A single-pass algorithm for spectrum estimation with fast convergence

Han Xiao; Wei Biao Wu

doi:10.1109/TIT.2011.2145610

A single-pass algorithm for spectrum estimation with fast convergence

Han Xiao, Wei Biao Wu

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We propose a single-pass algorithm for estimating spectral densities of stationary processes. Our algorithm is computationally fast in the sense that, when a new observation arrives, it can provide a real-time update within O(1) computation. The proposed algorithm is probabilistically fast in that, for stationary processes whose auto-covariances decay geometrically, the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor. We also establish asymptotic normality for the recursive estimate. A simulation study is carried out and it confirms the superiority over the classical batched mean estimates.

Original language	English (US)
Article number	5895109
Pages (from-to)	4720-4731
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	57
Issue number	7
DOIs	https://doi.org/10.1109/TIT.2011.2145610
State	Published - Jul 2011
Externally published	Yes

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Keywords

Batched mean estimate
bias reduction
nonparametric estimation
physical dependence measure
recursive algorithm
spectral density
stochastic process

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abstract = "We propose a single-pass algorithm for estimating spectral densities of stationary processes. Our algorithm is computationally fast in the sense that, when a new observation arrives, it can provide a real-time update within O(1) computation. The proposed algorithm is probabilistically fast in that, for stationary processes whose auto-covariances decay geometrically, the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor. We also establish asymptotic normality for the recursive estimate. A simulation study is carried out and it confirms the superiority over the classical batched mean estimates.",

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AB - We propose a single-pass algorithm for estimating spectral densities of stationary processes. Our algorithm is computationally fast in the sense that, when a new observation arrives, it can provide a real-time update within O(1) computation. The proposed algorithm is probabilistically fast in that, for stationary processes whose auto-covariances decay geometrically, the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor. We also establish asymptotic normality for the recursive estimate. A simulation study is carried out and it confirms the superiority over the classical batched mean estimates.

KW - Batched mean estimate

KW - bias reduction

KW - nonparametric estimation

KW - physical dependence measure

KW - recursive algorithm

KW - spectral density

KW - stochastic process

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A single-pass algorithm for spectrum estimation with fast convergence

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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