Summary
Let X 1, X 2...be a sequence of independent identically distributed random variables with a smooth density function f. We obtain central limit theorems for \(\int\limits_\infty ^\infty {|f_n (t) - f_{} (t)|^p d\mu (t)} ,{\text{ }}1\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } p < \infty \), where f n is a kernel estimate of f and μ is a measure on the Borel sets of ℝ.
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The research of both authors was supported by a NSERC Canada Grant and by an EMR Canada Grant of M. Csörgö at Carleton University, Ottawa
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Csörgő, M., Horváth, L. Central limit theorems for L p-Norms of density estimators. Probab. Th. Rel. Fields 80, 269–291 (1988). https://doi.org/10.1007/BF00356106
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DOI: https://doi.org/10.1007/BF00356106