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arXiv · 1604.06980

On exact and optimal recovering of missing values for sequences

Nikolai Dokuchaev
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Abstract

The paper studies recoverability of missing values for sequences in a pathwise setting without probabilistic assumptions. This setting is oriented on a situation where the underlying sequence is considered as a sole sequence rather than a member of an ensemble with known statistical properties. Sufficient conditions of recoverability are obtained; it is shown that sequences are recoverable if there is a certain degree of degeneracy of the Z-transforms. We found that, in some cases, this degree can be measured as the number of the derivatives of Z-transform vanishing at a point. For processes with non-degenerate Z-transform, an optimal recovering based on the projection on a set of recoverable sequences is suggested. Some robustness of the solution with respect to noise contamination and truncation is established.

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Nikolai Dokuchaev. 2016-04-24. On exact and optimal recovering of missing values for sequences. https://arxiv.org/abs/1604.06980

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