Skip to Main content Skip to Navigation
Theses

Probability bounds for the cross-validation estimate in the context of the statistical learning theory and statistical models applied to economics and finance

Abstract : The initial goal of this thesis is to get a better understanding of a methodology commonly used among practitioners : the cross-validation. The latter is designed to assess the risk of predictors. The second part of the thesis is dedicated to statistical models applied to real world issues encountered in the professional life. It consists mostly in time series models for economic and financial data. In chapter 1, we derive concentration inequalities for the cross-validation estimate of the generalization error for empirical risk minimizers. In the general setting, we prove sanity-check bounds: bounds showing that the worst-case error of this estimate is not much worse that of training error estimate. In chapter 2, we prove probability bounds for the cross-validation estimate of the generalization error for stable predictors in the context of risk assessment. The notion of stability characterizes class of predictors with infinite VC dimension, such as k-nearest neighbors rules, bayesian algorithm, boosting. In chapter 3, we obtain concentration inequalities for the cross-validation estimate of the generalization error for subagged estimators. An interesting consequence is that the probability upper bound is bounded by the minimum of a Hoeffding-type bound and a Vapnik-type bounds, and thus is smaller than 1 even for small learning set. Chapter 4 gives a monthly proxy of the French GDP growth rate through the Kalman filter methodology. Chapter 5 extracts a monthly leading indicator of the French business climate in the services sector. Eventually, chapter 6 gives a semi-parametric approach to simulate spot electricity prices for energy risk management.
Document type :
Theses
Complete list of metadatas

Cited literature [7 references]  Display  Hide  Download

https://pastel.archives-ouvertes.fr/tel-00530876
Contributor : Matthieu Cornec <>
Submitted on : Saturday, October 30, 2010 - 6:28:06 PM
Last modification on : Tuesday, April 2, 2019 - 2:24:49 AM
Long-term archiving on: : Monday, January 31, 2011 - 2:38:21 AM

Identifiers

  • HAL Id : tel-00530876, version 1

Collections

Citation

Matthieu Cornec. Probability bounds for the cross-validation estimate in the context of the statistical learning theory and statistical models applied to economics and finance. Mathematics [math]. Université de Nanterre - Paris X, 2009. English. ⟨tel-00530876⟩

Share

Metrics

Record views

582

Files downloads

16042