Generating random variates as generalisation of a given sample is an important task for stochastic simulations. The three main methods suggested in the literature are: fitting a standard distribution, constructing an empirical distribution that approximates the cumulative distribution function and generating variates from the kernel density estimate of the data. The last method is practically unknown in the simulation literature although it is as simple as the other two methods. The comparison of the theoretical performance of the methods and the results of three small simulation studies show that a variance corrected version of kernel density estimation performs best and should be used for generating variates directly from a sample. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We develop and evaluate algorithms for generating random variates for simulation input. One group called automatic, or black-box algorithms can be used to sample from distributions with known density. They are based on the rejection principle. The hat function is generated automatically in a setup step using the idea of transformed density rejection. There the density is transformed into a concave function and the minimum of several tangents is used to construct the hat function. The resulting algorithms are not too complicated and are quite fast. The principle is also applicable to random vectors. A second group of algorithms is presented that generate random variates directly from a given sample by implicitly estimating the unknown distribution. The best of these algorithms are based on the idea of naive resampling plus added noise. These algorithms can be interpreted as sampling from the kernel density estimates. This method can be also applied to random vectors. There it can be interpreted as a mixture of naive resampling and sampling from the multi-normal distribution that has the same covariance matrix as the data. The algorithms described in this paper have been implemented in ANSI C in a library called UNURAN which is available via anonymous ftp. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Ce mémoire propose une adaptation lisse de méthodes bootstrap par pseudo-population aux fins d'estimation de la variance et de formation d'intervalles de confiance pour des quantiles de population finie. Dans le cas de données i.i.d., Hall et al. (1989) ont montré que l'ordre de convergence de l'erreur relative de l’estimateur bootstrap de la variance d’un quantile échantillonnal connaît un gain lorsque l'on rééchantillonne à partir d’une estimation lisse de la fonction de répartition plutôt que de la fonction de répartition expérimentale. Dans cet ouvrage, nous étendons le principe du bootstrap lisse au contexte de population finie en le mettant en œuvre au sein des méthodes bootstrap par pseudo-population. Étant donné un noyau et un paramètre de lissage, cela consiste à lisser la pseudo-population dont sont issus les échantillons bootstrap selon le plan de sondage initial. Deux plans sont abordés, soit l'échantillonnage aléatoire simple sans remise et l'échantillonnage de Poisson. Comme l'utilisation des algorithmes proposés nécessite la spécification du paramètre de lissage, nous décrivons une méthode de sélection par injection et des méthodes de sélection par la minimisation d'estimés bootstrap de critères d'ajustement sur une grille de valeurs du paramètre de lissage. Nous présentons des résultats d'une étude par simulation permettant de montrer empiriquement l'efficacité de l'approche lisse par rapport à l'approche standard pour ce qui est de l'estimation de la variance d'un estimateur de quantile et des résultats plus mitigés en ce qui concerne les intervalles de confiance. / This thesis introduces smoothed pseudo-population bootstrap methods for the purposes of variance estimation and the construction of confidence intervals for finite population quantiles. In an i.i.d. context, Hall et al. (1989) have shown that resampling from a smoothed estimate of the distribution function instead of the usual empirical distribution function can improve the convergence rate of the bootstrap variance estimator of a sample quantile. We extend the smoothed bootstrap to the survey sampling framework by implementing it in pseudo-population bootstrap methods. Given a kernel function and a bandwidth, it consists of smoothing the pseudo-population from which bootstrap samples are drawn using the original sampling design. Two designs are discussed, namely simple random sampling and Poisson sampling. The implementation of the proposed algorithms requires the specification of the bandwidth. To do so, we develop a plug-in selection method along with grid search selection methods based on bootstrap estimates of two performance metrics. We present the results of a simulation study which provide empirical evidence that the smoothed approach is more efficient than the standard approach for estimating the variance of a quantile estimator together with mixed results regarding confidence intervals.