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Consistency of Kernel Density Estimators and Laws of Large Numbers in Co (R)

In: Mathematical Statistics and Probability Theory

Author

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  • R. L. Taylor

    (University of Georgia, Department of Statistics)

  • Tien-Chung Hu

    (University of Georgia, Department of Statistics)

Abstract

The kernel density estimators can be considered as averages of (usually) symmetric probability density functions which are centered at the sample data points. Consequently, the appropriate function-space setting for these kernel density estimators is of considerable interest and has been discussed in the literature. In this paper, the space of real-valued continuous functions which go to zero at ±∞, Co (R), with the supremum norm, is proposed for these considerations. Laws of large numbers are developed for Co (R) which have direct application in establishing the uniform strong consistency of the kernel density estimators. Moreover, under mild conditions on the kernel functions, it can be shown that no proper subspace of Co (R) will suffice for these considerations.

Suggested Citation

  • R. L. Taylor & Tien-Chung Hu, 1987. "Consistency of Kernel Density Estimators and Laws of Large Numbers in Co (R)," Springer Books, in: M. L. Puri & P. Révész & W. Wertz (ed.), Mathematical Statistics and Probability Theory, pages 253-266, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3963-9_19
    DOI: 10.1007/978-94-009-3963-9_19
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