Kernel density estimation for heavy-tailed distributions using the champernowne transformation

When estimating loss distributions in insurance, large and small losses are usually split because it is difficult to find a simple parametric model that fits all claim sizes. This approach involves determining the threshold level between large and small losses. In this article, a unified approach to the estimation of loss distributions is presented. We propose an estimator obtained by transforming the data set with a modification of the Champernowne cdf and then estimating the density of the transformed data by use of the classical kernel density estimator. We investigate the asymptotic bias and variance of the proposed estimator. In a simulation study, the proposed method shows a good performance. We also present two applications dealing with claims costs in insurance.     

On multiple constraint skewed models

The Azzalini [A. Azzalini, A class of distributions which includes the normal ones, Scandi. J. Statist. 12 (1985), pp. 171–178.] skew normal model can be viewed as one involving normal components subject to a single linear constraint. As a natural extension of this model, we discuss skewed models involving multiple linear and nonlinear constraints and possibly non-normal components. Particular attention is devoted to a distribution called the extended two-piece normal (ETN) distribution. This model is a two-constraint extension of the two-piece normal model introduced by Kim [H.J. Kim, On a class of two-piece skew normal distributions, Statistics 39(6) (2005), pp. 537–553.]. Likelihood inference for the ETN distribution is developed and illustrated using two data sets.     

Semiparametric estimation of plane similarities: application to fast computation of aeronautic loads

In the big data era, it is often needed to resolve the problem of parsimonious data representation. In this paper, the data under study are curves and the sparse representation is based on a semiparametric model. Indeed, we propose an original registration model for noisy curves. The model is built transforming an unknown function by plane similarities. We develop a statistical method that allows to estimate the parameters characterizing the plane similarities. The properties of the statistical procedure are studied. We show the convergence and the asymptotic normality of the estimators. Numerical simulations and a real-life aeronautic example illustrate and demonstrate the strength of our methodology.     

Multivariate Kendall's tau for change‐point detection in copulas

Statistical procedures for the detection of a change in the dependence structure of a series of multivariate observations are studied in this work. The test statistics that are proposed are $L_1$ , $L_2$ , and $L_{\infty }$ distances computed from vectors of differences of Kendall's tau; two multivariate extensions of Kendall's measure of association are used. Since the distributions of these statistics under the null hypothesis of no change depend on the unknown underlying copula of the vectors, a procedure based on the multiplier central limit theorem is used for the computation of p‐values; the method is shown to be valid both asymptotically and for moderate sample sizes. Alternative versions of the tests that take into account possible breakpoints in the marginal distributions are also investigated. Monte Carlo simulations show that the tests are powerful under many scenarios of change‐point. In addition, two estimators of the time of change are proposed and their efficiency is carefully studied. The methodologies are illustrated on simulated series from the Canadian Regional Climate Model. The Canadian Journal of Statistics 41: 65–82; 2013 © 2012 Statistical Society of Canada     

Importance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test

We study distributional properties of generalized order statistics (gos) related by a random shift or scaling scheme in the continuous and discrete case, respectively. In the continuous case, we obtain new characterizations of distributions relating non-neighbouring gos extending some results given in the literature for the neighbouring cases. On the other hand, in the discrete case, we investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose gos are related by a random translation.     

Semiparametric multiple kernel estimators and model diagnostics for count regression functions

Abstract

This study concerns semiparametric approaches to estimate discrete multivariate count regression functions. The semiparametric approaches investigated consist of combining discrete multivariate nonparametric kernel and parametric estimations such that (i) a prior knowledge of the conditional distribution of model response may be incorporated and (ii) the bias of the traditional nonparametric kernel regression estimator of Nadaraya-Watson may be reduced. We are precisely interested in combination of the two estimations approaches with some asymptotic properties of the resulting estimators. Asymptotic normality results were showed for nonparametric correction terms of parametric start function of the estimators. The performance of discrete semiparametric multivariate kernel estimators studied is illustrated using simulations and real count data. In addition, diagnostic checks are performed to test the adequacy of the parametric start model to the true discrete regression model. Finally, using discrete semiparametric multivariate kernel estimators provides a bias reduction when the parametric multivariate regression model used as start regression function belongs to a neighborhood of the true regression model.     

‘I shared the joy’: sport-related social support and communality on Instagram

The popularity of sharing photographs on digital platforms has increased significantly due to the communicative affordances of mobile media and the emergence of photo-sharing applications, such as Instagram. In this paper, we examine how social support and communality can be built and reinforced through digital visual communication. We focus especially on photo sharing in the context of recreational climbing and trail running. In a qualitative study with Finnish climbers and runners, we asked what meanings sports practitioners ascribe to the practice of sharing and observed how they communicate these meanings through photographs. The results indicate that different types of visual content build and reinforce communality in distinct ways. Whereas inspirational photographs drive practitioners to explore, motivational photographs pull practitioners to keep going through goal setting and peer support. We conclude that visual communication on Instagram mediates a stream of momentary encounters between practitioners that merge into communally meaningful experiences. Thus, we assert that in the context of recreational sport subcultures, photo sharing not only facilitates social relationships but can be perceived as a meaningful social practice that is integral to reinforcing physical activity.     

Strains in Sustainability Debates: Traditional Ecological Knowledge and Western Science through the Lens of Extension Agents in a Pastoral Region

Those involved in sustainability debates on developmental pathways concur in the synergistic potential of integrating traditional ecological knowledge (TEK) and Western scientific approaches. Transhumant pastoralism is a livelihood strategy adapted to spatiotemporal environmental variability in many mountainous and arid regions worldwide. This form of livelihood is based on a mobile logic that is increasingly threatened by novel lifestyles promoted from a Western mind-set and by climate change. The aim of this article is to identify and characterize the different perspectives of environmental and social issues in a pastoral region and their association with labor collaboration among extension agents, framed in an institutional action. We tackled the inquiry about viewpoints with Q methodology and related it to regional problems, alternative solutions, and future development pathways for transhumant pastoralism and landscape management in northwest Patagonia. We identified six perspectives and characterized them with their topological position in the social network. Mediating positions registered the highest network centrality of labor collaborations among agents, whereas more dominant perspectives emphasizing TEK or scientific knowledge registered intermediate centrality. There was consensus on the need for sustainable developmental options, but the emphasis on combining knowledge still needs convergent solutions.