Statistical Learning Theory and Stochastic Optimization: Ecole d'Eté de Probabilités de Saint-Flour XXXI- 2001 (Lecture Notes in Mathematics, Vol. 1851) (Lecture Notes in Mathematics, 1851)

Statistical Learning Theory Is Aimed At Analyzing Complex Data With Necessarily Approximate Models. This Book Is Intended For An Audience With A Graduate Background In Probability Theory And Statistics. It Will Be Useful To Any Reader Wondering Why It May Be A Good Idea, To Use As Is Often Done In Practice A Notoriously Wrong'' (i.e. Over-simplified) Model To Predict, Estimate Or Classify. This Point Of View Takes Its Roots In Three Fields: Information Theory, Statistical Mechanics, And Pac-bayesian Theorems. Results On The Large Deviations Of Trajectories Of Markov Chains With Rare Transitions Are Also Included. They Are Meant To Provide A Better Understanding Of Stochastic Optimization Algorithms Of Common Use In Computing Estimators. The Author Focuses On Non-asymptotic Bounds Of The Statistical Risk, Allowing One To Choose Adaptively Between Rich And Structured Families Of Models And Corresponding Estimators. Two Mathematical Objects Pervade The Book: Entropy And Gibbs Measures. The Goal Is To Show How To Turn Them Into Versatile And Efficient Technical Tools, That Will Stimulate Further Studies And Results. Universal Lossless Data Compression -- Links Between Data Compression And Statistical Estimation -- Non Cumulated Mean Risk -- Gibbs Estimators -- Randomized Estimators And Empirical Complexity -- Deviation Inequalities -- Markov Chains With Exponential Transitions -- References -- Index. Olivier Catoni ; Editor, Jean Picard. ... Lectures Were Given At The 31st Probability Summer School In Saint-flour (july 8-25, 2001) ... --pref. Includes Bibliographical References (p. [261]-265) And Index.

statistical Tools In Finance And Insurance Presents Ready-to-use Solutions, Theoretical Developments And Method Construction For Many Practical Problems In Quantitative Finance And Insurance. Written By Practitioners And Leading Academics In The Field, This Book Offers A Unique Combination Of Topics From Which Every Market Analyst And Risk Manager Will Benefit.

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Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may be a good idea, to use asis often done in practice a notoriously "wrong'' (i.e. over-simplified) model to predict, estimate or classify. This point of view takes its roots in three fields: information theory, statistical mechanics, and PAC-Bayesian theorems. Results on the large deviations of trajectories of Markov chains with rare transitions are also included. They are meant to provide a better understanding of stochastic optimization algorithms of common use in computing estimators. The author focuses on non-asymptotic bounds of the statistical risk, allowing one to choose adaptively between rich and structured families of models and corresponding estimators. Two mathematical objects pervade the book: entropy and Gibbs measures. The goal is to show how to turn them into versatile and efficient technical tools,that will stimulate further studies and results. TOC:Universal Lossless Data Compression.- Links Between Data Compression and Statistical Estimation.- Non Cumulated Mean Risk.- Gibbs Estimators.- Randomized Estimators and Empirical Complexity.- Deviation Inequalities.- Markov Chains with Exponential Transitions.- References.- Index Introduction....Pages 1-4 1. Universal lossless data compression....Pages 5-54 2. Links between data compression and statistical estimation....Pages 55-69 3. Non cumulated mean risk....Pages 71-95 4. Gibbs estimators....Pages 97-154 5. Randomized estimators and empirical complexity....Pages 155-197 6. Deviation inequalities....Pages 199-222 7. Markov chains with exponential transitions....Pages 223-260 References....Pages 261-265 Index....Pages 267-269 List of participants and List of short lectures....Pages 271-273 Statistical Tools for Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field, this book offers a unique combination of topics from which every market analyst and risk manager will benefit. Features of the significantly enlarged and revised second "Statistical Tools for Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field this book offers a unique combination of topics from which every market analyst and risk manager will benefit."--Jacket We consider in this chapter a finite set E, called in this context the alphabet, and a E valued random process (Xn)n?N.