Title: Continuous time scalar-on-function class of regression models with missing at random response
Authors: Mohamed Chaouch - United Arab Emirates University (United Arab Emirates) [presenting]
Abstract: The focus is on nonparametric estimation of the generalized regression function based on copies of a continuous time stationary ergodic process, where the response is a missing at random real random variable, whereas the predictor takes values in some infinite-dimensional space. Pointwise and uniform consistency rates of kernel-type estimator of the regression operator are established. Asymptotic evaluations of the conditional bias and the quadratic error of the estimator are given. A Central Limit Theorem is also established. Since in practice a discretized version of the process is observed rather than a continuous one, a discussion on the sampling scheme is given, and two methods to build a confidence interval are provided. The results are stated under ergodic assumption without assuming any classical mixing conditions. Some previous results are completed and extended to the case where the predictor takes values in some infinite dimensional space and the response variable is affected by a Missing At Random mechanism.