, Volume 22, Issue 1, pp 189–203 | Cite as

Consistency of a certain class of empirical density functions

  • R D. Reiss


Empirical density functionsf n of the class (1.1) are studied. Under certain regularity conditions the rate of probability one convergence (analoguous to the law of the iterated logarithm) is found for\(\mathop {\sup \left| {f_n (t) - f(t)} \right|}\limits_{t \in R} \) wheref is the Lebesgue density function of the underlying probability measure. The results enable us to choose an “optimal” sequence of bandwiths α n ,nN, forf n . Consistency properties of the probability measures determined byf n are discussed.


Density Function Stochastic Process Probability Measure Probability Theory Economic Theory 


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Copyright information

© Physica-Verlag Rudolf Liebing KG 1975

Authors and Affiliations

  • R D. Reiss
    • 1
  1. 1.Mathematisches InstitutUniversität KölnKöln 41

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