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The laws of the iterated logarithm for two kinds of PP statistics

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  • Hengjian, Cui

Abstract

Motivated by recent work on exploratory Projection Pursuit (PP), we define the smoothing PP Kolmogorov-Smirnov statistics and the smoothing PP Crámer-von Mises statistics based on one-dimensional projections. We demonstrate the Laws of the Iterated Logarithm (LIL) for the PP Kolmogorov-Smirnov statistics, the PP Crámer-von Mises statistics hold. The conditions and results of the LIL in this paper are same as those of the LIL in one-dimensional empirical processes.

Suggested Citation

  • Hengjian, Cui, 1997. "The laws of the iterated logarithm for two kinds of PP statistics," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 235-243, March.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:3:p:235-243
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    References listed on IDEAS

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    1. Zhang, J. & Zhu, L. X. & Cheng, P., 1993. "Exponential Bounds for the Uniform Deviation of a Kind of Empirical Processes, II," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 250-268, November.
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