The continuous and discrete Brownian bridges: Representations and applications
type: Item
instance of: scholarly article
title: The continuous and discrete Brownian bridges: Representations and applications
zbMATH Open document ID: 0887.62045
DOI: 10.1016/S0024-3795(97)00015-3
author: T. W. Anderson
author: Michael A. Stephens
published in: Linear Algebra and its Applications
publication date: 1997-01-01T00:00:00Z
review text: The authors give a brief exposition of (discrete) Brownian motion and Brownian bridge processes. In particular, they establish spectral representations of the (discrete) processes in terms of (finite) sums of weighted and independent standard normal random variables. Applications to goodness-of-fit testing for uniform distributions, discrete uniform distributions, uniform distributions with censored data, and locally invariant tests are given. In the last section, it is suggested how discrete representations could be used in simulation studies.
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62M15
zbMATH DE Number: 1076287
zbMATH Keywords: Gaussian process
zbMATH Keywords: time-series analysis
zbMATH Keywords: Brownian bridge
zbMATH Keywords: goodness-of-fit testing
zbMATH Keywords: locally invariant tests
reviewed by: R. L. Schilling
MaRDI profile type: Publication
cites work: Q5788953
cites work: Q5631966
cites work: Goodness of fit tests for spectral distributions
cites work: Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
cites work: A Test of Goodness of Fit
cites work: An omnibus test for the time series model AR(1).
cites work: Q4317918
cites work: Cramér‐von Mises statistics for discrete distributions
cites work: Q4324303
cites work: A continuous metric scaling solution for a random variable
cites work: Q4095679
cites work: Asymptotic results for goodness-of-fit statistics with unknown parameters
cites work: Multisample Tests for the von Mises Distribution
cites work: Distribution of the Ratio of the Mean Square Successive Difference to the Variance
cites work: Invariant tests for uniformity on the vertices of regular polygon
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description: scientific article; zbMATH DE number 1076287