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Asymptotic Statistics by A.W. van der Vaart

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24

Nonparametric Density Estimation

           This chapter is an introduction to estimating densities if the underlying density of a sample of observations is considered completely unknown, up to existence of derivatives. We derive rates of convergence for the mean square error of kernel estimators and show that these cannot be improved. We also consider regularization by monotonicity.

24.1 Introduction

Statistical models are called parametric models if they are described by a Euclidean parameter (in a nice way). For instance, the binomial model is described by a single parameter p, and the normal model is given through two unknowns: the mean and the variance of the observations. In many situations there is insufficient motivation for using ...

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