Abstract. Local polynomial regression is a generalization of local
mean smoothing as described by Nadaraya (1964) and Watson (1964). Instead of
fitting a local mean, one instead fits a local pth-order polynomial.
Calculations for local polynomial regression are naturally more complex than
those for local means, but local polynomial smooths have better statistical
properties. The computational complexity may, however, be alleviated by using a
Stata plugin. In this article, we describe the locpoly command for performing
local polynomial regression. The calculations involved are implemented in both
ado-code and with a plugin, allowing the user to assess the speed improvement
obtained from using the plugin. Source code for the plugin is also provided as
part of the package for this program.
ClevelandW. S.1979. Robust locally weighted regression and
smoothing scatterplots. Journal of the American
Statistical Association74: 829–836.
2.
DonohoD. L.1995. Nonlinear solution of linear inverse problems
by wavelet–vaguelette decomposition. Applied and
Computational Harmonic Analysis2: 101–126.
3.
EubankR. L.1988. Spline Smoothing and Nonparametric
Regression.New York: Marcel
Dekker.
4.
FanJ.1992. Design–adaptive nonparametric
regression. Journal of the American Statistical
Association87: 998–1004.
5.
FanJ., and GijbelsI.1996. Local Polynomial Modelling and Its
Applications.London: Chapman &
Hall.
6.
FanJ., and MarronJ.S.1994. Fast implementations of nonparametric curve
estimation. Journal of Computational and Graphical
Statistics3: 35–56.
7.
GasserT., and MüllerH.-G.1979. Kernel estimation of regression
functions. In Smoothing Techniques for Curve
Estimation, Lecture Notes in Mathematics, vol.
757, 23–68. New
York:
Springer.
8.
HallP., and WandM.P.1996. On the accuracy of binned kernel density
estimates. Journal of Multivariate Analysis56: 165–184.
9.
NadarayaE. A.1964. On estimating regression.
Theory of Probability and Its Application9: 141–142.