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Order of a kernel

From Wikipedia, the free encyclopedia

In statistics, the order of a kernel is the degree of the first non-zero moment of a kernel.[1]

Definitions

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The literature knows two major definitions of the order of a kernel. Namely are:

Definition 1

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Let be an integer. Then, is a kernel of order if the functions are integrable and satisfy [2]

Definition 2

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References

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  1. ^ Li, Qi; Racine, Jeffrey Scott (2011), "1.11 Higher Order Kernel Functions", Nonparametric Econometrics: Theory and Practice, Princeton University Press, ISBN 9781400841066
  2. ^ Tsybakov, Alexandre B. (2009). Introduction to Nonparametric Econometrics. New York, NY: Springer. p. 5. ISBN 9780387790510.