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

R. L. Taylor and Tien-Chung Hu
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R. L. Taylor: University of Georgia, Department of Statistics
Tien-Chung Hu: University of Georgia, Department of Statistics

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 253-266 from Springer

Abstract: 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.

Keywords: Kernel Density; Random Function; Random Element; Separable Banach Space; Kernel Density Estimator (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_19

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DOI: 10.1007/978-94-009-3963-9_19

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