| This thesis is about non-parametric estimation of the cumulative distribution function (cdf) and the density function. In the first work, we propose a new adaptive method for estimating a cdf. In the supnorm, we are able to control the distance of the estimator to the empirical distribution function (edf). This allows us to achieve the same asymptotic results like those obtained using the edf and this is done under the same minimum regularity conditions. The proposed estimator is, however, smoother and depends on three parameters of which an instrumental function H. This function allows us to include prior information about the target density function and therefore helps improve the estimation.; The second work deals with non-parametric density estimation. The proposed estimator is obtained by differentiating the estimator for the cdf proposed in the first work. This estimator consists of a finite convex combination of densities with supports that are randomly determined by the spacings of the order statistics. In a certain way, the proposed estimator is a generalization of the histogram with random partition and the histo-spline.; Key words. Non-parametric estimation, cumulative distribution function, density function, adaptive smoothing, splines, uniform convergence. |
