Functional Estimation for Density, Regression Models and Processes

The following sections are included:

• Preface

• Contents

The following sections are included:

• Estimation of a density

• Estimation of a regression curve

• Estimation of functionals of processes

• Content of the book

The following sections are included:

• Introduction

• Risks and optimal bandwidths for the kernel estimator

• Weak convergence

• Minimax and histogram estimators

• Estimation of functionals of a density

• Density of absolutely continuous distributions

• Hellinger distance between a density and its estimator

• Estimation of the density under right-censoring

• Estimation of the density of left-censored variables

• Kernel estimator for the density of a process

• Exercises

The following sections are included:

• Introduction and notation

• Risks and convergence rates for the estimator

• Optimal bandwidths

• Weak convergence of the estimator

• Estimation of a regression curve by local polynomials

• Estimation in regression models with functional variance

• Estimation of the mode of a regression function

• Estimation of a regression function under censoring

• Proportional odds model

• Estimation for the regression function of processes

• Exercises

The following sections are included:

• Introduction

• Estimation of densities

• Estimation of regression functions

• Estimation for processes

• Exercises

The following sections are included:

• Introduction

• Asymptotics for the quantile processes

• Bandwidth selection

• Estimation of the conditional density of Y given X

• Estimation of conditional quantiles for processes

• Inverse of a regression function

• Quantile function of right-censored variables

• Conditional quantiles with variable bandwidth

• Exercises

The following sections are included:

• Introduction

• Risks and convergences for estimators of the intensity
  • Kernel estimator of the intensity
  • Histogram estimator of the intensity

• Risks and convergences for multiplicative intensities
  • Models with nonparametric regression functions
  • Models with parametric regression functions

• Histograms for intensity and regression functions

• Estimation of the density of duration excess

• Estimators for processes on increasing intervals

• Models with varying intensity or regression coefficients

• Progressive censoring of a random time sequence

• Exercises

The following sections are included:

• Introduction

• Convergence of the estimators

• Nonparametric regression with a change of variables

• Exercises

The following sections are included:

• Introduction

• Estimation for continuous diffusions by discretization

• Estimation for continuous diffusion processes

• Estimation of discretely observed diffusions with jumps

• Continuous estimation for diffusions with jumps

• Transformations of a non-stationary Gaussian process

• Exercises

The following sections are included:

• Nonparametric estimation of the mean

• Periodic models for time series

• Nonparametric estimation of the covariance function

• Nonparametric transformations for stationarity

• Change-points in time series

• Exercises

The following sections are included:

• Appendix A

• Appendix B

• Appendix C

• Appendix D

The following sections are included:

• Notations

• Bibliography

• Index