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.
|Number of pages||28|
|Journal||Annals of Applied Probability|
|Publication status||Published - Feb 2009|
- logarithmic spacings
- central limit theorems
- spacing statistics
- information gain