Effective Signal Extraction Via Local Polynomial Approximation Under Long-Range Dependency Conditions

• Published in: Lobachevskii journal of mathematics Vol. 39; no. 3; pp. 309 - 320
• Main Author: Artemov, A. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2018; Springer Nature B.V
• Subjects: Algebra; Analysis; Digital signal processors; Flow control; Geometry; Mathematical analysis; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Numerical analysis; Numerical methods; Polynomials; Probability Theory and Stochastic Processes; Smooth trend; fractional Brownian motion; long-range dependence; local polynomial estimate; signal extraction

We study the signal extraction problemwhere a smooth signal is to be estimated against a long-range dependent noise. We consider an approach employing local estimates and derive a theoretically optimal (maximum likelihood) filter for a polynomial signal. On its basis, we propose a practical signal e...