Kernel entropy estimation for long memory linear processes with infinite variance

10/07/2022

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by   Hui Liu, et al.

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Let X={X_n: n∈ℕ} be a long memory linear process with innovations in the domain of attraction of an α-stable law (0<α<2). Assume that the linear process X has a bounded probability density function f(x). Then, under certain conditions, we consider the estimation of the quadratic functional ∫_ℝ f^2(x) dx by using the kernel estimator T_n(h_n)=2/n(n-1)h_n∑_1≤ j<i≤ nK(X_i-X_j/h_n). The simulation study for long memory linear processes with symmetric α-stable innovations is also given.