Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions

Dème, El Hadji; Girard, Sabine; Guillou, Armelle

doi:10.1016/j.insmatheco.2013.03.010

Cited by 11 publications

(12 citation statements)

References 18 publications

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“…As an example of heavy-tailed distributions satisfying the second order regularly varying condition (R U ), we have the so called and frequently used Hall's model which is a class of cdf's, such that U(t) = ct γ (1 + dρ −1 a(t) + o(t ρ )), as t → ∞, where γ > 0, ρ ≤ 0, c > 0, and d ∈ R * . This sub-class of heavy-tailed models contains the distributions such as Pareto, Burr, Fréchet and Student-t. For statistical inference concerning the second-order parameter ρ, we refer, for example, to [12] and [38].…”

Section: Resultsmentioning

confidence: 99%

“…The class of heavy-tailed distributions (the so-called Pareto-type distributions) includes distributions such as Pareto, Burr, Student, Lévy-stable, and log-gamma which are known to be appropriate models in Extreme Value Theory for fitting large insurance claims, large fluctuations of prices, log-returns, incomes of countries with very high economic inequality, etc. (see, e.g., [2]; [3]; [4]; [11] ; [13]; [14]; [15]; [25]; [34]; [39]; [41]).…”

Section: Definitions and Empirical Estimationmentioning

confidence: 99%

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Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions

Modou Kebe,

Deme,

Tchilabalo Abozou Kpanzou

et al. 2023

Eur. J. Pure Appl. Math.

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Evidence from micro-data shows that capital incomes are exceedingly volatile, which makes up a disproportionately high contribution to the overall inequality in populations with the heavy-tailed nature on the income distributions for many countries. The quintile share ratio (QSR) is a recently introduced measure of income inequality, also forming part of the European Laeken indicators and which cover four important dimensions of social inclusion (health, education, employment and financial poverty). In 2001, the European Council decided that income inequality in the European Union member states should be described using a number of indicators including the QSR. Non-parametric estimation has been developed on the QSR index for heavy-tailed capital incomes distributions. However, this method of estimation does not give satisfactory statistical performances, since it suffers badly from under coverage, and so we cannot rely on the non-parametric estimator. Hence, we need another estimator in the case of heavy tailed populations. This is the reason why we introduce, in this paper, a class of semi-parametric estimators of theQSR index of economic inequality for heavy-tailed income distributions. Our methodology is basedon the extreme value theory, which offers adequate statistical results for such distributions. Weestablish their asymptotic distribution, and through a simulation study, we illustrate their behaviorin terms of the absolute bias and the median squared error. The simulation results clearly showthat our estimators work well.

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Section: Resultsmentioning

confidence: 99%

Section: Definitions and Empirical Estimationmentioning

confidence: 99%

Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions

Modou Kebe,

Deme,

Tchilabalo Abozou Kpanzou

et al. 2023

Eur. J. Pure Appl. Math.

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“…k,n U(n/k) − −AB K (γ, ρ) γ (1 − ρ) (K (s) − K ρ (s))) + o P (1) .By the result of Lemma 5 of Deme et al (2013)[9], for any consistent estimator ρ of ρ, we have√ k γ L.S n,k ( ρ) − γ − sk n d (s (K (s) − K ρ (s))) + o P (1) ,and by using the consistency and the inequality | e x − 1 x − 1| ≤ e |x| − 1 for all x ∈ R.…”

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confidence: 80%

Kernel-type estimator of the mean for a heavy tailed distribution

Rassoul

2015

Statistics and Its Interface

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In this paper, we focus on the reduced bias of the mean estimator for a heavy-tailed distribution. It is well known that the classical mean estimator introduced by Peng (2001) is seriously biased under the second order regular variation. To reduce bias, many authors have proposed estimators, for both first and second order parameters of the distribution tail. In this work, we define a kernel type estimator for the mean and we propose a reduced bias estimator. The asymptotic distributional properties of our proposed estimators are derived and we compared their performances with other estimators.

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“…According to Theorem 1 in Deme et al (2013) and by the consistency in probability of γ H n,k , we have…”

Section: Lemma 1 Under the Assumptions Of Theorem 1 We Havementioning

confidence: 99%

Reduced-Bias Estimator of the Conditional Tail Expectation of Heavy-Tailed Distributions

Dème

Girard

Guillou

2015

Mathematical Statistics and Limit Theorems

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Several risk measures have been proposed in the literature. In this paper, we focus on the estimation of the Conditional Tail Expectation (CTE). Its asymptotic normality has been first established in the literature under the classical assumption that the second moment of the loss variable is finite, this condition being very restrictive in practical applications. Such a result has been extended by Necir et al. (2010) in the case of infinite second moment. In this framework, we propose a reduced-bias estimator of the CTE. We illustrate the efficiency of our approach on a small simulation study and a real data analysis.

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Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions

Cited by 11 publications

References 18 publications

Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions

Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions

Kernel-type estimator of the mean for a heavy tailed distribution

Reduced-Bias Estimator of the Conditional Tail Expectation of Heavy-Tailed Distributions

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