Kernel entropy estimation for linear processes

2017/12/01 by Hailing Sang, Sang, Hailing, Yongli Sang +3
Decision Sciences · Engineering · Physics and Astronomy · #Control Systems and Identification #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistical Mechanics and Entropy #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1712.00196

openalex publication_date 2017/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \X_n: n∈ ℕ\ be a linear process with bounded probability density function f(x). We study the estimation of the quadratic functional ∫_ℝ f²(x) dx. With a Fourier transform on the kernel function and the projection method, it is shown that, under certain mild conditions, the estimator \[ (2)/(n(n-1)h_n) ∑_1≤ i

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