Laplace deconvolution in the presence of indirect long-memory data

Rida Benhaddou

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arXiv · 1706.08648

Laplace deconvolution in the presence of indirect long-memory data

Rida Benhaddou

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Abstract

We investigate the problem of estimating a function $f$ based on observations from its noisy convolution when the noise exhibits long-range dependence. We construct an adaptive estimator based on the kernel method, derive minimax lower bound for the $L^2$-risk when $f$ belongs to Sobolev space and show that such estimator attains optimal rates that deteriorate as the LRD worsens.

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Rida Benhaddou. 2017-06-27. Laplace deconvolution in the presence of indirect long-memory data. https://arxiv.org/abs/1706.08648

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