Search results for "Odile Villois"
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Functional Estimation For Density, Regression Models And Processes
Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.This second edition presents minimax properties with Lp risks, for a positive real p, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.
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Orthonormal Series Estimators
The approximation and the estimation of nonparametric functions by projections on an orthonormal basis of functions are useful in data analysis. This book presents series estimators defined by projections on bases of functions, they extend the estimators of densities to mixture models, deconvolution and inverse problems, to semi-parametric and nonparametric models for regressions, hazard functions and diffusions. They are estimated in the Hilbert spaces with respect to the distribution function of the regressors and their optimal rates of convergence are proved. Their mean square errors depend on the size of the basis which is consistently estimated by cross-validation. Wavelets estimators are defined and studied in the same models.The choice of the basis, with suitable parametrizations, and their estimation improve the existing methods and leads to applications to a wide class of models. The rates of convergence of the series estimators are the best among all nonparametric estimators with a great improvement in multidimensional models. Original methods are developed for the estimation in deconvolution and inverse problems. The asymptotic properties of test statistics based on the estimators are also established.
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Estimations And Tests In Change-point Models
'This is a solid mathematical treatment of some topics in the analysis of change-point models. The book is intended for graduate students and scientific researchers using statistics in practice.'zbMATHThis book provides a detailed exposition of the specific properties of methods of estimation and test in a wide range of models with changes. They include parametric and nonparametric models for samples, series, point processes and diffusion processes, with changes at the threshold of variables or at a time or an index of sampling.The book contains many new results and fills a gap in statistics literature, where the asymptotic properties of the estimators and test statistics in singular models are not sufficiently developed. It is suitable for graduate students and scientific researchers working in the industry, governmental laboratories and academia.
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Inequalities In Analysis And Probability (Third Edition)
The book introduces classical inequalities in vector and functional spaces with applications to probability. It develops new analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales, to transformed Brownian motions and diffusions, to Markov and point processes, renewal, branching and shock processes.In this third edition, the inequalities for martingales are presented in two chapters for discrete and time-continuous local martingales with new results for the bound of the norms of a martingale by the norms of the predictable processes of its quadratic variations, for the norms of their supremum and their p-variations. More inequalities are also covered for the tail probabilities of Gaussian processes and for spatial processes.This book is well-suited for undergraduate and graduate students as well as researchers in theoretical and applied mathematics.
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Functional Estimation For Density, Regression Models And Processes
This book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book expounds on the construction of estimators for functionals of processes and densities, and provides asymptotic expansions and optimality properties from smooth estimators.It also presents new regular estimators for functionals of processes, compares histogram and kernel estimators, compares several new estimators for single-index models, and it examines the weak convergence of the estimators.
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