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http://dx.doi.org/10.5351/CKSS.2008.15.3.379

The Choice of a Primary Resolution and Basis Functions in Wavelet Series for Random or Irregular Design Points Using Bayesian Methods  

Park, Chun-Gun (Seoul Development Institute)
Publication Information
Communications for Statistical Applications and Methods / v.15, no.3, 2008 , pp. 379-386 More about this Journal
Abstract
In this paper, the choice of a primary resolution and wavelet basis functions are introduced under random or irregular design points of which the sample size is free of a power of two. Most wavelet methods have used the number of the points as the primary resolution. However, it turns out that a proper primary resolution is much affected by the shape of an unknown function. The proposed methods are illustrated by some simulations.
Keywords
Wavelet series; primary resolution; wavelet basis functions; Bayesian methods;
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1 Pensky, M. and Vidakovic, B. (2001). On non-equally spaced wavelet regression, Annals of the Institute of Statistical Mathematics, 53, 681-690   DOI
2 Cai, T. and Brown, L. D. (1998). Wavelet shrinkage for nonequispaced samples, The Annals of Statistics, 26, 1783-1799   DOI
3 HAardle, W., Kerkyacharian, G., Picard, D. and Tsybakov, A. (1998). Wavelets, Approximation and Statistical Applications, (Lecture notes in statistics), 129, Springer, New York
4 Mallat, S. G. (1989). A theory for multiresolution signal decomposition: The wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674-693   DOI   ScienceOn
5 Hall, P. and Patil, P. (1995). Formulae for mean integrated squared error of nonlinear wavelet-based density estimators, The Annals of statistics, 23, 905-928   DOI
6 Kovac, A. and Silverman, B. W. (2000). Extending the scope of wavelet regression methods by coefficient-dependent thresholding, Journal of the American Statistical Association, 95, 172-183   DOI
7 Maxim, V. (2002). Denoising signals observed on a random design, Paper presented to the fifth AFA-SMAI conference on curves and surfaces
8 Park, C. G., Oh, H. S. and Lee, H. (2008). Bayesian selection of primary resolution and wavelet basis functions for wavelet regression, Computational Statistics, 23, 291-302   DOI
9 Vidakovic, B. (1999). Linear versus nonlinear rules for mixture normal priors, Annals of Institute of Statistical Mathematics, 51, 111-124   DOI
10 Daubechies, I. (1992). Ten Lectures on Wavelets. (CBMS-NSF regional conference series in applied mathematics), SIAM: Society for industrial and applied mathmatics, Philadelphia
11 Abramovich, F., Bailey, T. C. and Sapatinas, T. (2000). Wavelet analysis and its statistical applications, The Statistician, 49, 1-29
12 Antoniadis, A., Bigot, J. and Sapatinas, T. (2001). Wavelet estimators in nonparametric regression: A comparative simulation study, Journal of Statistical Software, 6
13 Antoniadis, A., Gregoire, G. and Vial, P. (1997). Random design wavelet curve smoothing, Statistics & Probability Letters, 35, 225-232   DOI   ScienceOn
14 Antoniadis, A. and Sapatinas, T. (2001). Wavelet shrinkage for natural exponential families with quadratic variance functions, Biometrika, 88, 805-820   DOI   ScienceOn