Étude d'une classe d'estimateurs à noyau de la densité d'une loi de probabilité

Dans ce travail nous donnons un aperçu des plus intéressantes approches visant à déterminer la fenêtre optimale en estimation de la densité d’une loi de probabilité par la méthode du noyau. Nous construisons ensuite une classe d’estimateurs à noyau de la densité pour lesquels nous avons établi des conditions suffisantes de convergence uniforme presque sûre et L¹ presque sûre vers la densité à estimer f [f incliné vers la droite]. Cette classe d’estimateurs à noyau étant assez générale, elle nous a permis d’appliquer ces résultats de convergence à des estimateurs à noyau classiques comme ceux de Deheuvels (1977-a), Shanmugam (1977), Bierens (1983), et Devroye et Wagner (1983). Elle nous a permis également, de construire une famille d’estimateurs à noyau de moyenne μn et de matrice de variance-covariance Vn, où fin est un estimateur non spécifié de la moyenne de / et Vn, à une constante multiplicative près, la matrice de variance-covariance empirique. Enfin, en simulant quelques modèles univariés connus, nous avons comparé les performances de l’estimateur à noyau de Parzen-Rosenblatt avec celles de l’estimateur à noyau de variance la variance empirique et de moyenne /xn, où a été choisi comme étant la moyenne empirique X n ou bien la médiane X n ou bien la moyenne empirique a-tronquée (a = 0.1) ou bien l’estimateur de Gastwirth (1966).Québec Université Laval, Bibliothèque 201

Estimation of bivariate excess probabilities for elliptical models

Let $(X,Y)$ be a random vector whose conditional excess probability $\theta(x,y):=P(Y\leq y | X>x)$ is of interest. Estimating this kind of probability is a delicate problem as soon as $x$ tends to be large, since the conditioning event becomes an extreme set. Assume that $(X,Y)$ is elliptically distributed, with a rapidly varying radial component. In this paper, three statistical procedures are proposed to estimate $\theta(x,y)$ for fixed $x,y$, with $x$ large. They respectively make use of an approximation result of Abdous et al. (cf. Canad. J. Statist. 33 (2005) 317--334, Theorem 1), a new second order refinement of Abdous et al.'s Theorem 1, and a non-approximating method. The estimation of the conditional quantile function $\theta(x,\cdot)^{\leftarrow}$ for large fixed $x$ is also addressed and these methods are compared via simulations. An illustration in the financial context is also given.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ140 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Use of residential wood heating in a context of climate change: a population survey in Québec (Canada)

<p>Abstract</p> <p>Background</p> <p>Wood heating is recommended in several countries as a climate change (CC) adaptation measure, mainly to increase the autonomy of households during power outages due to extreme climatic events. The aim of this study was to examine various perceptions and individual characteristics associated with wood heating through a survey about CC adaptations.</p> <p>Methods</p> <p>A telephone survey (n = 2,545) of adults living in the southern part of the province of Québec (Canada) was conducted in the early fall season of 2005. The questionnaire used closed questions and measured the respondents' beliefs and current adaptations about CC. Calibration weighting was used to adjust the data analysis for the respondent's age and language under stratified sampling based on health regions.</p> <p>Results</p> <p>More than three out of four respondents had access to a single source of energy at home, which was mainly electricity; 22.2% combined two sources or more; 18.5% heated with wood occasionally or daily during the winter. The prevalence of wood heating was higher in the peripheral regions than in the more urban regions, where there was a higher proportion of respondents living in apartments. The prevalence was also higher with participants completely disagreeing (38.5%) with the eventual prohibition of wood heating when there is smog in winter, compared to respondents somewhat disagreeing (24.2%) or agreeing (somewhat: 17.5%; completely: 10.4%) with the adoption of this strategy. It appears that the perception of living in a region susceptible to winter smog, smog warnings in the media, or the belief in the human contribution to CC, did not influence significantly wood heating practices.</p> <p>Conclusion</p> <p>Increased residential wood heating could very well become a maladaptation to climate change, given its known consequences on winter smog and respiratory health. It would thus be appropriate to implement a long-term national program on improved and controlled residential wood heating. This would constitute a "no-regrets" adaptation to climate change, while reducing air pollution and its associated health impacts.</p

On semiparametric regression for count explanatory variables

International audienceWe study the problem of semiparametric estimation of a multivariate count regression function m : Nd -> R that can be represented as a product of an unknown discrete parametric function r and an unknown discrete smooth function w. For the construction of such estimators, we first find an approximation result br for the parametric part r, and then estimate the nonparametric multiplicative correction factor w = m/br by a discrete associated-kernel method. Comparisons are therefore carried out with the nonparametric count regression estimator of Nadaraya-Watson type. We point out that the new semiparametric count regression estimator can reduce the bias with respect to purely nonparametric count regression estimator, without affecting the variance

Aggregating the response in time series regression models, applied to weather-related cardiovascular mortality.

In environmental epidemiology studies, health response data (e.g. hospitalization or mortality) are often noisy because of hospital organization and other social factors. The noise in the data can hide the true signal related to the exposure. The signal can be unveiled by performing a temporal aggregation on health data and then using it as the response in regression analysis. From aggregated series, a general methodology is introduced to account for the particularities of an aggregated response in a regression setting. This methodology can be used with usually applied regression models in weather-related health studies, such as generalized additive models (GAM) and distributed lag nonlinear models (DLNM). In particular, the residuals are modelled using an autoregressive-moving average (ARMA) model to account for the temporal dependence. The proposed methodology is illustrated by modelling the influence of temperature on cardiovascular mortality in Canada. A comparison with classical DLNMs is provided and several aggregation methods are compared. Results show that there is an increase in the fit quality when the response is aggregated, and that the estimated relationship focuses more on the outcome over several days than the classical DLNM. More precisely, among various investigated aggregation schemes, it was found that an aggregation with an asymmetric Epanechnikov kernel is more suited for studying the temperature-mortality relationship

EMD-regression for modelling multi-scale relationships, and application to weather-related cardiovascular mortality.

In a number of environmental studies, relationships between nat4ural processes are often assessed through regression analyses, using time series data. Such data are often multi-scale and non-stationary, leading to a poor accuracy of the resulting regression models and therefore to results with moderate reliability. To deal with this issue, the present paper introduces the EMD-regression methodology consisting in applying the empirical mode decomposition (EMD) algorithm on data series and then using the resulting components in regression models. The proposed methodology presents a number of advantages. First, it accounts of the issues of non-stationarity associated to the data series. Second, this approach acts as a scan for the relationship between a response variable and the predictors at different time scales, providing new insights about this relationship. To illustrate the proposed methodology it is applied to study the relationship between weather and cardiovascular mortality in Montreal, Canada. The results shed new knowledge concerning the studied relationship. For instance, they show that the humidity can cause excess mortality at the monthly time scale, which is a scale not visible in classical models. A comparison is also conducted with state of the art methods which are the generalized additive models and distributed lag models, both widely used in weather-related health studies. The comparison shows that EMD-regression achieves better prediction performances and provides more details than classical models concerning the relationship