Kernel estimation for quadratic functional of long memory linear processes with infinite variance

Let (Formula presented.) be a long memory linear process with innovations in the domain of attraction of an α-stable law (Formula presented.). Assume that the linear process X has a bounded probability density function (Formula presented.). Then, under certain conditions, we estimate the quadratic functional (Formula presented.) of the linear process X by using the kernel estimator (Formula presented.) Moreover, using the Delta method, we obtain the corresponding results for the kernel estimator of the quadratic Rényi entropy (Formula presented.). When innovations are symmetric α-stable random variables, we give the simulation study for these two kernel estimators.