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B. G. Ivanoff, “Stopping Times and Tightness for Multiparameter martingales,” Statistics & Probability Letters, Vol. 28, No. 2, 1996, pp. 111-114. doi:10.1016/0167-7152(95)00103-4

has been cited by the following article:

• TITLE: Change-Point Detection for General Nonparametric Regression Models

  AUTHORS: Murray D. Burke, Gildas Bewa

  KEYWORDS: Change-Point Detection; Nonparametric Regression Models; Weighted Bootstrap

  JOURNAL NAME: Open Journal of Statistics, Vol.3 No.4, August 16, 2013

  ABSTRACT: A number of statistical tests are proposed for the purpose of change-point detection in a general nonparametric regression model under mild conditions. New proofs are given to prove the weak convergence of the underlying processes which assume remove the stringent condition of bounded total variation of the regression function and need only second moments. Since many quantities, such as the regression function, the distribution of the covariates and the distribution of the errors, are unspecified, the results are not distribution-free. A weighted bootstrap approach is proposed to approximate the limiting distributions. Results of a simulation study for this paper show good performance for moderate samples sizes.