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- W1415253603 abstract "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. 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 a particular parametric model, such as a normal model. An alternative at the other end of the scale is a nonparametric model , which leaves the underlying distribution of the observations essentially free. In this chapter we discuss one example of a problem of nonparametric estimation: estimating the density of a sample of observations if nothing is known a priori. From the many methods for this problem, we present two: kernel estimation and monotone estimation. Notwithstanding its simplicity, this method can be fully asymptotically efficient. Kernel Estimators The most popular nonparametric estimator of a distribution based on a sample of observations is the empirical distribution, whose properties are discussed at length in Chapter 19. This is a discrete probability distribution and possesses no density." @default.
- W1415253603 created "2016-06-24" @default.
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- W1415253603 date "1998-10-13" @default.
- W1415253603 modified "2023-09-26" @default.
- W1415253603 title "Nonparametric Density Estimation" @default.
- W1415253603 doi "https://doi.org/10.1017/cbo9780511802256.025" @default.
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