  In this article, we introduce a kernel-based consensual aggregation method
for regression problems. We aim to flexibly combine individual regression
estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights
are defined based on some kernel function to build a target prediction. This
work extends the context of Biau et al. (2016) to a more general kernel-based
framework. We show that this more general configuration also inherits the
consistency of the basic consistent estimators. Moreover, an optimization
method based on gradient descent algorithm is proposed to efficiently and
rapidly estimate the key parameter of the strategy. The numerical experiments
carried out on several simulated and real datasets are also provided to
illustrate the speed-up of gradient descent algorithm in estimating the key
parameter and the improvement of overall performance of the method with the
introduction of smoother kernel functions.
