Estimation of density functions by order statistics (Q1091698)

The properties of the empirical density function, \[ f_ n(x)=k/n(\xi^+_ j-\xi^+_{j-1}),\;if\;\xi^+_{j-1}<x\leq \xi^+_ j, \] where \(\xi^+_{j-1}\) and \(\xi^+_ j\) are sample elements and there are exactly k-1 sample elements between them, are studied in that practical point of view how to choose a suitable k for a ''good'' estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions.