Slepianwavelet variances for regularly and irregularly sampled time series

Debashis Mondal; Donald B. Percival

doi:10.1007/978-1-4614-3520-4_38

Slepianwavelet variances for regularly and irregularly sampled time series

Debashis Mondal
, Donald B. Percival

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We discuss approximate scale-based analysis of variance for Gaussian time series based upon Slepian wavelets. These wavelets arise as eigenfunctions of an energy maximization problem in a pass band of frequencies. Unlike the commonly used Daubechies wavelets, Slepian wavelets have the ability to accommodate both regularly and irregularly sampled data. For regularly sampled Gaussian time series, we derive statistical theory for Slepian-based wavelet variances and show that it is comparable to Daubechies-based variances. For irregularly sampled time series data, we derive a corresponding statistical theory for Slepian-based wavelet variances. We demonstrate its use on X-ray fluctuations from a binary star system and on a light curve from the variable star Z UMa.

Original language	English
Title of host publication	Statistical Challenges in Modern Astronomy V
Publisher	Springer Science and Business Media, LLC
Pages	403-418
Number of pages	16
ISBN (Print)	9781461435198
DOIs	https://doi.org/10.1007/978-1-4614-3520-4_38
State	Published - 2012
Event	5th Statistical Challenges in Modern Astronomy Symposium, SCMA 2011 - University Park, PA, United States Duration: Jun 13 2011 → Jun 15 2011

Publication series

Name	Lecture Notes in Statistics
Volume	209
ISSN (Print)	0930-0325
ISSN (Electronic)	2197-7186

Conference

Conference	5th Statistical Challenges in Modern Astronomy Symposium, SCMA 2011
Country/Territory	United States
City	University Park, PA
Period	06/13/11 → 06/15/11

Access to Document

10.1007/978-1-4614-3520-4_38

Cite this

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title = "Slepianwavelet variances for regularly and irregularly sampled time series",

abstract = "We discuss approximate scale-based analysis of variance for Gaussian time series based upon Slepian wavelets. These wavelets arise as eigenfunctions of an energy maximization problem in a pass band of frequencies. Unlike the commonly used Daubechies wavelets, Slepian wavelets have the ability to accommodate both regularly and irregularly sampled data. For regularly sampled Gaussian time series, we derive statistical theory for Slepian-based wavelet variances and show that it is comparable to Daubechies-based variances. For irregularly sampled time series data, we derive a corresponding statistical theory for Slepian-based wavelet variances. We demonstrate its use on X-ray fluctuations from a binary star system and on a light curve from the variable star Z UMa.",

author = "Debashis Mondal and Percival, \{Donald B.\}",

year = "2012",

doi = "10.1007/978-1-4614-3520-4\_38",

language = "English",

isbn = "9781461435198",

series = "Lecture Notes in Statistics",

publisher = "Springer Science and Business Media, LLC",

pages = "403--418",

booktitle = "Statistical Challenges in Modern Astronomy V",

note = "5th Statistical Challenges in Modern Astronomy Symposium, SCMA 2011 ; Conference date: 13-06-2011 Through 15-06-2011",

}

Mondal, D & Percival, DB 2012, Slepianwavelet variances for regularly and irregularly sampled time series. in Statistical Challenges in Modern Astronomy V. Lecture Notes in Statistics, vol. 209, Springer Science and Business Media, LLC, pp. 403-418, 5th Statistical Challenges in Modern Astronomy Symposium, SCMA 2011, University Park, PA, United States, 06/13/11. https://doi.org/10.1007/978-1-4614-3520-4_38

TY - GEN

T1 - Slepianwavelet variances for regularly and irregularly sampled time series

AU - Mondal, Debashis

AU - Percival, Donald B.

PY - 2012

Y1 - 2012

N2 - We discuss approximate scale-based analysis of variance for Gaussian time series based upon Slepian wavelets. These wavelets arise as eigenfunctions of an energy maximization problem in a pass band of frequencies. Unlike the commonly used Daubechies wavelets, Slepian wavelets have the ability to accommodate both regularly and irregularly sampled data. For regularly sampled Gaussian time series, we derive statistical theory for Slepian-based wavelet variances and show that it is comparable to Daubechies-based variances. For irregularly sampled time series data, we derive a corresponding statistical theory for Slepian-based wavelet variances. We demonstrate its use on X-ray fluctuations from a binary star system and on a light curve from the variable star Z UMa.

AB - We discuss approximate scale-based analysis of variance for Gaussian time series based upon Slepian wavelets. These wavelets arise as eigenfunctions of an energy maximization problem in a pass band of frequencies. Unlike the commonly used Daubechies wavelets, Slepian wavelets have the ability to accommodate both regularly and irregularly sampled data. For regularly sampled Gaussian time series, we derive statistical theory for Slepian-based wavelet variances and show that it is comparable to Daubechies-based variances. For irregularly sampled time series data, we derive a corresponding statistical theory for Slepian-based wavelet variances. We demonstrate its use on X-ray fluctuations from a binary star system and on a light curve from the variable star Z UMa.

UR - https://www.scopus.com/pages/publications/84896636646

U2 - 10.1007/978-1-4614-3520-4_38

DO - 10.1007/978-1-4614-3520-4_38

M3 - Conference contribution

AN - SCOPUS:84896636646

SN - 9781461435198

T3 - Lecture Notes in Statistics

SP - 403

EP - 418

BT - Statistical Challenges in Modern Astronomy V

PB - Springer Science and Business Media, LLC

T2 - 5th Statistical Challenges in Modern Astronomy Symposium, SCMA 2011

Y2 - 13 June 2011 through 15 June 2011

ER -

Slepianwavelet variances for regularly and irregularly sampled time series

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