Gaussian limits for generalized spacings
Open Access
- 1 February 2009
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 19 (1)
- https://doi.org/10.1214/08-aap537
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 otherKeywords
All Related Versions
This publication has 35 references indexed in Scilit:
- Gaussian limits for generalized spacingsThe Annals of Applied Probability, 2009
- Laws of large numbers in stochastic geometry with statistical applicationsBernoulli, 2007
- A general estimation method using spacingsJournal of Statistical Planning and Inference, 2001
- Goodness of Fit Testing in $\mathbb{R}^m$ Based on the Weighted Empirical Distribution of Certain Nearest Neighbor StatisticsThe Annals of Statistics, 1983
- Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit TestThe Annals of Probability, 1983
- Asymptotic spacings theory with applications to the two‐sample problemThe Canadian Journal of Statistics / La Revue Canadienne de Statistique, 1981
- Asymptotic Normality of Sum-Functions of SpacingsThe Annals of Probability, 1979
- On the Asymptotic Distribution of $k$-Spacings with Applications to Goodness-of-Fit TestsThe Annals of Statistics, 1979
- The Asymptotic Power of Certain Tests of Fit Based on Sample SpacingsThe Annals of Mathematical Statistics, 1957
- The Random Division of an IntervalJournal of the Royal Statistical Society Series B: Statistical Methodology, 1947