INTERACTIVE KERNEL DENSITY ESTIMATION WITH LISP-STAT
Kernel Density Estimation is, due to its conceptual simplicity and good
mathematical properties, one of the most commonly used methods for
density estimation. Its actual application and practical use has
two main problems: the high computational cost of the involved
algorithms and the amount of discretionality present in the choice of
the parameters and the general set-up of the estimation.
We have used LISP-STAT to develop a highly interactive package for
Kernel Density Estimation (KDE). Using a standard graphical interface
the user can select the kernel function to use and adjust the
smoothing parameter while seeing the effect of the changes. Graphical
facilities include comparison of several estimations, histograms and
other data summaries, drawing a normal density function fitted to data
or user defined normal mixture densities, visualization of the kernel
function, output to postscript files via GNUplot, etc. We have
implemented some techniques for fast computation for KDE, namely
binned FFT and binned updating methods. Some of the currently
preferred methods for automatic bandwidth selection are implemented.
Variable bandwidth is available via a new and general LISP-STAT object
aimed to implement user-controlled transformation of parameters, where
the user defines the shape of the transformation graph by moving the
knots of a spline-generated curve. Then, the caller program can apply the
transformed data or parameter to any computation.
Some extensions currently being developed include hazard function
estimation, kernel regression and histogram exploration. Future
development will include multivariate density estimation and
visualization, and addressing the problem of discontinuities in the
density function.