On the integrated mean squared error of wavelet density estimation for linear processes

Aleksandr Beknazaryan (), Hailin Sang () and Peter Adamic ()
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Aleksandr Beknazaryan: University of Tyumen
Hailin Sang: University of Mississippi
Peter Adamic: Laurentian University

Statistical Inference for Stochastic Processes, 2023, vol. 26, issue 2, No 1, 235-254

Abstract: Abstract Let $$\{X_n: n\in {{\mathbb {N}}}\}$$ { X n : n ∈ N } be a linear process with density function $$f(x)\in L^2({{\mathbb {R}}})$$ f ( x ) ∈ L 2 ( R ) . We study wavelet density estimation of f(x). Under some regular conditions on the characteristic function of innovations, we achieve, based on the number of nonzero coefficients in the linear process, the minimax optimal convergence rate of the integrated mean squared error of density estimation. Considered wavelets have compact support and are twice continuously differentiable. The number of vanishing moments of mother wavelet is proportional to the number of nonzero coefficients in the linear process and to the rate of decay of characteristic function of innovations. Theoretical results are illustrated by simulation studies with innovations following Gaussian, Cauchy and chi-squared distributions.

Keywords: Linear process; Wavelet method; Density estimation; Projection operator; Primary 62G07; Secondary 62G05; 62M10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11203-022-09281-9

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