Contributions to the nonparametric analysis of chance functions on multivariate and censored data.

Summary Generalizing the concepts introduced by dabrowska (1988), the author defines multidimensional hazard functions, associated with vectors of possibly independently right-censored durations. He proposes nonparametric estimators of these functions, by the convolution kernel method, and studies their statistical properties: almost sure, pointwise and uniform convergence on a pavement, convergence in law of the associated process. The main tool consists in an almost sure development of the estimator in a sum of independent and identically distributed variables plus a remainder. The speed of uniform convergence towards zero of this remainder is limited. Moreover, a choice of window, inspired by the one proposed by jones, marron and park (1991) in the case of density in dimension one, is studied in depth. The author shows that this choice is asymptotically optimal. Moreover, the speed of relative convergence of this window to the optimum in the sense of the integrated mean square deviation, takes place in root of n. Finally, the author shows that with positive kernels, it is not possible to obtain a higher speed in the previous case. If we work according to the criterion of the integrated mean square deviation, the corresponding relative speed is then n to the power of one tenth, the speed reached with the cross-validation method (Patil, 1993).