Titlebook: Lectures on the Nearest Neighbor Method; Gérard Biau,Luc Devroye Book 2015 Springer International Publishing Switzerland 2015 Density Esti

下边深陷

The ,-nearest neighbor density estimatef . is a small ball about ., the probability that . falls in . is about .(.) times the volume of .. It thus serves as a tool for computing probabilities of sets and, as a function that reveals the local concentration of probability mass, it may be used to visualize distributions of random variables.

PAGAN

Collar

The nearest neighbor regression function estimate . depend on the values of the observation vector .. The objective is to find a Borel measurable function . such that | . − .(.) | is small, where “small” could be defined in terms of the .. risk . (. > 0), for example. Of particular interest is the .. risk of .,

cuticle

The 1-nearest neighbor regression function estimatewill also offer the opportunity to familiarize the reader with concepts that will be encountered in the next few chapters. Recall that this very simple estimation procedure is defined by setting . where . is a reordering of the data according to increasing values of ., and distance ties are broken by looking at indices.

预定

Regression: the noiseless case. errors with respect to the Lebesgue measure on compacts. Others use it for Monte Carlo purposes, wanting to estimate . over a compact set .. The model we study here takes a sample . of i.i.d. random vectors with a density . on . that is not known.

草率女

Gérard Biau,Luc DevroyePresents a rigorous overview of nearest neighbor methods.Many different components covered: statistical, probabilistic, combinatorial, and geometric ideas.Extensive appendix material provided

Alveoli

胆大

Order statistics and nearest neighborsWe start with some basic properties of uniform order statistics. For a general introduction to probability, see Grimmett and Stirzaker (2001). Some of the properties of order statistics presented in this chapter are covered by Rényi (1970); Galambos (1978), and Devroye (1986).

Retrieval

礼节

Uniform consistencyThis chapter is devoted to the study of the uniform consistency properties of the .-nearest neighbor density estimate ... Before embarking on the supremum norm convergence, it is useful to understand the behavior of .. on bounded densities. We denote the essential supremum (with respect to the Lebesgue measure .) of the density . by