The asymptotic distribution of the scan statistic under uniformity

DOI10.1214/aop/1176994669zbMath0438.60035OpenAlexW1967671668MaRDI QIDQ1141971

Noel Cressie

Publication date: 1980

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176994669

zbMATH Keywords

asymptotic distributionuniform distributionPoisson processscan statisticsupremum distributionclustering alternative distribution

Mathematics Subject Classification ID

Gaussian processes (60G15) Asymptotic distribution theory in statistics (62E20) Signal detection and filtering (aspects of stochastic processes) (60G35)

Related Items (20)

Some limit results on supremum of Shepp statistics for fractional Brownian motion ⋮ Extremes of a class of nonhomogeneous Gaussian random fields ⋮ The Cameron-Martin theorem for (\(p\)-)Slepian processes ⋮ Minimal spacings of non-uniform densities ⋮ Boundary crossing probabilities for \((q,d)\)-Slepian-processes ⋮ Maximal type test statistics based on conditional processes ⋮ On the limiting distribution of the spatial scan statistic ⋮ BARRIER OPTIONS PRICING WITH JOINT DISTRIBUTION OF GAUSSIAN PROCESS AND ITS MAXIMUM ⋮ Large deviations of Shepp statistics for fractional Brownian motion ⋮ Extremes of a type of locally stationary Gaussian random fields with applications to Shepp statistics ⋮ Approximating probabilities of first passage in a particular gaussian process ⋮ The joint distribution of running maximum of a Slepian process ⋮ Extremes of Shepp statistics for fractional Brownian motion ⋮ Boundary non-crossing probabilities for Slepian process ⋮ Importance sampling for spatial scan analysis: computing scan statistic \(p-\)values for marked point processes. ⋮ Limit laws on extremes of nonhomogeneous Gaussian random fields ⋮ Tail asymptotics for Shepp-statistics of Brownian motion in \(\mathbb{R}^d \) ⋮ Bounds on the distributions of extremal values of a scanning process ⋮ Scan statistics on Enron graphs ⋮ On the distribution of functionals of stationary Gaussian processes

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