Modeling test results: evaluation of adaptive methodologies.

Summary This thesis is composed of three parts: discriminant analysis, regression by revealing directions (also known as projection pursuit regression) and neural networks. In discriminant analysis, we are interested in the assignment of a new individual, assuming that the different classes of the response are known. Gaussian assumptions are adopted in the problem, the assignment criterion is based on the maximum likelihood. It is optimal if the means and the covariance matrices are known. The covariance matrices are unknown, the assignment indicator is computed by taking their estimates on the samples of the different populations. Our approach is to help a user to choose between linear (equal covariance matrices) and quadratic (distinct covariance matrices) methodologies from the starting data at his disposal. Expressions for the error majorants of the assignment are given in the thesis. In regression by revealing directions, we first evaluated existing methods such as that of j. Friedman and w. Stuetzle and P. Hall for practical situations likely to be encountered in an industrial domain. We propose a new version of the regression by revealing directions, whose procedure is automated. Finally, we are interested in neural methods for the approximation of unknown functions. The neural networks used are very simple, as is the learning algorithm. The approach adopted was to separate the domain of variation of the input variables but also of the output variable. This separation is much more natural for a non-statistician user of statistics, it allows to improve very clearly the results. This is illustrated in a practical case treated in this part.