Kernel entropy estimation for long memory linear processes with infinite variance

2022/10/07 by Liu, Hui, Xu, Fangjun
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2210.03644

Abstract

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&lt;α&lt;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 f²(x) dx by using the kernel estimator \[ T_n(h_n)=(2)/(n(n-1)h_n)∑_1≤ j<i></i>

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