Conditional density function for surrogate scalar response

his paper presents the estimator of the conditional density function of surrogated scalar response variable given a functional random one. We construct a conditional density function by using the available (true) response data and the surrogate data. Then, we build up some asymptotic properties of the constructed estimator in terms of the almost complete convergences. As a result, we compare our estimator with the classical estimator through the Relatif Mean Square Errors (RMSE). Finally, we end this analysis by displaying the superiority of our estimator in terms of prediction when we are lacking complete data.