On a Method of Histogram Smoothing and Application in Nonparametric Density Estimation

This talk will highlight some recent development in the area of
nonparametric functional estimation with emphasis on nonparametric density
estimation for restricted support which is based on a well-known lemma
attributed to Hille, a good account of which is contained in Feller (1965,
An Introduction to Probability Theory and Applications, Vol. 2). Chaubey
and Sen (1996, Stat. & Dec.) adapted this lemma for estimation of the
survival function replacing u(x) by the empirical distribution function.
The resulting estimator also provides a natural smooth nonparametric density estimator. Different
aspects of this estimator including the selection of smoothing parameter
and a modification for length biased data are outlined.