#### DMCA

## Ideal spatial adaptation by wavelet shrinkage (1994)

Venue: | Biometrika |

Citations: | 1236 - 5 self |

### Citations

5781 | Classification and Regression Trees - Breiman, Friedman, et al. - 1984 |

2163 | Orthonormal bases of compactly supported wavelets - DAUBECHIES - 1988 |

1012 | An introduction to wavelets - Chui - 1992 |

361 | Subset Selection in Regression - Miller - 2002 |

201 | Littlewood-Paley theory and the study of function spaces - Frazier, Jawerth, et al. - 1991 |

197 |
Classi cation and regression trees
- Breiman, Friedman, et al.
- 1984
(Show Context)
Citation Context ...e thatLis a variable. The reconstruction formula is TPC(y� )(t)= LX `=1 Ave(yi :ti 2I`)1I ` (t)� piecewise constant reconstruction using the mean of the data within each piece to estimate the pieces. =-=[2]-=-. Piecewise PolynomialsT PP(D)(y� ). Here the interpretation of is the same as in [1], only the reconstruction uses polynomials of degreeD. T PP(D)(y� )(t)= 2 LX `=1 ^p`(t)1I ` (t)�swhere ^p`(t) = PD ... |

112 |
Multiresolution Analysis, Wavelets, and Fast Algorithms on an Interval," Comptes Rendus Academie des Sciences
- Cohen, Daubechies, et al.
- 1993
(Show Context)
Citation Context ...ty, and if f = T V K;2 (y; ffi ) thensf(t) = 1 n n X i=1 y i K ` t \Gamma t i ffi (t) ' OE ffi (t): (3) More refined versions of this formula would adjust K for boundary effects near t = 0 and t = 1. =-=[5]-=-. Variable-Bandwidth High-Order Kernels T V K;D (y; ffi ), D ? 2. Here ffi is again the local bandwidth, and the reconstruction formula is as in (3), only K(\Delta) is a C D function integrating to 1,... |

110 | Flexible parsimonious smoothing and additive modeling - Friedman, Silverman - 1989 |

107 | Variable kernel density estimation - Terrell, Scott - 1992 |

46 | Ondelettes sur l'intervalle - Meyer - 1991 |

45 |
Locally Adaptive Bandwidth Choice for Kernel Regression Estimators
- Brockmann, Gasser, et al.
- 1993
(Show Context)
Citation Context ...(t) = L X `=1sp ` (t)1 I ` (t); wheresp ` (t) = P D k=0 a k t k is determined by applying the least squares principle to the data arising for interval I ` X t i 2I ` (p ` (t i ) \Gamma y i ) 2 = min! =-=[3]-=-. Variable-Knot Splines T spl;D (y; ffi ). Here ffi defines a partition as above, and on each interval of the partition the reconstruction formula is a polynomial of degree D, but now the reconstructi... |

45 | An adaptive algorithm of nonparametric filtering - Pinsker - 1984 |

43 | Variable bandwidth kernel estimators of regression curves - Müller, Stadtmuller - 1987 |

27 | Ondelettes et Opérateurs I: Ondelettes, Hermann Éditeurs - Meyer - 1990 |

20 | Selection of subsets of regression variables (with discussion - Miller - 1984 |

19 | On problems of adaptive estimation in white Gaussian noise - Lepskii - 1992 |

11 |
Minimax estimation of a normal mean subject to doing well at a point
- Bickel
- 1983
(Show Context)
Citation Context ...onstruction formula with "spatial smoothing" parameter ffi , and d(y) is a data-adaptive choice of the spatial smoothing parameter ffi. A clearer picture of what we intend emerges from five =-=examples. [1]-=-. Piecewise Constant Reconstruction T PC (y; ffi ). Here ffi is a finite list of, say, L real numbers defining a partition (I 1 ; : : : ; I L ) of [0; 1] via I 1 = [0; ffi 1 ); I 2 = [ffi 1 ; ffi 1 + ... |

6 | Multivariate additive regression splines, (with discussion - Friedman - 1991 |

4 | A learning algorithm for nonparametric ltering - Pinsker - 1984 |

1 |
Superefficiency and lack of adaptability in nonparametric functional estimation. To appear, Annals of Statistics
- BROWN
- 1993
(Show Context)
Citation Context ...mials s(t) satisfying / d dt k s ! (�� ` \Gamma) = / d dt k s ! (�� ` +) for k = 0; : : : ; D \Gamma 1, ` = 2; : : : ; L; subject to this constraint, one solves n X i=1 (s(t i ) \Gamma y i ) 2=-= = min! [4]. Variable-=- Bandwidth Kernel Methods T V K;2 (y; ffi). Now ffi is a function on [0; 1]; ffi (t) represents the "bandwidth of the kernel at t"; the smoothing kernel K is a C 2 function of compact suppor... |

1 | The risk inflation of variable selection in regression - GEORGE |

1 | Ondelettes sur l'Intervalle: algorithmes rapides - MALGOUYRES - 1991 |

1 | Variable bandwidth kernel estimators of regression curves - ULLER, Hans-Georg - 1987 |

1 |
Supere ciency and lack of adaptability in nonparametric functional estimation. To appear, Annals of Statistics
- BROWN, LOW
- 1993
(Show Context)
Citation Context ...ion is chosen from among those piecewise polynomialss(t) satisfying k d s dt ! ( `;) = k d s dt ! ( `+) fork =0�:::�D; 1,` =2�:::�L� subject to this constraint, one solves nX i=1 (s(ti) ;yi) 2 = min! =-=[4]-=-. Variable Bandwidth Kernel MethodsTVK�2(y� ). Now is a function on [0� 1]� (t) represents the \bandwidth of the kernel att"� the smoothing kernelKis aC 2 function of compact support which is also a p... |

1 | The risk in ation of variable selection in regression - GEORGE, Foster |