## Nonlinear Wavelet Shrinkage With Bayes Rules and Bayes Factors (1998)

Venue: | Journal of the American Statistical Association |

Citations: | 125 - 19 self |

### BibTeX

@ARTICLE{Vidakovic98nonlinearwavelet,

author = {Brani Vidakovic},

title = {Nonlinear Wavelet Shrinkage With Bayes Rules and Bayes Factors},

journal = {Journal of the American Statistical Association},

year = {1998},

volume = {93},

pages = {173--179}

}

### Years of Citing Articles

### OpenURL

### Abstract

this article a wavelet shrinkage by coherent

### Citations

1475 |
Statistical Decision Theory and Bayesian Analysis
- Berger
- 1985
(Show Context)
Citation Context ... Thus the choice is most uninformative, given the moment: oe 2sE(); (f(oe 2 j) = e \Gammaoe 2 ): (3) There are several other standard ways of integrating out oe 2 . (For an account of that issue, see =-=Berger 1985-=-.) The marginal model (marginal likelihood) for dj` is the double exponential, dj`sDE(`; 1 p 2 ); (4) with the density given by f(dj`) = 1 2 p 2e \Gamma p 2jd\Gamma`j : Equation (4) follows from the f... |

959 | Ideal spatial adaptation by wavelet shrinkage - Donoho, Johnstone - 1994 |

839 | An Introduction to Wavelets - Chui - 1992 |

800 | Adapting to unknown smoothness via wavelet shrinkage - Donoho, Johnstone - 1995 |

377 | Wavelets and Operators - Meyer - 1992 |

276 | Minimax Estimation via Wavelet Shrinkage - Donoho, Johnstone - 1998 |

258 | Wavelet Shrinkage: Asymptopia - Donoho, Johnstone, et al. - 1994 |

186 | Adaptive Bayesian wavelet shrinkage - Chipman, Kolaczyk, et al. - 1997 |

128 | Multiple shrinkage and subset selection in wavelets - Clyde, Parmigiani, et al. - 1998 |

119 | Nonlinear wavelet methods for recovery of signals, densities, and spectra from noisy and incomplete data - Donoho |

107 |
Essential Wavelets for Statistical Applications and Data Analysis. Birkhauser
- Ogden
- 1997
(Show Context)
Citation Context ...he most interesting, applicable, and burgeoning research areas in mathematics, signal processing, and statistics today. (For a nice overview of wavelet applications in statistics, see Walter 1994 and =-=Ogden 1996-=-. The standard reference on wavelets is the monograph of Daubechies 1992; For an elementary introduction to wavelets, see Vidakovic and Muller 1994.) 3 Nonlinear wavelet shrinkage is the main focus of... |

87 | The discrete wavelet transform in S - Nason, Silverman - 1994 |

75 |
Wavelets and other orthogonal systems with applications
- Walter
- 1994
(Show Context)
Citation Context ...ke them one of the most interesting, applicable, and burgeoning research areas in mathematics, signal processing, and statistics today. (For a nice overview of wavelet applications in statistics, see =-=Walter 1994-=- and Ogden 1996. The standard reference on wavelets is the monograph of Daubechies 1992; For an elementary introduction to wavelets, see Vidakovic and Muller 1994.) 3 Nonlinear wavelet shrinkage is th... |

71 | Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criterion - Saito - 1994 |

46 | Wavelet methods for curve estimation - Antoniadis, Grégoire, et al. - 1994 |

46 | On scale mixtures of normal distributions - West - 1987 |

36 | Function estimation via wavelet shrinkage for long-memory data - Wang - 1996 |

35 | Understanding waveShrink: variance and bias estimation.Biometrika - Bruce, Gao - 1996 |

26 | Wavelet regression by cross-validation - Nason - 1994 |

23 | Choice of the threshold parameter in wavelet function estimation - Nason - 1995 |

13 | New Minimax Theorems, Thresholding, and Adaptation - Donoho, Johnstone - 1992 |

12 |
Testing precise hypothesis
- Berger, Delampady
- 1987
(Show Context)
Citation Context ...inuous prior density will give the prior (and hence the posterior) probability of 0 to the precise hypothesis. (For a discussion on testing precise hypotheses in Bayesian fashion, see Berger 1985 and =-=Berger and Delampady 1987-=-.) Start with the marginal likelihood (the parameter oe 2 is integrated out) dj`sf(dj`); where the meanings of d and ` are the same as in the previous section. After observing d; test the hypothesis H... |

12 | Choice of thresholds for wavelets estimation of the log-spectrum - Gao - 1993 |

12 | Bayesian inference with wavelets: density estimation
- MuÈller, Vidakovic
- 1998
(Show Context)
Citation Context ...itening property of wavelet transformations), address uncertainty about the variances, and yield almost closed-form posterior expectations. The ongoing research (Clyde, Parmigiani and Vidakovic 1997; =-=Muller and Vidakovic 1995-=-) make the prior structure more realistic by addressing the issue of dependence issue by making priors dependent on the levels. The price for such prior modeling is increased calculational complexity ... |

10 | Wavelets for kids - a tutorial introduction - Vidakovíc, Müller |

10 | On Smoothing a Probability Density Function - Whittle - 1958 |

10 | Bayesian method of moments/instrumental variable (BMOM/IV) analysis of mean and regression models - Zellner - 1994 |

9 | Function estimation via wavelets for data with long-range dependence - Wang - 1994 |

8 |
Univariate density estimation by orthogonal series
- Brunk
- 1978
(Show Context)
Citation Context ...nt thresholding methods was given by Nason (1995). Motivated by a body of work in nonparametric density estimation using orthogonal series and their intrinsic connections with Bayesian methods (e.g., =-=Brunk 1978-=-; Wahba 1981), I approached the problem of wavelet regression from a Bayesian standpoint. Bayes rules generally are shrinkers, and estimating wavelet coefficients in Bayesian fashion is a form of wave... |

7 | Density estimation by orthogonal series - Watson - 1969 |

5 | A note on random densities via wavelets - Vidakovic - 1996 |

4 |
Data Based Optimal Smoothing or Orthogonal Series Density Estimates
- Wahba
- 1981
(Show Context)
Citation Context ...ing methods was given by Nason (1995). Motivated by a body of work in nonparametric density estimation using orthogonal series and their intrinsic connections with Bayesian methods (e.g., Brunk 1978; =-=Wahba 1981-=-), I approached the problem of wavelet regression from a Bayesian standpoint. Bayes rules generally are shrinkers, and estimating wavelet coefficients in Bayesian fashion is a form of wavelet shrinkag... |

4 | Minimax risk over l p -balls for l q -error - DONOHO, JOHNSTONE - 1992 |

4 | Spectral density estimation via wavelet shrinkage - Gao - 1993 |

3 | Wavelets and Bayesian Statistics, Invited Talk at Interface 94 - Vidakovic - 1994 |

3 | Jump and sharp cusp detection by wavelets - One dimensional case - Wang - 1994 |

2 | Estimating a Holder Continuous Function from a Noisy Sample via Shrinkage and Truncation of Wavelet Coefficients - Wang - 1993 |

1 |
Wavelets for Kids, Tutorial Introduction," Discussion Paper 94-13
- Vidakovic, Muller
- 1994
(Show Context)
Citation Context ...overview of wavelet applications in statistics, see Walter 1994 and Ogden 1996. The standard reference on wavelets is the monograph of Daubechies 1992; For an elementary introduction to wavelets, see =-=Vidakovic and Muller 1994-=-.) 3 Nonlinear wavelet shrinkage is the main focus of this article. A formal statement of the problem is given next. Let t i ; i = 1; : : : ; N be a sequence of equally spaced points. Let f i = f(t i ... |

1 | An introduction to the Daubechies D4 wavelet with statistical applications - Bock - 1994 |

1 | Wavelet transformations for non-uniform designs. Interface '94 - Bock, Lu - 1994 |

1 | Heuristic estimation of probability densities - Fellner - 1974 |

1 | The Bayesian Choice. Springer-Verlag. The discrete wavelet transform in S - Robert - 1994 |