Functional estimation for density, regression models and processes / / Odile Pons

• Record Nr.: UNINA9910828634503321
• Autore: Pons Odile
• Pubbl/distr/stampa: Singapore ; ; London, : World Scientific, 2011
• ISBN: 1-283-23504-8; 9786613235046; 981-4343-74-9
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (210 p.)
• Disciplina: 519.5
• Soggetti: Mathematical statistics; Econometrics; Estimation theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 191-196) and index.
• Nota di contenuto: Preface; Contents; 1. Introduction; 1.1 Estimation of a density; 1.2 Estimation of a regression curve; 1.3 Estimation of functionals of processes; 1.4 Content of the book; 2. Kernel estimator of a density; 2.1 Introduction; 2.2 Risks and optimal bandwidths for the kernel estimator; 2.3 Weak convergence; 2.4 Minimax and histogram estimators; 2.5 Estimation of functionals of a density; 2.6 Density of absolutely continuous distributions; 2.7 Hellinger distance between a density and its estimator; 2.8 Estimation of the density under right-censoring; 2.9 Estimation of the density of left-censored variables2.10 Kernel estimator for the density of a process; 2.11 Exercises; 3. Kernel estimator of a regression function; 3.1 Introduction and notation; 3.2 Risks and convergence rates for the estimator; 3.3 Optimal bandwidths; 3.4 Weak convergence of the estimator; 3.5 Estimation of a regression curve by local polynomials; 3.6 Estimation in regression models with functional variance; 3.7 Estimation of the mode of a regression function; 3.8 Estimation of a regression function under censoring; 3.9 Proportional odds model; 3.10 Estimation for the regression function of processes3.11 Exercises; ; 4. Limits for the varying bandwidths estimators; 4.1 Introduction; 4.2 Estimation of densities; 4.3 Estimation of regression functions; 4.4 Estimation for processes; 4.5 Exercises; 5. Nonparametric estimation of quantiles; 5.1 Introduction; 5.2 Asymptotics for the quantile processes; 5.3 Bandwidth selection; 5.4 Estimation of the conditional density of Y given X; 5.5 Estimation of conditional quantiles for processes; 5.6 Inverse of a regression function; 5.7 Quantile function of right-censored variables; 5.8 Conditional quantiles with variable bandwidth5.9 Exercises; 6. Nonparametric estimation of intensities for stochastic processes; 6.1 Introduction; 6.2 Risks and convergences for estimators of the intensity; 6.2.1 Kernel estimator of the intensity; 6.2.2 Histogram estimator of the intensity; 6.3 Risks and convergences for multiplicative intensities; 6.3.1 Models with nonparametric regression functions; 6.3.2 Models with parametric regression functions; 6.4 Histograms for intensity and regression functions; 6.5 Estimation of the density of duration excess; 6.6 Estimators for processes on increasing intervals6.7 Models with varying intensity or regression coefficients; 6.8 Progressive censoring of a random time sequence; 6.9 Exercises; 7. Estimation in semi-parametric regression models; 7.1 Introduction; 7.2 Convergence of the estimators; 7.3 Nonparametric regression with a change of variables; 7.4 Exercises; 8. Diffusion processes; 8.1 Introduction; 8.2 Estimation for continuous diffusions by discretization; 8.3 Estimation for continuous diff usion processes; 8.4 Estimation of discretely observed diffusions with jumps; 8.5 Continuous estimation for di usions with jumps
• Sommario/riassunto: 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