EAN: 9789819918614

SPRINGERBRIEFS IN STATISTICS STATISTICAL INFE...

This book presents a study of statistical inferences based on the kernel-type estimators of
distribution functions. The inferences involve matters such as quantile estimation 
nonparametric tests  and mean residual life expectation  to name just some. Convergence rates
for the kernel estimators of density functions are slower than ordinary parametric estimators 
which have root-n consistency. If the appropriate kernel function is used  the kernel
estimators of the distribution functions recover the root-n consistency  and the inferences
based on kernel distribution estimators have root-n consistency. Further  the kernel-type
estimator produces smooth estimation results. The estimators based on the empirical
distribution function have discrete distribution  and the normal approximation cannot be
improved-that is  the validity of the Edgeworth expansion cannot be proved. If the support of
the population density function is bounded  there is a boundary problem  namely the estimator
does not have consistency near the boundary. The book also contains a study of the mean squared
errors of the estimators and the Edgeworth expansion for quantile estimators.

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