Probability

Download Concentration inequalities and model selection: Ecole d'Ete by Professor Pascal Massart (auth.), Jean Picard (eds.) PDF

Posted On March 4, 2017 at 3:59 am by / Comments Off on Download Concentration inequalities and model selection: Ecole d'Ete by Professor Pascal Massart (auth.), Jean Picard (eds.) PDF

By Professor Pascal Massart (auth.), Jean Picard (eds.)

Since the extraordinary works of Talagrand, focus inequalities were famous as basic instruments in different domain names akin to geometry of Banach areas or random combinatorics. in addition they develop into crucial instruments to enhance a non-asymptotic conception in information, precisely because the primary restrict theorem and big deviations are recognized to play a significant half within the asymptotic conception. an summary of a non-asymptotic conception for version choice is given right here and a few chosen purposes to variable choice, switch issues detection and statistical studying are mentioned. This quantity displays the content material of the path given through P. Massart in St. Flour in 2003. it's generally self-contained and available to graduate students.

Show description

Read or Download Concentration inequalities and model selection: Ecole d'Ete de Probabilites de Saint-Flour XXXIII - 2003 PDF

Similar probability books

Extreme value distributions: theory and applications

This significant e-book offers an up to date complete and down-to-earth survey of the idea and perform of maximum worth distributions - essentially the most famous luck tales of recent utilized likelihood and records. Originated via E J Gumbel within the early forties as a device for predicting floods, severe worth distributions developed over the last 50 years right into a coherent thought with functions in essentially all fields of human recreation the place maximal or minimum values (the so-called extremes) are of relevance.

Distribution theory for tests based on the sample ditribution function

Offers a coherent physique of thought for the derivation of the sampling distributions of a variety of attempt facts. Emphasis is at the improvement of sensible options. A unified remedy of the idea was once tried, e. g. , the writer sought to narrate the derivations for assessments at the circle and the two-sample challenge to the elemental conception for the one-sample challenge at the line.

Linear model theory. Univariate, multivariate, and mixed models

An exact and available presentation of linear version idea, illustrated with info examples Statisticians usually use linear types for facts research and for constructing new statistical equipment. so much books at the topic have traditionally mentioned univariate, multivariate, and combined linear versions individually, while Linear version idea: Univariate, Multivariate, and combined versions offers a unified therapy on the way to clarify the differences one of the 3 periods of types.

Extra resources for Concentration inequalities and model selection: Ecole d'Ete de Probabilites de Saint-Flour XXXIII - 2003

Example text

Let t be given such that σt = E X 2 (t) > 0. 2 above and choosing z such that P [Z > z] ≤ 1/4, if we denote by Φ the cumulative distribution function of the standard normal distribution, we derive from the inequalities 3 ≤ P [Z ≤ z] ≤ P [X (t) ≤ z] = Φ 4 z σt , that σt ≤ z/Φ−1 (3/4). 1), it appears that the hard work to study the continuity question is to get dimension free bounds on the supremum of the components of a Gaussian random vector. One reason for focusing on supt∈T X (t) rather than supt∈T |X (t)| is that one can freely use the formula E sup (X (t) − Y ) = E sup X (t) t∈T t∈T for any centered random variable Y .

The product of a collection of Borel sets which are trivial except for a finite subcollection). The law of X is determined by the collection of all marginal distributions of the finite dimensional random vectors (X (t1 ) , . . , X (tN )) when {t1 , . . , tN } varies. , any stochastic process Y with same law as X is almost surely continuous on T (equipped with some given distance). s. for all t ∈ T . A (centered) Gaussian process is a stochastic process X = (X (t))t∈T , such that each finite linear combination αt X (t) is (centered) Gaussian (in other words, each finite dimensional random vector (X (t1 ) , .

42) implies that n Q [Xi = Yi ] ≤ minn Q∈P(P ,Q) i=1 n K (Q, P n ) 2 which is the original statement in [86]. On the other hand some other coupling result due to Marton (see [87]) ensures that n minn Q∈P(P ,Q) i=1 Ωn Q2 [Xi = Yi | Yi = yi ] dQ (y) ≤ 2K (Q, P n ) . 42) but with the suboptimal constant 2 instead of 1/2. Proof. We follow closely the presentation in [87]. 42) by induction on n. 20. Let us now assume that for any distribution Q on Ω n−1 , An−1 , P n−1 which is absolutely continuous with respect to P n−1 , the following coupling inequality holds true n−1 min n−1 Q∈P(P ,Q ) Q2 (x, y) ∈ Ω n−1 × Ω n−1 : xi = yi ≤ i=1 1 K Q , P n−1 .

Download PDF sample

Rated 4.20 of 5 – based on 6 votes