Boundary crossing probabilities and statistical applications

DOI10.1214/aos/1176349928zbMath0632.62077OpenAlexW2054875221MaRDI QIDQ1095541

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1214/aos/1176349928

zbMATH Keywords

large deviations discrete time survival data change-point problems linear boundaries boundary crossing probabilities repeated significance tests sequential clinical trials first passage distributions of Brownian motion fixed sample statistical problems nonlinear boundaries recent results

Mathematics Subject Classification ID

Brownian motion (60J65) Sequential statistical analysis (62L10) Boundary theory for Markov processes (60J50)

Related Items (76)

CONDITIONAL PROBABILITY OF SIGNIFICANCE FOR EARLY STOPPING IN FAVOR OFH₀ ⋮ Testing for change-points with rank and sign statistics ⋮ Exact asymptotics for boundary crossings of the Brownian bridge with trend with application to the Kolmogorov test ⋮ Ergodicity and first passage probability of regime-switching geometric Brownian motions ⋮ Large deviations for the maxima of some random fields ⋮ Semiparametric tests for change-points with epidemic alternatives ⋮ Sign tests for change under alternatives ⋮ Nonlinear renewal theory for Markov random walks ⋮ Bayesian approach to change point problems ⋮ Estimations of a threshold parameter in cox regression ⋮ Boundary crossing probabilities for \((q,d)\)-Slepian-processes ⋮ Stochastic Boundary Crossing Probabilities for the Brownian Motion ⋮ Two-phase regression with nonhomogeneous errors ⋮ An O'Brien-Fleming sequential trial for comparing three treatments ⋮ Ladder heights, Gaussian random walks and the Riemann zeta function ⋮ Crossing probabilities for diffusion processes with piecewise continuous boundaries ⋮ Graphically based interval estimation for the change-point ⋮ On the asymptotic distribution of the scan statistic for empirical distributions ⋮ CRITICAL VALUES AND P VALUES OF BESSEL PROCESS DISTRIBUTIONS: COMPUTATION AND APPLICATION TO STRUCTURAL BREAK TESTS ⋮ Asymptotic properties for the sequential CUSUM procedure ⋮ Nonparametric functionals of spectral distributions and their applications to time series analy\-sis ⋮ Approximations for the boundary crossing probabilities of moving sums of normal random variables ⋮ The asymptotic distribution of MLE of treatment lag threshold ⋮ Adaptive sampling for detecting a change point in the past ⋮ A note on Erdős and Kac's identity: boundary crossing probabilities of Brownian motion over constant boundaries. A finite Markov chain imbedding approach ⋮ Linear programming and the inverse method of images ⋮ Local limit theorem for the distibution of s_n ⋮ Locally optimal invariant tests for change in level ⋮ Estimation of change-point models ⋮ Likelihood-ratio-based confidence sets for the timing of structural breaks ⋮ Detection and estimation of multiple transient changes ⋮ A consistent on‐line Bayesian procedure for detecting change points ⋮ Exact change point detection with improved power in small‐sample binomial sequences ⋮ Change point detection with robust control chart ⋮ Detecting non-simultaneous changes in means of vectors ⋮ Identifying the time of step change in the mean of autocorrelated processes ⋮ A Note on Signed Rank Tests for the Changepoint Problem ⋮ Bayesian change-point problem using Bayes factor with hierarchical prior distribution ⋮ Detecting a change in variances ⋮ Detecting change points and monitoring biomedical data ⋮ Interactive martingale tests for the global null ⋮ Herbert Robbins and sequential analysis ⋮ Flexible supply contracts under price uncertainty ⋮ Asymptotic estimation theory of multipoint linkage analysis under perfect marker information. ⋮ First passage times for Slepian process with linear and piecewise linear barriers ⋮ First hitting time distributions for Brownian motion and regions with piecewise linear boundaries ⋮ A modified sequential probability ratio test ⋮ Nonparametric estimation in a two change-point model ⋮ Approximations for the boundary crossing probabilities of moving sums of random variables ⋮ Fast calculation of boundary crossing probabilities for Poisson processes ⋮ First passage time for Brownian motion and piecewise linear boundaries ⋮ Estimates of the Exit Probability for Two Correlated Brownian Motions ⋮ Saddlepoint approximations to p-values for comparison of density estimates ⋮ Burn-in and covariates ⋮ Testing for the number of change points in a sequence of exponential random variables ⋮ On double-boundary non-crossing probability for a class of compound processes with applications ⋮ Sequential Change-Point Detection and Estimation ⋮ Bayesian isotonic changepoint analysis ⋮ Linear and Nonlinear Boundary Crossing Probabilities for Brownian Motion and Related Processes ⋮ Hybrid regions for post-change mean in a sequence of normal variables ⋮ The compound Poisson process perturbed by a diffusion with a threshold dividend strategy ⋮ Power of the MOSUM test for online detection of a transient change in mean ⋮ On the Moments of a Semi-Markovian Random Walk with Gaussian Distribution of Summands ⋮ Maximally selected chi-squared statistics and non-monotonic associations: an exact approach based on two cutpoints ⋮ The asymptotic power function of GLR tests for local change of parameter ⋮ Change-point problems: bibliography and review ⋮ On excursion sets, tube formulas and maxima of random fields. ⋮ A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend ⋮ Nonanticipating estimation applied to sequential analysis and changepoint detection ⋮ A Nonparametric bootstrapped estimate of the change-point ⋮ Multiscale Change Point Inference ⋮ An explicit expression for the distribution of the supremum of brownian motion with a change point ⋮ Group sequential tests under fractional Brownian motion in monitoring clinical trials ⋮ Information and effective number of meioses in linkage analysis ⋮ First passage probabilities of one-dimensional diffusion processes ⋮ Piecewise exponential survival curves with smooth transitions

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