Nonparametric tests in regression.

Summary In this thesis, we study tests of the type: (H0): E [U | X] = 0 p.s. versus (H1): P {E [U | X] = 0} < 1 where U is the residual of modeling a variable Y as a function of X. In this framework and for several special cases - significativity of variables, quantile regression, functional data, single-index model - we propose a test statistic to obtain critical values from an asymptotic pivotal distribution. In each case, we also give an appropriate bootstrap method for small sample sizes. We show the consistency towards local-or Pitman-like-alternatives of the proposed tests, when this type of alternative does not tend too quickly to the null hypothesis. In each case, we vérifions from simulations under the null hypothesis and under a sequence of alternative hypotheses that the theoretical results are in agreement with practice.