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corso IAMI
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= C.N.R. - I.A.M.I. =
= Istituto per le Applicazioni della Matematica e dell'Informatica =
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= http://www.iami.mi.cnr.it =
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= =
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Comunico che nei giorni 13, 14 e 15 Dicembre 1999, presso la sede
del C.N.R. (via Ampere 56, Milano), aula A, il Professor Brani Vidakovic,
ISDS, Duke University, terra` un corso sul tema
WAVELETS: BASICS AND STATISTICAL APPLICATIONS
Con l'invito ad intervenire, La prego di dare la piu` ampia
diffusione al presente annuncio.
Il Direttore dell'Istituto
Eugenio Regazzini
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Programma del corso
Lunedi` 13 Dicembre 1999 14.30 - 16.30
Martedi` 14 Dicembre 1999 10.30 - 12.30, 14.30 - 16.30
Mercoledi` 15 Dicembre 1999 10.30 - 12.30
WAVELETS: BASICS AND STATISTICAL APPLICATIONS
Brani Vidakovic, ISDS, Duke University
This mini-course on wavelets and statistics will
have 2 parts consisting of four 1-hour lectures each.
The first part introduces multiscale methods to a
novice. Familiarity with the Fourier transformation
and Hilbert spaces is desirable, but not crucial.
The second part discusses various applications of wavelets
in statistics. It covers standard statistical applications,
such as regression, density estimation and analysis
of time series, and some non-traditional methods as well.
Exposure to statistics at an introductory or intermediate level
is desirable.
Extensive references are provided as well as pointers to
web sources. Plans for the lectures are provided next.
Recommended Text: Vidakovic, B. Statistical Modeling By Wavelets, Wiley 1999.
Recommended Additional Reading: Daubechies, I. 10 Lectures on Wavelets, Siam.
Nguyen, Strang, Wavelets
Mallat, Wavelet Tour, AP 1998.
PART 1
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Lecture 1. Wavelets: Why?
This introductory lecture is a ``commercial'' for usage of
wavelet based tools. It discusses, at an informal level,
decorrelating, self-similarity, and ``disbalancing'' properties
of wavelets.
Interesting applications are presented and ramifications of
wavelet methods are discussed.
Lecture 2. Wavelets: How?
By utilizing the Haar basis the construction and basic properties
of wavelets are illustrated. Several techniques of
constructing wavelets are explored as well.
Standard families of wavelets (Shannon, Meyer, Franklin,
Daubechies) are briefly overviewed.
Lecture 3. Discrete Wavelet Transformations and Variations
In this lecture we discuss Mallat's algorithm and its connection
with continuous wavelet transformations and wavelet series.
Wavelet packets and stationary wavelet transforms are discussed.
Links between regularity of functions and rates of decay of their
wavelet coefficients are discussed. Moment conditions (Strang-Fix
condition, interpolating wavelets, coiflets) are overviewed, as well.
Lecture 4. Beyond Orthogonal Wavelet Transformations
In this lecture we discuss bivariate wavelets, wavelet-like bases,
matching pursuit methods and more general classes of time/scale
representations (Cohen Class Distributions).
PART 2.
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Lecture 5. Regression via Wavelet Shrinkage.
Standard wavelet regression problem is presented.
Shrinkage paradigm, Minimax, Exact risk, Bayesian and Bayesian decision-theoretic
shrinkage and their optimality properties are discussed.
Lecture 6. Standard Statistical Wavelet Based Methods.
In this lecture an application of wavelets in density estimation
and time series is covered. Wavelet methods of dealing with self-similar data
and use of wavelets for generating random objects (random functions
and densities) is discussed.
Lecture 7. Non-Standard Statistical Wavelet Based Methods.
Wavelet methods in statistical computations, indirect methods (deconvolutions),
statistical turbulence.
Lecture 8. A Case Study: Functional Data Analysis via Wavelets
Utilizing multiresolution methods in functional
data analysis (FDA) is beneficial in several respects.
The fact that wavelets decorrelate the data makes
the functional inference in the wavelet domain easy to
implement and interpret.
We discuss two FDA applications: Dimension reduction
problem and wavelet-based ANOVA.
The application in the second problem is illustrated by an
ongoing research project at Cancer Center at Duke University.
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per informazioni rivolgersi a:
Renata Rotondi
Istituto per le Applicazioni della Matematica e dell'Informatica
Via Ampere, 56
20131 Milano
reni@iami.mi.cnr.it
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