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

Rates of convergence for the distance between distribution function estimators

  • D. D. Boos


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(·).


Distribution Function Stochastic Process Probability Theory Economic Theory Normed Difference 
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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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