A Note on the L1 Consistency of Variable Kernel Estimates

1 . Introduction . Most consistent nonparametric density estimates have a built-in smoothing parameter . Numerous schemes have been proposed (see, e.g ., references found in Rudemo, 1982 ; or Devroye and Penrod, 1984) for selecting the smoothing parameter as a function of the data only (a process called automatization), and for introducing locally adaptable smoothing parameters . In this note, we give conditions which insure that estimators of the form