Local regression or loess has become a popular method for
smoothing scatterplots and for nonparametric regression in general.
The final result is a ``smoothed'' version of the 
data. In order to obtain the value of the smooth estimate associated
with a given covariate a polynomial, usually a line, is fitted
locally using weighted least squares. 
In this paper we will present a version of local
regression that fits
more general parametric functions. In certain
cases, the fitted parameters may be interpreted in some way and we
call them meaningful parameters. Examples
showing how this procedure is useful for signal processing, physiological, 
and financial data are included.