OnL
p
-convergence rates for statistical functions with application toL-estimates |
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Authors: | Ibrahim A Ahmad |
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Institution: | (1) University of Maryland Baltimore County, USA |
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Abstract: | Summary A parameter which may be represented as a functionalT(F) of a distribution functionF may be estimated by the “statistical function”T(F
n
), whereF
n
is the empirical distribution function. Recently, Boos and Serfling (1979, Florida State University Statistics Report No.
M 499) obtained sufficient conditions for the Berry-Esseen theorem to hold forT(F
n
)-T(F) and applied the results to derive rates of convergence inL
∞ forL-estimates. The present note complements their work by obtaining theL
p
-rates of convergence, 1≦p<∞ forT(F
n
)-T(F) and its application toL-estimates. |
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Keywords: | Primary 60F05 Secondary 60J80 60F99 |
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