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Implementation of a goodness-of-fit test through Khmaladze martingale transformation

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  • Jiwoong Kim

    (Ajou University Medical Center)

Abstract

Khmaladze martingale transformation provides an asymptotically-distribution-free method for a goodness-of-fit test. With its usage not being restricted to testing for normality, it can also be selected to test for a location-scale family of distributions such as logistic and Cauchy distributions. Despite its merits, the Khmaladze martingale transformation, however, could not have enjoyed deserved celebrity since it is computationally expensive; it entails the complex and time-consuming computations, including optimization, integration of a fractional function, matrix inversion, etc. To overcome these computational challenges, this paper proposes a fast algorithm which provides a solution to the Khmaladze martingale transformation method. To that end, the proposed algorithm is equipped with a novel strategy, named integration-in-advance, which rigorously exploits the structure of the Khmaladze martingale transformation.

Suggested Citation

  • Jiwoong Kim, 2020. "Implementation of a goodness-of-fit test through Khmaladze martingale transformation," Computational Statistics, Springer, vol. 35(4), pages 1993-2017, December.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00971-7
    DOI: 10.1007/s00180-020-00971-7
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    References listed on IDEAS

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    1. Lauren Bin Dong & David E. A. Giles, 2004. "An Empirical Likelihood Ratio Test for Normality in Linear Regression," Econometrics Working Papers 0402, Department of Economics, University of Victoria.
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    5. Koul, Hira L. & Sakhanenko, Lyudmila, 2005. "Goodness-of-fit testing in regression: A finite sample comparison of bootstrap methodology and Khmaladze transformation," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 290-302, October.
    6. Koul, Hira L. & Zhu, Xiaoqing, 2015. "Goodness-of-fit testing of error distribution in nonparametric ARCH(1) models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 141-160.
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    Cited by:

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    2. El-Aroui, Mhamed-Ali, 2021. "Real-time prequential goodness-of-fit testing of life distributions in renewal processes," Statistics & Probability Letters, Elsevier, vol. 176(C).

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