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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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Ibrahim Ahmad                                     March 15, 2001
Department of Statistics                          304 Whitehead Hall
University of Central Florida                     Preseminar: 3:00 p.m.
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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     KERNEL DENSITY ESTIMATION OF FUNCTIONS OF RANDOM VARIABLES
              AND AN APPLICATION TO TESTING NORMALITY

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                             ABSTRACT

In this talk, the usual kernel density estimation method is adopted to
estimate the density of a function of a set of random variables.  The
integrated square error (ISE) and its mean (MISE) are given and
approximated.  Further, a central limit theorem for the difference
ISE - MISE  is developed.  A short discussion of the bandwidth selection
problem is then presented, and finally an application of this
generalization to testing normality is briefly offered.  Some interesting
open questions will conclude the presentation.

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