Abstract: The paper is devoted to the study of a parametric deformation model of independent and identically random variables. We construct an efficient and easy-to-compute recursive estimate of the parameter. Our stochastic estimator is similar to the Robbins-Monro procedure where the contrast function is the Wasserstein distance. We then propose a recursive estimator similar to that of Parzen-Rosenblatt kernel density estimator in order to estimate the density of the random variables. This estimate takes into account the previous estimation of the parameter of the model. Finally, we illustrate the performance of our estimation procedure on simulations for the Box-Cox transformation and the arcsinh transformation.

Key words and phrases: Asymptotic properties, estimation of a regression function, estimation of shifts, semiparametric estimation.