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Metrika

, Volume 33, Issue 1, pp 197–202 | Cite as

Rates of convergence for the distance between distribution function estimators

  • D. D. Boos
Publications

Summary

The normed difference between “kernel” distribution function estimators\(\hat F_n \) and the empirical distribution functionF n is investigated. Conditions on the kernel and bandwidth of\(\hat F_n \) are given so that\(a_n \left\| {\hat F_n - F_n } \right\|\xrightarrow{{wpl}}0\) as n→∞ for both the sup-norm\(\left\| g \right\|_\infty = \mathop {\sup }\limits_x \left| {g(x)} \right|and L_1 \) andL1 norm\(\left\| g \right\|_1 = f\left| {g(x)} \right|dx\). Applications include equivalence in asymptotic distribution ofT\(\hat F_n \) andT(F n ) (to ordern n ) for certain robust functionalsT(·).

Keywords

Distribution Function Stochastic Process Probability Theory Economic Theory Normed Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Physica-Verlag 1986

Authors and Affiliations

  • D. D. Boos
    • 1
  1. 1.Department of StatisticsNorth Carolina State UniversityRaleighUSA

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