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Permutation tests for equality of distributions of functional data

Author

Listed:
  • Federico A. Bugni

    (Institute for Fiscal Studies and Duke University)

  • Joel L. Horowitz

    (Institute for Fiscal Studies and Northwestern University)

Abstract

Economic data are often generated by stochastic processes that take place in continuous time, though observations may occur only at discrete times. For example, electricity and gas consumption take place in continuous time. Data generated by a continuous time stochastic process are called functional data. This paper is concerned with comparing two or more stochastic processes that generate functional data. The data may be produced by a randomized experiment in which there are multiple treatments. The paper presents a test of the hypothesis that the same stochastic process generates all the functional data. In contrast to existing methods, the test described here applies to both functional data and multiple treatments. The test is presented as a permutation test, which ensures that in a finite sample, the true and nominal probabilities of rejecting a correct null hypothesis are equal. The paper also presents the asymptotic distribution of the test statistic under alternative hypotheses. The results of Monte Carlo experiments and an application to an experiment on billing and pricing of natural gas illustrate the usefulness of the test.

Suggested Citation

  • Federico A. Bugni & Joel L. Horowitz, 2018. "Permutation tests for equality of distributions of functional data," CeMMAP working papers CWP18/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:18/18
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    References listed on IDEAS

    as
    1. Kim, Myung Suk & Wang, Suojin, 2006. "Sizes of two bootstrap-based nonparametric specification tests for the drift function in continuous time models," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1793-1806, April.
    2. Cuesta-Albertos, J.A. & del Barrio, E. & Fraiman, R. & Matran, C., 2007. "The random projection method in goodness of fit for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4814-4831, June.
    3. Federico A. Bugni & Peter Hall & Joel L. Horowitz & George R. Neumann, 2009. "Goodness-of-fit tests for functional data," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 1-18, January.
    4. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(2), pages 426-468, April.
    5. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
    6. Peter Hall, 2002. "Permutation tests for equality of distributions in high-dimensional settings," Biometrika, Biometrika Trust, vol. 89(2), pages 359-374, June.
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    More about this item

    Keywords

    Functional data; permutation test; randomized experiment; hypothesis test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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