THE USE OF VARIABLE KERNEL MASS IN DENSITY ESTIMATION
Michael L. Sturgeon
Abstract: A new theoretical approach is developed for estimating a univariate density
for large using a nonnegative symmetric kernel with variable mass.
Compared to kernels of order kernels of variable mass asymptotically achieve (i)
smaller variance, (ii) essentially the same bias, and so (iii) a reduced MISE of order
The analysis uses a common MISE-optimal bandwidth and locally
adapted kernel mass to be estimated at
the kernel center, where is the average value over an interval of length
centered on Mass adaptation derives from considering the expected effect
of negative mass, in kernels of order upon the positive part of such kernels.
Unlike the Abramson procedure for varying local bandwidth, this procedure does not
require any special accommodation for small values of for in
for large 
using a nonnegative symmetric kernel with variable mass.
Compared to kernels of order 
kernels of variable mass asymptotically achieve (i)
smaller variance, (ii) essentially the same bias, and so (iii) a reduced MISE of order
The analysis uses a common MISE-optimal bandwidth 
and locally
adapted kernel mass 
to be estimated at
the kernel center, where 
is the average 
value over an interval of length
centered on 
Mass adaptation derives from considering the expected effect
of negative mass, in kernels of order 
upon the positive part of such kernels.
Unlike the Abramson procedure for varying local bandwidth, this procedure does not
require any special accommodation for small values of 
for 
in 