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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 8, Fasc. ,
pages 183 - 189
 

BAHADUR’S REPRESENTATION OF SAMPLE QUANTILES BASED ON SMOOTHED ESTIMATES OF A DISTRIBUTION FUNCTION

Y. P. Mack

Abstract: Suppose ^F n is a convolution-smoother of the standard empirical distribution function based on a random sample from a distribution F with a positive density. Consider the smoothed sample quantile function F^-1(p) = inf(x : ^F (x) > p). n n Under appropriate conditions, we establish a pointwise Bahadur type representation theorem [1] from which local behavior can be inferred.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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