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Multivariate tests-of-fit and uniform confidence bands using a weighted bootstrap

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  • Burke, Murray D.

Abstract

Many tests of fit procedures use the empirical distribution function (e.d.f.) of the data and have limiting distribution dependent on the data's underlying distribution or family of distribution functions. This paper uses a weighted bootstrap method based on independent random variables instead of sampling from the uniform. A proof of convergence of the weighted bootstrap is given using strong martingales. This approach is applied to the problem of obtaining uniform confidence bands for the distribution function of multivariate data. The multivariate two-sample problem, testing whether two independent random samples come from the same multivariate distribution function, is also discussed.

Suggested Citation

  • Burke, Murray D., 2000. "Multivariate tests-of-fit and uniform confidence bands using a weighted bootstrap," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 13-20, January.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:1:p:13-20
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    References listed on IDEAS

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    1. Ivanoff, B. Gail, 1996. "Stopping times and tightness for multiparameter martingales," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 111-114, June.
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    Cited by:

    1. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2017. "Fast tests for the two-sample problem based on the empirical characteristic function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 390-410.
    2. Ali Al-Sharadqah & Majid Mojirsheibani & William Pouliot, 2020. "On the performance of weighted bootstrapped kernel deconvolution density estimators," Statistical Papers, Springer, vol. 61(4), pages 1773-1798, August.
    3. Liu, Bo & Mojirsheibani, Majid, 2015. "On a weighted bootstrap approximation of the Lp norms of kernel density estimators," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 65-73.
    4. M. D. Jiménez-Gamero & A. Batsidis, 2017. "Minimum distance estimators for count data based on the probability generating function with applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 503-545, July.
    5. Ali Al-Sharadqah & Majid Mojirsheibani, 2020. "A simple approach to construct confidence bands for a regression function with incomplete data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 81-99, March.
    6. G. I. Rivas-Martínez & M. D. Jiménez-Gamero & J. L. Moreno-Rebollo, 2019. "A two-sample test for the error distribution in nonparametric regression based on the characteristic function," Statistical Papers, Springer, vol. 60(4), pages 1369-1395, August.
    7. Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.
    8. Mojirsheibani, Majid, 2012. "A weighted bootstrap approximation of the maximal deviation of kernel density estimates over general compact sets," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 230-241.
    9. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    10. Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2021. "A test for the geometric distribution based on linear regression of order statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 103-123.
    11. Quessy, Jean-François & Éthier, François, 2012. "Cramér–von Mises and characteristic function tests for the two and k-sample problems with dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2097-2111.
    12. Majid Mojirsheibani & William Pouliot, 2017. "Weighted bootstrapped kernel density estimators in two-sample problems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 61-84, January.

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