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Test to distinguish a Brownian motion from a Brownian bridge using Polya tree process

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  • Bharath, Karthik
  • Dey, Dipak K.

Abstract

The problem of distinguishing a Brownian bridge from a Brownian motion, both with possible drift, on the closed unit interval, is investigated via a pair of hypothesis tests. The first, tests for observations obtained at n discrete time points to be arising from a Brownian bridge with drift by embedding the Brownian bridge into a mixture of Polya trees which represents the non-parametric alternative. The second test, tests in an identical manner, for the observations to be coming from a Brownian motion with drift. The Bayes factors for the two tests are derived and then combined to obtain the Bayes factor for the test to distinguish between the two Gaussian processes. The Tierney-Kadane approximation of the Bayes factor is derived with an error approximation of order O(n-4).

Suggested Citation

  • Bharath, Karthik & Dey, Dipak K., 2011. "Test to distinguish a Brownian motion from a Brownian bridge using Polya tree process," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 140-145, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:140-145
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    References listed on IDEAS

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    1. Berger J. O & Guglielmi A., 2001. "Bayesian and Conditional Frequentist Testing of a Parametric Model Versus Nonparametric Alternatives," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 174-184, March.
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    Cited by:

    1. Angela Schörgendorfer & Adam J. Branscum & Timothy E. Hanson, 2013. "A Bayesian Goodness of Fit Test and Semiparametric Generalization of Logistic Regression with Measurement Data," Biometrics, The International Biometric Society, vol. 69(2), pages 508-519, June.
    2. Chen, Yuhui & Hanson, Timothy E., 2014. "Bayesian nonparametric k-sample tests for censored and uncensored data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 335-346.
    3. Ma, Zichen & Hanson, Timothy E., 2020. "Bayesian nonparametric test for independence between random vectors," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).

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