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Central limit theorems for k-nearest neighbour distances

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  • Penrose, Mathew D.

Abstract

Let X1,X2,X3,... be independent d-dimensional variables with common density function f. Let Ri,k,n be the distance from Xi to its kth nearest neighbour in {X1,...,Xn}. Suppose (kn) is a sequence with 1

Suggested Citation

  • Penrose, Mathew D., 2000. "Central limit theorems for k-nearest neighbour distances," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 295-320, February.
    • Handle: RePEc:eee:spapps:v:85:y:2000:i:2:p:295-320
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    References listed on IDEAS

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    1. S. Jammalamadaka & Xian Zhou & Ram Tiwari, 1989. "Asymptotic efficiencies of spacings tests for goodness of fit," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 355-377, December.
    2. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    3. Mack, Y. P. & Rosenblatt, M., 1979. "Multivariate k-nearest neighbor density estimates," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 1-15, March.
    4. Hall, Peter, 1986. "On powerful distributional tests based on sample spacings," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 201-224, August.
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