R3 on "What are the most important statistical ideas of the past 50 years? " Andrew Gelman, Aki Vehtari(34)


R3(References on References on References) on "What are the most important statistical ideas of the past 50 years? " Andrew Gelman, Aki Vehtari(34)

R3 on "What are the most important statistical ideas of the past 50 years? " Andrew Gelman, Aki Vehtari(0)
https://qiita.com/kaizen_nagoya/items/a8eac9afbf16d2188901


What are the most important statistical ideas of the past 50 years?
Andrew Gelman, Aki Vehtari
https://arxiv.org/abs/2012.00174

# References 

# 34
Donoho, D. L. (1995). De-noising by soft-thresholding. IEEE Transactions on Information Theory 41, 613–627.

https://www.semanticscholar.org/paper/De-noising-by-soft-thresholding-Donoho/2cc257b0c7db92f90c3224c35df7b8e85f57a090#references

## References on 34
## 34.1

Adapting to Unknown Smoothness via Wavelet Shrinkage
D. Donoho, I. Johnstone
Mathematics
1995
Abstract We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet… 

## References on 34.1

### 34.1.1


Wavelet Shrinkage: Asymptopia?
D. Donoho, I. Johnstone, G. Kerkyacharian, D. Picard
Mathematics
1995
Much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects-curves, densities, spectral densities, images-from noisy data. A now rich and complex body of… Expand
1,616
PDF

Save

Alert
Ideal spatial adaptation by wavelet shrinkage
D. Donoho, I. Johnstone
Mathematics
1994
SUMMARY With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline,… Expand
7,680
PDF

Save

Alert
Locally Adaptive Bandwidth Choice for Kernel Regression Estimators
M. Brockmann, T. Gasser, E. Herrmann
Mathematics
1993
Abstract Kernel estimators with a global bandwidth are commonly used to estimate regression functions. On the other hand, it is obvious that the choice of a local bandwidth can lead to better… Expand
163

Save

Alert
Data‐Driven Bandwidth Selection in Local Polynomial Fitting: Variable Bandwidth and Spatial Adaptation
Jianqing Fan, I. Gijbels
Mathematics
1995
When estimating a mean regression function and its derivatives, locally weighted least squares regression has proven to be a very attractive technique. The present paper focuses on the important… Expand
581
PDF

Save

Alert
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
S. Mallat
Computer Science, Mathematics
IEEE Trans. Pattern Anal. Mach. Intell.
1989
TLDR
It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/Sup j/ can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. Expand

### 34.1.6
A discrete transform and decompositions of distribution spaces
Michael Frazier, B. Jawerth
Mathematics
1990
Abstract We study a representation formula of the form ƒ = ∑ Q 〈ƒ, ϑ Q 〉ψ Q for a distribution ƒ on R n. This formula is obtained by discretizing and localizing a standard Littlewood-Paley… Expand
937
PDF

View 1 excerpt

Save

Alert
Empirical functionals and e cient smoothing parameter selection
P. Hall, I. Johnstone
Mathematics
1992
A striking feature of curve estimation is that the smoothing parameter h 0 , which minimizes the squared error of a kernel or smoothing spline estimator, is very difficult to estimate. This is… Expand
80

Save

Alert
Wavelets and Dilation Equations: A Brief Introduction
G. Strang
Mathematics, Computer Science
SIAM Rev.
1989
TLDR
It is shown in Part 1 how conditions on the $c_k $ lead to approximation properties and orthogonality properties of the wavelets, and the recursive algorithms that decompose and reconstruct f. Expand
1,081
PDF

View 1 excerpt

Save

Alert
Minimax risk overlp-balls forlp-error
D. Donoho, I. Johnstone
Mathematics
1994
SummaryConsider estimating the mean vector θ from dataNn(θ,σ2I) withlq norm loss,q≧1, when θ is known to lie in ann-dimensionallp ball,p∈(0, ∞). For largen, the ratio of minimaxlinear risk to minimax… Expand
140

Save

Alert
Asymptotic equivalence of nonparametric regression and white noise
L. Brown, Mark G. Low
Mathematics
1996
The principal result is that, under conditions, to any nonparametric regression problem there corresponds an asymptotically equivalent sequence of white noise with drift problems, and conversely.… Expand

### 34.1.11
Robust Locally Weighted Regression and Smoothing Scatterplots
W. Cleveland
Mathematics
1979
Abstract The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for… Expand
9,413
PDF

Save

Alert
Non‐Parametric Estimation of a Smooth Regression Function
R. M. Clark
Mathematics
1977
SUMMARY This paper presents a new family of non-parametric estimators of a smooth regression function, which are shown to have theoretical advantages in small samples over some alternative… Expand
61

View 1 excerpt, references background

Save

Alert
Interpolating Wavelet Transforms
D. Donoho
Computer Science
1992
We describe several \wavelet transforms" which characterize smoothness spaces and for which the coe cients are obtained by sampling rather than integration. We use them to re-interpret the empirical… Expand
288
PDF

Save

Alert
Littlewood-Paley Theory and the Study of Function Spaces
Michael Frazier, B. Jawerth, G. Weiss
Mathematics
1991
Calderon's formula and a decomposition of $L^2(\mathbb R^n)$ Decomposition of Lipschitz spaces Minimality of $\dot B^0,1_1$ Littlewood-Paley theory The Besov and Triebel-Lizorkin spaces The $\varphi$… Expand
726

View 2 excerpts, references background and methods

Save

Alert
Multifrequency channel decompositions of images and wavelet models
S. Mallat
Computer Science
IEEE Trans. Acoust. Speech Signal Process.
1989
TLDR
The author describes the mathematical properties of such decompositions and introduces the wavelet transform, which relates to the decomposition of an image into a wavelet orthonormal basis. Expand

### 34.1.16
Interpolation of Besov-Spaces
R. DeVore, V. Popov
Mathematics
1988
We investigate Besov spaces and their connection with dyadic spline approximation in Lp(Q), 0 < p < oo. Our main results are: the determination of the interpolation spaces between a pair of Besov… Expand
300
PDF

Save

Alert
Ten Lectures on Wavelets
I. Daubechies, C. Heil
Mathematics, Computer Science
1992
TLDR
This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases. Expand
15,205
Highly Influential
PDF

View 4 excerpts, references methods and background

Save

Alert
Orthonormal bases of compactly supported wavelets
I. Daubechies
Mathematics
1988
We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept… Expand
8,687
PDF

View 2 excerpts, references methods and background

Save

Alert
Theory Of Function Spaces
H. Triebel
Mathematics
1983
How to Measure Smoothness.- Atoms and Pointwise Multipliers.- Wavelets.- Spaces on Lipschitz Domains, Wavelets and Sampling Numbers.- Anisotropic Function Spaces.- Weighted Function Spaces.- Fractal… Expand
3,557

Save

Alert
Multiresolution analysis, wavelets and fast algorithms on an interval
A. Cohen, I. Daubechies, B. Jawerth, P. Vial
Mathematics
1993
Nous adaptons la construction classique des analyses multiresolutions et des bases orthonormees d'ondelettes au cadre des fonctions definies sur [0,1]. Les proprietes importantes des bases… Expand

### 34.1.21
Spline Smoothing in Regression Models and Asymptotic Efficiency in $L_2$
M. Nussbaum
Mathematics
1985
168
PDF

View 1 excerpt, references background

Save

Alert
Theory of point estimation
E. Lehmann
Mathematics, Computer Science
1950
TLDR
This paper presents a meta-analyses of large-sample theory and its applications in the context of discrete-time reinforcement learning, which aims to clarify the role of reinforcement learning in the reinforcement-gauging process. Expand
5,544
PDF

Save

Alert
Estimation d'une densité de probabilité par méthode d'ondelettes
Iain M. Johnstone, G. Kerkyacharian, D. Picard
Mathematics
1992
Nous proposons un cadre ou des estimateurs explicitement construits a partir des coefficients d'ondelettes se revelent strictement plus efficaces que les estimateurs habituels (noyaux, series… Expand
43

View 3 excerpts, references background

Save

Alert
From Stein's Unbiased Risk Estimates to the Method of Generalized Cross Validation
Ker-Chau Li
Mathematics
1985
On considere une methode interessante pour le choix d'estimateurs lineaires et on presente une nouvelle approche basee sur les estimateurs de Stein (1981)
160
PDF

Save

Alert
A Learning Algorithm for Nonparametric Filtering
Automat. i Telemeh
1984
Ten Lectures on Wavelets SIAM: Philadelphia
Ten Lectures on Wavelets SIAM: Philadelphia
1992
Spline smoothing and asymptotic e ciency in L2
Ann. Statist.,
1985
Universal Near Minimaxity of Wavelet Shrinkage
D. Donoho, I. Johnstone, G. Kerkyacharian, D. Picard
Mathematics
1997
We discuss a method for curve estimation based on n noisy data; one translates the empirical wavelet coefficients towards the origin by an amount \( \sqrt {{2\log \left( n \right)}} \cdot \sigma… Expand
52
PDF

Save

Alert
Minimax Estimation via Wavelet Shrinkage," submitted to The Annals of Statistics
Minimax Estimation via Wavelet Shrinkage," submitted to The Annals of Statistics
1995
S + WAVELETS Toolkit Statistics, a division of MathSoft Inc., Seattle WA
1995

### 34.1.31
S + WAVELETS Toolkit Statistics, a division of MathSoft Inc., Seattle WA
1995
Wavelet Shrinkage: Asymptopia?" (with discussion)
Journal of the Royal Statistical Society, Ser. B
1995
Ideal Spatial Adaptation via Wavelet ShrinkageMinimax Risk Over lp-Balls for lq-Errorl Probability Theory and Related Fields
Neo-Classical Minimax Problems, Thresholding, and Adaptation
1994
Ideal spacial adaptation via wavelet shrinkage
D. Donoho
Computer Science
1994
2,030

View 1 excerpt

Save

Alert
Comptes Rendus Academie des Sciences Paris (A)
Comptes Rendus Academie des Sciences Paris (A)
1992
Empirical Functionals and Efficient Smoothing Parameter Selection " ( with discussion ) , Journal of the Royal Statistical Society
1992
Empirical Functionals and Efficient Smoothing Parameter Selection" (with discussion)
Journal of the Royal Statistical Society, Ser. B
1992
Minimax risk over `p-balls for lq loss
Technical Report No. 401,
1992
Minimax risk overover`over`p -balls for l q loss
Minimax risk overover`over`p -balls for l q loss
1992
Multivariate Adaptive Regression Splines
J. Friedman
Mathematics
1991

### 34.1.41
Multivariate adaptive regression splines (with discussion)
J. Friedman
Mathematics
1991
1,235

Save

Alert
Ondelettes sur l'Intervalle. Revista Mathematica I b ero-Americana
1991
Ondelettes sur l'intervalle.
Y. Meyer
Mathematics
1991
194
PDF

Save

Alert
A Risk Bound in Sobolev Class Regression
G. Golubev, M. Nussbaum
Mathematics
1990
43
PDF

Save

Alert
Ondelettes et Operateurs; I: Ondelettes, II: Operateurs de Calder6n-Zygmund
1990
Ondelettes et Operateurs; I: Ondelettes, II: Operateurs de Calder6n-Zygmund, III: (with R. Coifman) Operateurs multilineaires
Hermann. (English translation
1990
Ondelettes. P
Ondelettes. P
1990
Ondelettes. P aris: Hermann
1990
Multiresolution approximation and wavelet orthonormal bases of L 2(IR)
Trans. Amer. Mat. Soc.,
1989

Multiresolution approximation and wavelet orthonormal bases of L2(IR)
Trans. Amer. Mat. Soc.,
1989
### 34.1.51
Adaptive asymptotically minimax estimates of smooth signals
Problemy Peredatsii Informatsii
1987
Izv. Akad. Nauk. SSR Teckhn. Kibernet. J. Comput. Syst. Sci
Izv. Akad. Nauk. SSR Teckhn. Kibernet. J. Comput. Syst. Sci
1986
Ondelettes et bases Hilbertiennes. Revista Mathematica I b ero-Americana
Ondelettes et bases Hilbertiennes. Revista Mathematica I b ero-Americana
1986
Ondelettes et bases hilbertiennes.
P. Lemarié-Rieusset, Y. Meyer
Mathematics
1986
340
PDF

View 2 excerpts, references background

Save

Alert
Nonparametric Estimation of Smooth Regression Function , " Izv
Akad . Nauk . SSR Teckhn . Kibernet
1985
Nonparametric estimation of smooth regression functions
Izv. Akad. Nauk. SSR Teckhn. Kibernet
1985
Nonparametric estimation of smooth regression functions . Izv . Akad . Nauk . SSR Teckhn . Kibernet . 3 , 50 - 60 ( in Russian )
J . Comput . Syst . Sci .
1985
Rate of Convergence of Nonparametric Estimates of Maximum-Likelihood Type
Problems of Information Transmission Journal of the American Statistical Association
1985
Spline Smoothing and Asymptotic Efficiency in 12
The Annals of Statistics
1985
Spline smoothing and asymptotic eciency in L 2

### 34.1.61
Spline smoothing and asymptotic eeciency in L 2
Ann. Statist
1985

A learning algorithm for nonparametric ltering
Automat. i Telemeh
1984
Birkh auser Verlag: Basel. List of Figures 1. Four spatially variable functions. N=2048. Formulas below. 2. Four functions with Gaussian white noise, = 1, rescaled to have signal-to-noise ratio
1983
Theory of Function Spaces, Basel: Birkhauser Verlag
1983
OPTIMAL GLOBAL RATES OF CONVERGENCE FOR NONPARAMETRIC ESTIMATORS
C. J. Stone
Mathematics
1982
83

View 1 excerpt, references background

Save

Alert
Optimal Global Rates of Convergence for Nonparametric Regression
C. J. Stone
Mathematics
1982
1,361
PDF

View 1 excerpt, references background

Save

Alert
Estimation of the Mean of a Multivariate Normal Distribution
C. Stein
Mathematics
1981
2,505
PDF

View 1 excerpt, references methods

Save

Alert
Optimal ltering of square integrable signals in Gaussian white noise
Problemy Peredatsii Informatsii
1980
New Thoughts on Besov Spaces. D u k e Univ
Math. Series. Number
1976
New Thoughts on Besov Spaces. Duke Univ
Math. Series. Number
1976
### 34.1.71

New thoughts on Besov spaces
J. Peetre
Mathematics
1976
736

Save

Alert
5. 'typical' rows of the wavelet transform matrix W corresponding to j = 6 k= 3 2 i n four cases
5. 'typical' rows of the wavelet transform matrix W corresponding to j = 6 k= 3 2 i n four cases
LPJS reconstruction, deened in Section 4.2, with cutoo L = 5
LPJS reconstruction, deened in Section 4.2, with cutoo L = 5
LPJS reconstruction, dened in Section 4.2, with cuto L = 5
LPJS reconstruction, dened in Section 4.2, with cuto L = 5
Mallat's multiresolution decomposition of the four basic functions using the S8 wavelet
Mallat's multiresolution deomposition of Blocks and HeaviSine using the Haar and D4 wavelets
Mallat's multiresolution deomposition of Blocks and HeaviSine using the Haar and D4 wavelets.L = 4
Mallat's multiresolution deomposition of Blocks and HeaviSine using the Haar and D4 wavelets.L = 4
Plot of wavelet coe cients using S8. Display a t l e v el j depicts w jk by a v ertical line of height proportional to w j k at horizontal position k2 ;j
Plot of wavelet coecients using S8. Display a t l e v el j depicts w jk by a v ertical line of height proportional to w j;k at horizontal position k2 j
Plot of wavelet coecients using S8. Display a t l e v el j depicts w jk by a v ertical line of height proportional to w j;k at horizontal position k2 j
Plot of wavelet coeecients using S8. Display a t l e v el j depicts w jk by a v ertical line of height proportional to w jjk at horizontal position k2 ;j
Plot of wavelet coeecients using S8. Display a t l e v el j depicts w jk by a v ertical line of height proportional to w jjk at horizontal position k2 ;j


### 34.1.81
Reconstructions from noisy data using WaveJS, L = 5 , S 8 w avelet
Reconstructions from noisy data using WaveJS, L = 5 , S 8 w avelet
Root mean squared errors for simulated data at varying levels of sparsity when threshold is chosen by a) SURE, b
Root mean squared errors for simulated data at varying levels of sparsity when threshold is chosen by a) SURE, b
SureShrink reconstruction using soft thresholding
Most Nearly Symmetric Daubechies Wavelet with N = 8, and cuto L = 5
SureShrink reconstruction using soft thresholding, Most Nearly Symmetric Daubechies Wavelet with N = 8, and cuto L = 5
SureShrink reconstruction using soft thresholding, Most Nearly Symmetric Daubechies Wavelet with N = 8, and cuto L = 5
SureShrink reconstruction using soft thresholding, Most Nearly Symmetric Daubechies Wavelet with N = 8, and cutoo L = 5
SureShrink reconstruction using soft thresholding, Most Nearly Symmetric Daubechies Wavelet with N = 8, and cutoo L = 5
Wavelet coecients using the Haar wavelet Compare amounts of compression with Figure 8
Wavelet coecients using the Haar wavelet Compare amounts of compression with Figure 8
Wavelet coeecients using the Haar wavelet Compare amounts of compression with Figure 8
Wavelet coeecients using the Haar wavelet Compare amounts of compression with Figure 8


## 34.2
Noise Reduction By Constrained Reconstructions In The Wavelet-transform Domain
J. Lu, Yansun Xu, J. Weaver, D. Healy
Computer Science
Proceedings of the Seventh Workshop on Multidimensional Signal Processing
1991
TLDR
A technique of suppressing noise while preserving or even enhancing the sharpness of edges, combined with Mallat and Zhong's technique for compact image coding and a modification of Witkin’s edge identification method is presented. Expand
## 34.3
Wavelet Shrinkage: Asymptopia?
D. Donoho, I. Johnstone, G. Kerkyacharian, D. Picard
Mathematics
1995
Much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects-curves, densities, spectral densities, images-from noisy data. A now rich and complex body of… Expand
## 34.4
Nonlinear Solution of Linear Inverse Problems by Wavelet–Vaguelette Decomposition
D. Donoho
Mathematics
1995
We describe the wavelet–vaguelette decomposition (WVD) of a linear inverse problem. It is a substitute for the singular value decomposition (SVD) of an inverse problem, and it exists for a class of… Expand
## 34.5
Shiftable multiscale transforms
Eero P. Simoncelli, W. Freeman, E. Adelson, D. Heeger
Mathematics, Computer Science
IEEE Trans. Inf. Theory
1992
TLDR
Two examples of jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored and the usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement is demonstrated. Expand
## 34.6
Smooth Wavelet Decompositions with Blocky Coefficient Kernels
D. Donoho
Mathematics
1993
We describe bases of smooth wavelets where the coe cients are obtained by integration against ( nite combinations of) boxcar kernels rather than against traditional smooth wavelets. Bases of this… Expand
## 34.7
A discrete transform and decompositions of distribution spaces
Michael Frazier, B. Jawerth
Mathematics
1990
Abstract We study a representation formula of the form ƒ = ∑ Q 〈ƒ, ϑ Q 〉ψ Q for a distribution ƒ on R n. This formula is obtained by discretizing and localizing a standard Littlewood-Paley… Expand
## 34.8
Unconditional Bases Are Optimal Bases for Data Compression and for Statistical Estimation
D. Donoho
Mathematics
1993
Abstract An orthogonal basis of L2 which is also an unconditional basis of a functional space F is an optimal basis for compressing, estimating, and recovering functions in F . Simple thresholding… Expand
## 34.9
Singularity detection and processing with wavelets
S. Mallat, W. Hwang
Computer Science, Mathematics
IEEE Trans. Inf. Theory
1992
TLDR
It is proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents. Expand
## 34.10
Statistical Estimation and Optimal Recovery
D. Donoho
Mathematics
1994
New formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random Gaussian noise. The formulas cover a variety of… Expand

## 34.11
Asymptotic minimax risk for sup-norm loss: Solution via optimal recovery
D. Donoho
Mathematics
1994
SummaryWe study the problem of estimating an unknown function on the unit interval (or itsk-th derivative), with supremum norm loss, when the function is observed in Gaussian white noise and the… Expand

Symmetric iterative interpolation processes
Gilles Deslauriers, S. Dubuc
1989
Using a baseb and an even number of knots, we define a symmetric iterative interpolation process. The main properties of this process come from an associated functionF. The basic functional equation… Expand

Minimax Risk Over Hyperrectangles, and Implications
D. Donoho, Richard C. Liu, B. MacGibbon
Mathematics
1990
Consider estimating the mean of a standard Gaussian shift when that mean is known to lie in an orthosymmetric quadratically convex set in l 2 . The minimax risk among linear estimates is within 25%… Expand

Biorthogonal bases of compactly supported wavelets
A. Cohen, I. Daubechies, J. Feauveau
Mathematics
1992
Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under… Expand

Littlewood-Paley Theory and the Study of Function Spaces
Michael Frazier, B. Jawerth, G. Weiss
Mathematics
1991
Calderon's formula and a decomposition of $L^2(\mathbb R^n)$ Decomposition of Lipschitz spaces Minimality of $\dot B^0,1_1$ Littlewood-Paley theory The Besov and Triebel-Lizorkin spaces The $\varphi$… Expand

## 34.16
Empirical functionals and e cient smoothing parameter selection
P. Hall, I. Johnstone
Mathematics
1992
A striking feature of curve estimation is that the smoothing parameter h 0 , which minimizes the squared error of a kernel or smoothing spline estimator, is very difficult to estimate. This is… Expand
80

Save

Alert
Density estimation in Besov spaces
G. Kerkyacharian, D. Picard
Mathematics
1992
One can slightly modify the usual Lp differentiability constraints of Sobolev types on densities with the help of Besov norms. This has the advantage, using the wavelets characterization of Besov… Expand
215

Save

Alert
Completeness of Context-Free Grammar Forms
H. Maurer, A. Salomaa, D. Wood
Computer Science
J. Comput. Syst. Sci.
1981
TLDR
The present paper continues the approach of [8] focussing on the characterization of complete grammar forms, that is grammar forms which generate all’ context-free languages, and introduces the central concept of expansion spectrum. Expand
12
PDF

Save

Alert
Interpolating Wavelet Transforms
D. Donoho
Computer Science
1992
We describe several \wavelet transforms" which characterize smoothness spaces and for which the coe cients are obtained by sampling rather than integration. We use them to re-interpret the empirical… Expand
288
PDF

View 3 excerpts, references methods

Save

Alert
Extremes and Related Properties of Random Sequences and Processes
M. R. Leadbetter, G. Lindgren, H. Rootzén
Mathematics
1983

## 34.21
A Survey of Optimal Recovery
C. Micchelli, T. J. Rivlin
Computer Science
1977
The problem of optimal recovery is that of approximating as effectively as possible a given map of any function known to belong to a certain class from limited, and possibly error-contaminated,… Expand
321

Save

Alert
Multiresolution analysis, wavelets and fast algorithms on an interval
A. Cohen, I. Daubechies, B. Jawerth, P. Vial
Mathematics
1993
Nous adaptons la construction classique des analyses multiresolutions et des bases orthonormees d'ondelettes au cadre des fonctions definies sur [0,1]. Les proprietes importantes des bases… Expand
234

Save

Alert
Spline Smoothing in Regression Models and Asymptotic Efficiency in $L_2$
M. Nussbaum
Mathematics
1985
168
PDF

Save

Alert
A completely automatic french curve: fitting spline functions by cross validation
G. Wahba, S. Wold
Mathematics
1975
The cross validation mean square error technique is used to determine the correct degree of smoothing, in fitting smoothing solines to discrete, noisy observations from some unknown smooth function.… Expand
393

Save

Alert
Orthonormal bases of compactly supported wavelets
I. Daubechies
Mathematics
1988
We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept… Expand

## 34.26
Orthonormal bases of compactly supported wavelets
I. Daubechies
Mathematics
1988
We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept… Expand
8,687
PDF

Save

Alert
A New Approach to Least-Squares Estimation, with Applications
S. Geer
Mathematics
1986
On montre que les conditions d'entropie sur la classe #7B-G des fonctions de regression impliquent une consistance L 2 forte de l'estimateur des moindres carres
48
PDF

Save

Alert
Estimation d'une densité de probabilité par méthode d'ondelettes
Iain M. Johnstone, G. Kerkyacharian, D. Picard
Mathematics
1992
Nous proposons un cadre ou des estimateurs explicitement construits a partir des coefficients d'ondelettes se revelent strictement plus efficaces que les estimateurs habituels (noyaux, series… Expand
43

Save

Alert
Information-based complexity
J. Traub, G. Wasilkowski, H. Wozniakowski
Computer Science, Medicine
Nature
1987
Information-based complexity seeks to develop general results about the intrinsic difficulty of solving problems where available information is partial or approximate and to apply these results to… Expand
558
PDF

Save

Alert
From Stein's Unbiased Risk Estimates to the Method of Generalized Cross Validation
Ker-Chau Li
Mathematics
1985
On considere une methode interessante pour le choix d'estimateurs lineaires et on presente une nouvelle approche basee sur les estimateurs de Stein (1981)

## 34.31

Adapting to unknown smoothness by w a v elet shrinkage
Adapting to unknown smoothness by w a v elet shrinkage
1992
Minimax estimation by wavelet shrinkage
Technical Report,
1992
New minimax theorems, thresholding, and adaptation
1992
Adapting to unknown smoothness by wavelet shrinkage,'' to appear
J. Amer. Statist. Assoc
1995
Minimax estimation by wavelet shrinkage
Ann. Starisr
1995
Neo-classical minimax theorems, thresholding, and adaptation
Neo-classical minimax theorems, thresholding, and adaptation
1995
Nonlinear solution of linear inverse problems via waveletvaguelette decomposition, " to appear in Appl
Compufat. Harmonic Anal
1995
Wavelet shrinkage : Asymptopia ? ’ to appear in J . Roy
1995
Wavelet shrinkage: Asymptopia?' to appear in
J. Roy. Srat. Soc., ser B
1995
Ideal spacial adaptation via wavelet shrinkage
D. Donoho
Computer Science
1994

## 34.41
Interpolating wavelet transforms, " to appear in Appl
Computaf. Harmonic Anal
1994
Empirical functionals and efficient smoothing parameter selection Estimation d'une densit6 de probabilitC par mCthode d'ondelettes
Compt. Rend. Acad. Sci. Paris (A)
1992
Estima- tion d'une densit e de probabilit e par m ethode d'ondelettes
Comptes Rendus Acad. Sciences Paris (A)
1992
IEEE Trans. Inform. Theory
IEEE Trans. Inform. Theory
1992
Noise reductin by constrained reconstructions in the wavelet-transform domain
Noise reductin by constrained reconstructions in the wavelet-transform domain
1992
The Core Mantle Boundary and the Cosmic Mi- crowave Background: a tale of two CMB's
Technical Report, Depart- ment of Statistics,
1992
The Core Mantle Boundary and the Cosmic Microwave Background: a tale of two CMB's
The Core Mantle Boundary and the Cosmic Microwave Background: a tale of two CMB's
1992
Manuscript, Mathematical Sciences Research Institute
Manuscript, Mathematical Sciences Research Institute
1991
Math. Sci. Res. Inst
Math. Sci. Res. Inst
1991
Ondelettes sur l'intervalle.
Y. Meyer
Mathematics
1991

## 34.51
Ondelettes sur l'intervalle. Revista Mat. Ibero- Americana
Ondelettes sur l'intervalle. Revista Mat. Ibero- Americana
1991
Singularity detection and processing with Boston
Singularity detection and processing with Boston
1991
Asymptotic Minimax Estimation with Prescribed Properties
O. Lepskii
Mathematics
1990
5

Save

Alert
Ondelettes et op erateurs I: Ondelettes. Hermann, Paris
1990
Ondelettes et op erateurs I: Ondelettes
1990
Ondelettes et opirateurs I: OndelettesEnglish translation: Wavelets and Operators Ondelettes sur l'intervalle
Revista Mar. Ibero-Americana
1990
Spline Methods for Observational Data
Spline Methods for Observational Data
1990
Spline Methods for Observational Data. SIAM: Philadelphia
Spline Methods for Observational Data. SIAM: Philadelphia
1990
Statistical Estimation and Optimal recovery. T o appear
Annals of Statistics
1989
Informution-Based Complexity
Informution-Based Complexity
1988

## 34.61
Adaptive asymptotically minimax estimates of smooth signals
Probl. Pered. Inform
1987
J. Comput. Syst. Sci
J. Comput. Syst. Sci
1986
Nonparametric estimation of smooth regression functions
Izv. Akud. Nauk. SSR Teckhn. Kibemet. J. Comput. Sysr. Sci
1986
Ondelettes et bases Hilbertiennes. Revista Mathematica I b ero-Americana
Ondelettes et bases Hilbertiennes. Revista Mathematica I b ero-Americana
1986
Ondelettes et bases hilbertiennes.
P. Lemarié-Rieusset, Y. Meyer
Mathematics
1986
340
PDF

Save

Alert
Nonparametric estimation of smooth regression functions . Izv . Akad . Nauk . SSR Teckhn . Kibernet . 3 , 50 - 60 ( in Russian )
J . Comput . Syst . Sci .
1985
Rate of convergence of nonparametric estimates of maximum-likelihood type
Probl. Inform. Trans
1985
A learning algorithm for nonparametric filtering
Auromat. i Telemeh
1984
A learning algorithm for nonparametric ltering
Automat. i Telemeh
1984
Probability, Statistics and Analysis: Some properties of a test for multimodality based on kernel density estimates
B. Silverman
Mathematics, Computer Science
1983
## 34.71

Some properties of a test for multimodality based on kernel density estimation. in Probability, Statistics, and Anal- ysis, J.F.C. Kingman and G.E.H
1983

Some properties of a test for multimodality based on kernel density estimation
1983
Some properties of a test for multimodality based on kernel density estimation
Probability
1983
Some properties of a test for multimodality based on kernel density estimation. in Probability, Statistics, and Analysis
Some properties of a test for multimodality based on kernel density estimation. in Probability, Statistics, and Analysis
1983
Some properties of a test for multimodality based on kernel density estimation. in Probability, Statistics, and Analysis, J.F.C. Kingman and G.E.H
1983
OPTIMAL GLOBAL RATES OF CONVERGENCE FOR NONPARAMETRIC ESTIMATORS
C. J. Stone
Mathematics
1982
83

Save

Alert
Optimal Global Rates of Convergence for Nonparametric Regression
C. J. Stone
Mathematics
1982
1,361
PDF

Save

Alert
Optimal filtering of square integrable signals in Gaussian white noise
Probl. Pered. Inform. Probl. Inform. Trans
1980
Optimal filtering of square integrable signals in Gaussian white noise , ”
Probl . Pered . Inform .
1980
Optimal ltering of square integrable signals in Gaussian white noise. Problemy Peredatsii Informatsii 16 52-68 (in Rus- sian); Problems of Information Transmission
glish)
1980

## 34.81
Optimal ltering of square integrable signals in Gaussian white noise
Problemy Peredatsii Informatsii
1980
A . S . Nemirovskii , “ Nonparametric estimation of smooth regression functions , ” Izv . Akud . Nauk . SSR Teckhn . Kibemet . , vol . 3 , pp . 50 - 60 , 1986 ( in Russian )
1977
A completely automatic French curve
Commun. Statist
1975
Ordinary Diferential Equafions
Ordinary Diferential Equafions
1969
The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
T. W. Anderson
Mathematics
1955
492
PDF

Save

Alert
DONOHO: DE-NOISING BY SOFFTHRESHOLDING 621
DONOHO: DE-NOISING BY SOFFTHRESHOLDING 621
Near-Dominance: Note that for y < u
Near-Dominance: Note that for y < u
Picard for interesting discussion and correspondence on related topics
Picard for interesting discussion and correspondence on related topics
u -' ( p ) 2 u;'(p) for all p > 0, and hence that u ( y ) < u
u -' ( p ) 2 u;'(p) for all p > 0, and hence that u ( y ) < u

# 参考資料(References)
Data Scientist の基礎(2)
https://qiita.com/kaizen_nagoya/items/8b2f27353a9980bf445c

岩波数学辞典　二つの版がCDに入ってお得
https://qiita.com/kaizen_nagoya/items/1210940fe2121423d777

岩波数学辞典
https://qiita.com/kaizen_nagoya/items/b37bfd303658cb5ee11e

アンの部屋（人名から学ぶ数学：岩波数学辞典）英語(24)
https://qiita.com/kaizen_nagoya/items/e02cbe23b96d5fb96aa1



 ＜この記事は個人の過去の経験に基づく個人の感想です。現在所属する組織、業務とは関係がありません。＞
 
### 最後までおよみいただきありがとうございました。
いいね　💚、フォローをお願いします。
####  Thank you very much for reading to the last sentence.
Please press the like icon 💚　and follow me for your happy life.