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Page 8996 of Mathematical Reviews Vol. , Issue 99m
[page]
1999
Mathematical Reviews
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(x) = x~‘sinc(log(x)) = a a This paper has the aim of mathematically establishing the expo- nential sampling theorem using the Mellin transform approach. ...
sampling theorem. ...
Wavelet Packets of Fractional Brownian Motion: Asymptotic Analysis and Spectrum Estimation
2010
IEEE Transactions on Information Theory
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From this analysis, we derive wavelet packet based spectrum estimation for fractional Brownian motions and wide-sense stationary random processes. ...
This paper provides asymptotic properties of the autocorrelation functions of the wavelet packet coefficients of a fractional Brownian motion. ...
A. Wavelet Packet Based Spectrum Estimation From Theorems 1 and 3, we have that is close to with a good precision when and are large 6 . ...
doi:10.1109/tit.2010.2053865
fatcat:uqgtns5iznhkzhkgacj5z7oame
Using wavelets to obtain a consistent ordinary least squares estimator of the long‐memory parameter
1999
Journal of Forecasting
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Using the wavelet transform from a fractionally integrated process, we establish a log-linear relationship between the wavelet coecients' variance and the scaling parameter equal to the log-memory parameter ...
We derive the small sample bias and variance of the ordinary least squares estimator and test it against the GPH estimator and the McCoy±Walden maximum likelihood wavelet estimator by conducting a number ...
The Monte Carlo simulations bore this out and showed that the wavelet OLS estimator possesses a smaller mean square error than the GPH estimator for small and large sample sizes and for dierent values ...
doi:10.1002/(sici)1099-131x(199901)18:1<17::aid-for686>3.3.co;2-d
fatcat:d2tqj6kwlnajnfkhlt2jvrqime
Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter
1999
Journal of Forecasting
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A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
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Using the wavelet transform from a fractionally integrated process, we establish a log-linear relationship between the wavelet coecients' variance and the scaling parameter equal to the log-memory parameter ...
We derive the small sample bias and variance of the ordinary least squares estimator and test it against the GPH estimator and the McCoy±Walden maximum likelihood wavelet estimator by conducting a number ...
The Monte Carlo simulations bore this out and showed that the wavelet OLS estimator possesses a smaller mean square error than the GPH estimator for small and large sample sizes and for dierent values ...
doi:10.1002/(sici)1099-131x(199901)18:1<17::aid-for686>3.0.co;2-m
fatcat:dwjtxmsisvfi7p3r4yaleyjyca
MEDL and MEDLA: Methods for Assessment of Scaling by Medians of Log-Squared Nondecimated Wavelet Coefficients
[article]
2017
arXiv
pre-print
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In a simulation study we use fractional Brownian motions with a range of theoretical Hurst exponents. ...
At the same time, non-decimated transforms have a number of advantages when employed for calculation of wavelet spectra and estimation of Hurst exponents: the variance of the estimator is smaller, input ...
The following theorem serves as a basis for the MEDL estimator: Theorem 3.1. ...
arXiv:1703.04180v1
fatcat:d4smnmsuyzdbdkgtr6md276s6a
Fractal estimation from noisy data via discrete fractional Gaussian noise (DFGN) and the Haar basis
1993
IEEE Transactions on Signal Processing
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The auditory wavelet transform simulates the human auditory periphery as a first-order approximation because the wavelet theory requires the use of time invariant filters that all have the same shape on ...
The auditory wavelet transform and the reconstruction algorithm may nevertheless improve signal production for auditory psychological experiments and other applications. ...
Editor coordinating the review of this paper and approving it for publication was Dr. Ahmed Tewfik. This work was supported by a National ...
doi:10.1109/78.258096
fatcat:bwjj33q3kjfxflequkeks2mbzu
Continuous wavelet estimation for multivariate fractional Brownian motion
2022
Pakistan Journal of Statistics and Operation Research
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In this paper, we propose a method using continuous wavelets to study the multivariate fractional Brownian motion through the deviations of the transformed random process to find an efficient estimate ...
The estimation process was made by calculating the eigenvalues for the variance-covariance matrix of Meyer's continuous wavelet details coefficients. ...
In this section, Meyer wavelets will be used for the purpose of obtaining an efficient estimate of the Hurst parameter, starting with the definition of the general form for the wavelet transformation in ...
doi:10.18187/pjsor.v18i3.3657
fatcat:jtg56gjvzjegvnt34mlg4guwoi
Wavelet Power: Wavelet Energy Ratio Unit Root Tests
2012
Social Science Research Network
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This paper uses wavelet theory to propose a frequency domain nonparametric and tuning parameter free family of unit root tests indexed by the fractional parameter d. ...
The proposed test exploits the wavelet power spectrum of the observed series and its fractional partial sum to construct a test of the unit root based on the ratio of the resulting scaling energies. ...
In fact, the latter test requires the estimation of the long-term variance of the error terms using the Newey and West (1987) estimator using a Bartlett kernel with a bandwidth tuning parameter. ...
doi:10.2139/ssrn.2131529
fatcat:i5h6szhadbbn7mru3gpzrzfj2q
A wavelet lifting approach to long-memory estimation
2016
Statistics and computing
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This article proposes a new Hurst exponent estimation method which naturally copes with data sampling irregularity. ...
The new method is based on a multiscale lifting transform exploiting its ability to produce wavelet-like coefficients on irregular data and, simultaneously, to effect a necessary powerful decorrelation ...
, Jensen (1999, Theorem 2) for fractionally integrated processes or Theorem 5.1 of Craigmile and Percival (2005) for fractionally differenced processes, our proposition establishes the result for the ...
doi:10.1007/s11222-016-9698-2
pmid:32025109
pmcid:PMC6979511
fatcat:bgrgeyu6bjhr7hxwukz3wnamiy
Wavelet Transform Method of Waveform Estimation for Hilbert Transform of Fractional Stochastic Signals with Noise
[chapter]
2001
Lecture Notes in Computer Science
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H ] become another processes, that firstly taking Hilbert transform for the wavelet function ) (t φ and forming a new wavelet function ) (t ψ , secondly taking the wavelet transform for ) (t B H . ...
In this paper, those splendid characters of the Hilbert transform let the processes that taking wavelet transform after taking Hilbert transform for the statistic self-similarity processes FBM [ ) (t B ...
by inverse Hilbert transform of the signal infigure 4, where M=2, and the error of signal's estimation deta=0.5591. ...
doi:10.1007/3-540-45333-4_36
fatcat:n6hqnvdkdndpdmxdrqvd7f4zle
Asymptotically Sufficient Statistics in Nonparametric Regression Experiments with Correlated Noise
2009
Journal of Probability and Statistics
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These results provide a theoretical motivation for some commonly proposed wavelet estimation techniques. ...
fractional Brownian motion. ...
This is a convenient form for the error, but not completely unrealistic. Wavelet decompositions nearly whiten the fractional Brownian motion process. ...
doi:10.1155/2009/275308
fatcat:dcsqe3ztlzhuzkrux6mjntwfbu
Prediction Based on a Multiscale Decomposition
2003
International Journal of Wavelets, Multiresolution and Information Processing
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A wavelet-based forecasting method for time series is introduced. ...
In its simplest form it is a linear prediction based on a wavelet transform of the signal. ...
A j = 2 for all resolution levels j, and a wavelet transform with five scales (four wavelet scales + the smoothed array). ...
doi:10.1142/s0219691303000153
fatcat:kxf2le6osnfsriqzvtyeg7zcrq
Intermittent process analysis with scattering moments
2015
Annals of Statistics
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They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and modulus nonlinearities, which preserves the variance. ...
The Generalized Method of Simulated Moments is applied to scattering moments to estimate data generating models. ...
The following theorem, proved in Appendix G in [10] , gives an upper bound of the mean squared estimation error at each scale: Theorem 5.1. ...
doi:10.1214/14-aos1276
fatcat:glc7xogqivf7nihkh4pidcfyie
Estimation of 1/f noise
1998
IEEE Transactions on Information Theory
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Combined with a survey of non-wavelet-based methods, these new results give a perspective on the various tradeoffs to be considered when modeling and estimating 1=f noise processes. ...
sense to mean a process with spectrum like 1=f with any not necessarily equal to one. ...
To begin with, given a signal and wavelet , the wavelet transform of at time and scale is defined as [9] d (4) A key feature of this transform [16] , [32] is that if , then even though is nonstationary ...
doi:10.1109/18.650986
fatcat:imci3dh5y5dcxkxhd2mhtqht7q
Estimation of fractional Brownian motion embedded in a noisy environment using nonorthogonal wavelets
1999
IEEE Transactions on Signal Processing
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For fractal signal estimation, Wiener ltering is explicitly formulated as a function of the signal and noise parameters and the wavelets. We show that the estimated signal is an 1 f process. ...
We show that non-orthogonal wavelets can characterize the fractional Brownian motion (fBm) that is in white noise. ...
Liu, Jen-Chang for helping me with the simulation data. Also, I would like to thank Professor Cheng, Hsuanjen and Professor Stephane Mallat for valuable advice and comments. ...
doi:10.1109/78.774764
fatcat:2sokbd3qdfg5pikyvccp7o4qwy
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