametric procedure features the flexibility of nonparametric estimators and the simple estimation and interpretation of parametric estimators. Alternatively, we consider pure parametric estimators for the density. For the semiparametric density estimator, we prove rates of uniform, almost sure convergence which coincide with the corresponding rates of one-dimensional kernel density estimators when excluding the center of the distribution. We show that the standardized density estimator is asymptotically normally distributed. Moreover, the almost sure convergence rate of the estimated distribution function of the star-generalized radius is derived. A particular new two-dimensional distribution class is adapted here to agricultural and financial data sets. Full article
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405 KiB  
Article
Parameter Estimation in Stable Law
by Annika Krutto
Risks 2016, 4(4), 43; https://doi.org/10.3390/risks4040043 - 25 Nov 2016
Cited by 5 | Viewed by 3423
Abstract
For general stable distribution, cumulant function based parameter estimators are proposed. Extensive simulation experiments are carried out to validate the effectiveness of the estimates over the entire parameter space. An application to non-life insurance losses distribution is made. Full article
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