A new estimation method for Weibull-type tails based on the mean excess function

Studying the right tail of a distribution, one can classify the distributions into three classes based on the extreme value index γ$\gamma$. The class γ>0$\gamma >0$ corresponds to Pareto-type or heavy tailed distributions, while γ<0$\gamma <0$ indicates that the underlying distribution has a finite endpoint. The Weibull-type distributions form an important subgroup within the Gumbel class with γ=0$\gamma =0$. The tail behaviour can then be specified using the Weibull tail index. Classical estimators of this index show severe bias. In this paper we present a new estimation approach based on the mean excess function, which exhibits improved bias and mean squared error. The asserted properties are supported by simulation experiments and asymptotic results. Illustrations with real life data sets are provided.     

Age,religious beliefs,and sexual attitudes

Age effects on sexual attitudes were examined using the Hendrick and Hendrick (1987a) Sexual Attitude Scale. The study was cross-sectional, including people from various age groups, from young adults to older adults. The religious beliefs variable, which covaries substantially both with age and sexual attitudes, was controlled. Three main questions guided the study: (a) Is the four-factor structure (Permissiveness, Instrumentality, Communion, and Sexual Practices) previously identified in a sample of young students able to accurately account for data gathered over a full range of adult ages, (b) are older adults much less permissive and less instrumentalist than young people, and (c) to what extent are believers less permissive and instrumentalist than young people when age is taken into account? Factor analyses showed that at least five correlated factors were needed to account for the data; the fourth factor, Sexual Practices, divided itself into two distinct factors: Pleasure and Responsibility. Older adults and believers were shown to be less permissive than young people and nonbelievers, and this result held regardless of the participants educational level. As regards to instrumentality, however, the pattern of differences was extremely complex.     

Approximation of the distribution of excesses through a generalized probability-weighted moments method

The POT (peaks-over-threshold) approach consists in using the generalized Pareto distribution (GPD) to approximate the distribution of excesses over a threshold. In this paper, we consider this approximation using a generalized probability-weighted moments (GPWM) method. We study the asymptotic behaviour of our new estimators and also the functional bias of the GPD as an estimate of the distribution function of the excesses. A simulation study is provided in order to appreciate the efficiency of our approach.     

Reporting Errors in Siblings’ Survival Histories and Their Impact on Adult Mortality Estimates: Results From a Record Linkage Study in Senegal

Estimates of adult mortality in countries with limited vital registration (e.g., sub-Saharan Africa) are often derived from information about the survival of a respondent’s siblings. We evaluated the completeness and accuracy of such data through a record linkage study conducted in Bandafassi, located in southeastern Senegal. We linked at the individual level retrospective siblings’ survival histories (SSH) reported by female respondents (n = 268) to prospective mortality data and genealogies collected through a health and demographic surveillance system (HDSS). Respondents often reported inaccurate lists of siblings. Additions to these lists were uncommon, but omissions were frequent: respondents omitted 3.8 % of their live sisters, 9.1 % of their deceased sisters, and 16.6 % of their sisters who had migrated out of the DSS area. Respondents underestimated the age at death of the siblings they reported during the interview, particularly among siblings who had died at older ages (≥45 years). Restricting SSH data to person-years and events having occurred during a recent reference period reduced list errors but not age and date errors. Overall, SSH data led to a 20 % underestimate of ₄₅ q ₁₅ relative to HDSS data. Our study suggests new quality improvement strategies for SSH data and demonstrates the potential use of HDSS data for the validation of “unconventional” demographic techniques.     

Weibull tail-distributions revisited: A new look at some tail estimators

In this paper, we propose to include Weibull tail-distributions in a more general family of distributions. In particular, the considered model also encompasses the whole Fréchet maximum domain of attraction as well as log-Weibull tail-distributions. The asymptotic normality of some tail estimators based on the log-spacings between the largest order statistics is established in a unified way within the considered family. This result permits to understand the similarity between most estimators of the Weibull tail-coefficient and the Hill estimator. Some different asymptotic properties, in terms of bias, rate of convergence, are also highlighted.     

Khmer Potent Places: Pāramī and the Localisation of Buddhism and Monarchy in Cambodia

Cambodia is strewn with places of national, local or, most frequently, village importance, considered as potent places, that is to say, places that are said to have agency and a positive or negative power of interaction with human beings. This paper emphasises the constituent principles of potency using case studies based on ethnographic research conducted between 2007 and 2015 in Pursat province, western Cambodia. Beginning with the analysis of the sanctuary of a powerful land guardian spirit called Khleang Muang, the author progressively guides the reader to all the potent places that form a network which spatially tells the legend of the sixteenth-century Khmer King Ang Chan who passed by Pursat, coming from Angkor and settled in Lovek (south of Tonle Sap Lake). Violent death and sacrifices, rituals, spiritual energy called paramī, old buildings, monasteries, precious tableware kept in the soil, trees, stones, termite mounds?…?all those constituents of the potency of the places are analysed. The author’s discussion of the core of potency (pāramī and paramī) enables her to show how Buddhism and land guardian spirit cults are entangled in a single still hierarchical religious system. Finally, the author analyses how potent places in Cambodia embody a process of localisation of the nation-level institution of monarchy.     

Nonparametric regression estimation of conditional tails: the random covariate case

We present families of nonparametric estimators for the conditional tail index of a Pareto-type distribution in the presence of random covariates. These families are constructed from locally weighted sums of power transformations of excesses over a high threshold. The asymptotic properties of the proposed estimators are derived under some assumptions on the conditional response distribution, the weight function and the density function of the covariates. We also introduce bias-corrected versions of the estimators for the conditional tail index, and propose in this context a consistent estimator for the second-order tail parameter. The finite sample performance of some specific examples from our classes of estimators is illustrated with a small simulation experiment.     

Estimating the conditional tail index by integrating a kernel conditional quantile estimator

This paper deals with the estimation of the tail index of a heavy-tailed distribution in the presence of covariates. A class of estimators is proposed in this context and its asymptotic normality established under mild regularity conditions. These estimators are functions of a kernel conditional quantile estimator depending on some tuning parameters. The finite sample properties of our estimators are illustrated on a small simulation study.     

Estimation of extreme quantiles from heavy and light tailed distributions

In Gardes et al. (2011), a new family of distributions is introduced, depending on two parameters τ$\tau$ and θ$\theta$, which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for θ$\theta$ and extreme quantiles are also proposed, but they both depend on the unknown parameter τ$\tau$, making them useless in practical situations. In this paper, we propose an estimator of τ$\tau$ which is independent of θ$\theta$. Plugging our estimator of τ$\tau$ in the two previous ones allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unified way. The asymptotic distributions of our three new estimators are established and their efficiency is illustrated on a small simulation study and on a real data set.     

Projection estimators of Pickands dependence functions

The authors consider the construction of intrinsic estimators for the Pickands dependence function of an extreme‐value copula. They show how an arbitrary initial estimator can be modified to satisfy the required shape constraints. Their solution consists in projecting this estimator in the space of Pickands functions, which forms a closed and convex subset of a Hilbert space. As the solution is not explicit, they replace this functional parameter space by a sieve of finite‐dimensional subsets. They establish the asymptotic distribution of the projection estimator and its finite‐dimensional approximations, from which they conclude that the projected estimator is at least as efficient as the initial one.