Abstract
Nearest neighbor cells in Rd, d∈ℕ, are used to define coefficients of divergence (φ-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a variance depending on the underlying point density. In d=1, this extends classical central limit theory for sum functions of spacings. The general results yield central limit theorems for logarithmic k-spacings, information gain, log-likelihood ratios and the number of pairs of sample points within a fixed distance of each other.
Original language | English |
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Pages (from-to) | 158-185 |
Number of pages | 28 |
Journal | Annals of Applied Probability |
Volume | 19 |
Issue number | 1 |
DOIs | |
Publication status | Published - Feb 2009 |
Keywords
- φ-divergence
- logarithmic spacings
- log-likelihood
- central limit theorems
- spacing statistics
- information gain