Gaussian limits for generalized spacings

8 Gaussian Limits for Generalized Spacings ∗

Nearest neighbor cells in Rd 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. The finite-dimensional distributions of the point measures induced by the coefficients of divergence converge to those of a gener...

Generalized Covering Groups and Direct Limits

Gaussian and Sparse Processes Are Limits of Generalized Poisson Processes

The theory of sparse stochastic processes offers a broad class of statistical models to study signals. In this framework, signals are represented as realizations of random processes that are solution of linear stochastic differential equations driven by white Lévy noises. Among these processes, generalized Poisson processes based on compoundPoisson noises admit an interpretation as random L-spl...

Ordering Conditional Distributions of Spacings of Generalized Order Statistics

The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters, on which the generalized order statistics are based on, to establish the usual stochastic and the likelihood ratio orderings of general p-spacings by conditioning on the right tail of another lower indexed generalized order statistics. Some potential applications are also given.

Gaussian limits for random geometric measures

Given n independent random marked d-vectors Xi with a common density, define the measure νn = ∑ i ξi, where ξi is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near Xi. Technically, this means here that ξi stabilizes with a suitable power-law decay of the tail of the radius of stabilization. For bounded test functions f on R, we give a central l...