Wavelet shrinkage for regression models with random design and correlated errors

Wavelet shrinkage for regression models with random design and correlated errors

Extraction of a signal in the presence of stochastic noise via wavelet shrinkage has been studied under assumptions that the noise is independent and identically distributed (IID) and that the samples are equispaced (evenly spaced in time). Previous work has relaxed these assumptions either to allow...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:Brazilian Journal of Probability and Statistics. - Brazilian Statistical Association. - 30(2016), 4, Seite 614-652
1. Verfasser: Porto, Rogério (VerfasserIn)
Weitere Verfasser: Morettin, Pedro, Percival, Donald, Aubin, Elisete
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2016
Zugriff auf das übergeordnete Werk:Brazilian Journal of Probability and Statistics
Schlagworte:Mathematics Biological sciences Applied sciences Physical sciences
LEADER 01000caa a22002652 4500
001 JST139318666
003 DE-627
005 20240626004559.0
007 cr uuu---uuuuu
008 240117s2016 xx |||||o 00| ||eng c
035 |a (DE-627)JST139318666 
035 |a (JST)24913885 
040 |a DE-627  |b ger  |c DE-627  |e rakwb 
041 |a eng 
100 1 |a Porto, Rogério  |e verfasserin  |4 aut 
245 1 0 |a Wavelet shrinkage for regression models with random design and correlated errors 
264 1 |c 2016 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
520 |a Extraction of a signal in the presence of stochastic noise via wavelet shrinkage has been studied under assumptions that the noise is independent and identically distributed (IID) and that the samples are equispaced (evenly spaced in time). Previous work has relaxed these assumptions either to allow for correlated observations or to allow for random sampling, but very few papers have relaxed both together. In this paper we relax both assumptions by assuming the noise to be a stationary Gaussian process and by assuming a random sampling scheme dictated either by a uniform distribution or by an evenly spaced design subject to jittering. We show that, if the data are treated as if they were autocorrelated and equispaced, the resulting wavelet-based shrinkage estimator achieves an almost optimal convergence rate. We investigate the efficacy of the proposed methodology via simulation studies and illustrate it by the extraction of the light curve for a variable star. 
540 |a Copyright © 2016 Brazilian Statistical Association 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Error rates 
650 4 |a Biological sciences  |x Agriculture  |x Farming  |x Crop production  |x Crop harvesting  |x Manual harvesting  |x Threshing 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Inferential statistics  |x Statistical estimation  |x Estimation methods  |x Estimators 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Measures of variability  |x Statistical variance 
650 4 |a Applied sciences  |x Engineering  |x Electrical engineering  |x Signal processing  |x Signal noise 
650 4 |a Physical sciences  |x Metrology  |x Optical measurement  |x Photometry  |x Light curves 
650 4 |a Applied sciences  |x Engineering  |x Electrical engineering  |x Signal processing  |x Autocorrelation 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Correlations  |x Correlation analysis  |x Correlation coefficients 
650 4 |a Physical sciences  |x Astronomy  |x Astronomical objects  |x Stars  |x Variable stars 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables 
655 4 |a research-article 
700 1 |a Morettin, Pedro  |e verfasserin  |4 aut 
700 1 |a Percival, Donald  |e verfasserin  |4 aut 
700 1 |a Aubin, Elisete  |e verfasserin  |4 aut 
773 0 8 |i Enthalten in  |t Brazilian Journal of Probability and Statistics  |d Brazilian Statistical Association  |g 30(2016), 4, Seite 614-652  |w (DE-627)563175516  |w (DE-600)2422319-0  |x 23176199  |7 nnns 
773 1 8 |g volume:30  |g year:2016  |g number:4  |g pages:614-652 
856 4 0 |u http://www.jstor.org/stable/24913885  |3 Volltext 
912 |a GBV_USEFLAG_A 
912 |a SYSFLAG_A 
912 |a GBV_JST 
912 |a GBV_ILN_11 
912 |a GBV_ILN_20 
912 |a GBV_ILN_22 
912 |a GBV_ILN_23 
912 |a GBV_ILN_24 
912 |a GBV_ILN_31 
912 |a GBV_ILN_39 
912 |a GBV_ILN_40 
912 |a GBV_ILN_60 
912 |a GBV_ILN_62 
912 |a GBV_ILN_63 
912 |a GBV_ILN_65 
912 |a GBV_ILN_69 
912 |a GBV_ILN_70 
912 |a GBV_ILN_73 
912 |a GBV_ILN_95 
912 |a GBV_ILN_100 
912 |a GBV_ILN_101 
912 |a GBV_ILN_105 
912 |a GBV_ILN_110 
912 |a GBV_ILN_120 
912 |a GBV_ILN_151 
912 |a GBV_ILN_161 
912 |a GBV_ILN_170 
912 |a GBV_ILN_206 
912 |a GBV_ILN_213 
912 |a GBV_ILN_230 
912 |a GBV_ILN_285 
912 |a GBV_ILN_293 
912 |a GBV_ILN_370 
912 |a GBV_ILN_374 
912 |a GBV_ILN_602 
912 |a GBV_ILN_702 
912 |a GBV_ILN_2001 
912 |a GBV_ILN_2003 
912 |a GBV_ILN_2005 
912 |a GBV_ILN_2006 
912 |a GBV_ILN_2008 
912 |a GBV_ILN_2009 
912 |a GBV_ILN_2010 
912 |a GBV_ILN_2011 
912 |a GBV_ILN_2014 
912 |a GBV_ILN_2015 
912 |a GBV_ILN_2018 
912 |a GBV_ILN_2020 
912 |a GBV_ILN_2021 
912 |a GBV_ILN_2026 
912 |a GBV_ILN_2027 
912 |a GBV_ILN_2044 
912 |a GBV_ILN_2050 
912 |a GBV_ILN_2056 
912 |a GBV_ILN_2057 
912 |a GBV_ILN_2061 
912 |a GBV_ILN_2088 
912 |a GBV_ILN_2107 
912 |a GBV_ILN_2110 
912 |a GBV_ILN_2190 
912 |a GBV_ILN_2949 
912 |a GBV_ILN_2950 
912 |a GBV_ILN_4012 
912 |a GBV_ILN_4035 
912 |a GBV_ILN_4037 
912 |a GBV_ILN_4046 
912 |a GBV_ILN_4112 
912 |a GBV_ILN_4125 
912 |a GBV_ILN_4126 
912 |a GBV_ILN_4242 
912 |a GBV_ILN_4249 
912 |a GBV_ILN_4251 
912 |a GBV_ILN_4305 
912 |a GBV_ILN_4306 
912 |a GBV_ILN_4307 
912 |a GBV_ILN_4313 
912 |a GBV_ILN_4322 
912 |a GBV_ILN_4323 
912 |a GBV_ILN_4324 
912 |a GBV_ILN_4325 
912 |a GBV_ILN_4326 
912 |a GBV_ILN_4335 
912 |a GBV_ILN_4338 
912 |a GBV_ILN_4346 
912 |a GBV_ILN_4367 
912 |a GBV_ILN_4393 
912 |a GBV_ILN_4700 
951 |a AR 
952 |d 30  |j 2016  |e 4  |h 614-652