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Beknazaryan, Aleksandr; Sang, Hailin; Adamic, Peter
Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems, 07/2023, Letnik: 26, Številka: 2Journal Article
Let { X n : n ∈ N } be a linear process with density function 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.
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