Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution

Brazauskas, Vytaras; Serfling, Robert

doi:10.1080/10920277.2000.10595935

Cited by 70 publications

(36 citation statements)

References 17 publications

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“…This is in agreement with Brazauskas and Serfl ing, 2000 showing that small errors in the estimation of the tail index can already produce large errors in the estimation of quantiles based on the tail index. Hence robust operators and procedures have to be implemented.…”

Section: Discussionsupporting

confidence: 79%

On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

Potocký¹,

Waldl²,

Stehlík³

2014

Prague Economic Papers

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Abstract:The problem that assets of a fund are not suffi cient to cover its liabilities is of extreme importance both for its members as well as for fund managers. We show that this problem can be solved via total claims distributions and give answers to the following questions: How much money will be needed in the fi rst pillar in order to satisfy the requirements of pensioners in a time horizon and which groups of working people should join also the second pillar because their benefi ts from it will be greater than those from the fi rst pillar? Though the paper concentrates primarily on the situation with Slovakian pension funds we believe that our fi ndings are more general. We show that the alternative methods should be used for calculation of extremes. We discuss the so-called barrier strategy for treating the surplus of an insurance company and bring some new results concerning it.

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Section: Discussionsupporting

confidence: 79%

On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

Potocký¹,

Waldl²,

Stehlík³

2014

Prague Economic Papers

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“…On the other hand, the robust estimatorη (2,2) remains quite stable with value unchanged (although for some data sets its value would change somewhat, but not dramatically). We would expect similar results with the more efficient competitorη (5,5) , whose computation, however, requires for each of µ and σ taking the median of = 4950 as forη (2,2) . This computation may be carried out via an efficient algorithm or by the modified method described in Appendix A.5.…”

Section: Summary Discussionmentioning

confidence: 69%

“…A good overall estimator appears to beη (5,5) , which offers quite high ARE above 0.91 uniformly over σ, combined with favorable BP of 0.13 and acceptable standardized GES * within the range 2.4 to 2.8. The estimatorη (9,9) , however, which offers ARE above 0.96 uniformly over σ, is more attractive if lower BP of 0.07 and higher GES * in the range 2.9 to 3.8 can be tolerated.…”

Section: Summary Discussionmentioning

confidence: 99%

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Efficient and Robust Fitting of Lognormal Distributions

Serfling¹

2002

North American Actuarial Journal

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In parametric modeling of loss distributions in actuarial science, a versatile choice with intermediate tail weight is the lognormal distribution. Surprisingly, however, the fitting of this model using estimators which are at once efficient and robust has not been seriously addressed in the extensive literature. Consequently, for example, typical estimators of the lognormal mean and variance fail to be both efficient and robust. In particular, the highly efficient maximum likelihood estimators lack robustness. By robustness is meant limited sensitivity to outliers in the sample. For the two-parameter lognormal estimation problem, we consider equivalently the problem of efficient and robust joint estimation of the mean and variance of a normal model and introduce generalized median type estimators which are robust while also possessing very high efficiency compared to competitors already in the literature. These yield efficient and robust estimators of various parameters of interest in the lognormal model, and in this regard we provide detailed treatment of the lognormal mean. Extension of the approach to the much more complicated problem of estimation for the three-parameter lognormal model is also discussed.

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“…However, in the presence of data contamination or when the sample deviates from the Pareto model, the MLE is not robust and becomes severely biased (Victoria-Feser and Ronchetti 1994;Finkelstein et al 2006). To make matters worse, even small errors in estimation of the Pareto exponent can produce large errors in estimation of quantities based on estimates of the exponent such as extreme quantiles, upper-tail probabilities and mean excess functions (Brazauskas and Serfling 2000). Similarly, inequality measures computed for the data simulated from the Pareto model are largely affected by even small or moderate data contamination (Cowell and Victoria-Feser 1996).…”

Section: Introductionmentioning

confidence: 99%

Robust estimation of the Pareto tail index: a Monte Carlo analysis

Brzeziński

2015

Empir Econ

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The Pareto distribution is often used in many areas of economics to model the right tail of heavy-tailed distributions. However, the standard method of estimating the shape parameter (the Pareto tail index) of this distribution-the maximum likelihood estimator (MLE), also known as the Hill estimator-is non-robust, in the sense that it is very sensitive to extreme observations, data contamination or model deviation. In recent years, a number of robust estimators for the Pareto tail index have been proposed, which correct the deficiency of the MLE. However, little is known about the performance of these estimators in small-sample setting, which often occurs in practice. This paper investigates the small-sample properties of the most popular robust estimators for the Pareto tail index, including the optimal B-robust estimator (Victoria-Feser and Ronchetti in Can J Stat 22:247-258, 1994), the weighted maximum likelihood estimator (Dupuis and Victoria-Feser in Can J Stat 34:639-658, 2006), the generalized median estimator (Brazauskas and Serfling in Extremes 3:231-249, 2001), the partial density component estimator (Vandewalle et al. in Comput Stat Data Anal 51:6252-6268, 2007), and the probability integral transform statistic estimator (PITSE) (Finkelstein et al. in N Am Actuar J 10:1-10, 2006). Monte Carlo simulations show that the PITSE offers the desired compromise between ease of use and power to protect against outliers in the small-sample setting.

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Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution

Cited by 70 publications

References 17 publications

On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

Efficient and Robust Fitting of Lognormal Distributions

Robust estimation of the Pareto tail index: a Monte Carlo analysis

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