| lpepa {lpridge} | R Documentation |
Fast and stable algorithm for nonparametric estimation of regression functions and their derivatives via local polynomials with Epanechnikov weight function.
lpepa(x, y, bandwidth, deriv = 0, n.out = 200, x.out = NULL,
order = deriv+1, mnew = 100, var = FALSE)
x |
vector of design points, not necessarily ordered. |
y |
vector of observations of the same length as x. |
bandwidth |
bandwidth(s) for nonparametric estimation. Either a
number or a vector of the same length as x.out. |
deriv |
order of derivative of the regression function to be
estimated; defaults to deriv = 0. |
n.out |
number of output design points where the function has to
be estimated. The default is n.out=200. |
x.out |
vector of output design points where the function has to
be estimated. The default value is an equidistant grid of n.out
points from min(x) to max(x). |
order |
integer, order of the polynomial used for local
polynomials. Must be <= 10 and defaults to
order = deriv+1. |
mnew |
integer forcing to restart the algorithm after mnew
updating steps.
The default is mnew = 100. For mnew = 1 you get a numerically
“super-stable” algorithm (see reference SBE&G below). |
var |
logical flag: if TRUE, the variance of the estimator
proportional to the residual variance is computed (see details). |
More details are described in the first reference SBE&G (1994)
below. In S&G, a bad finite sample behaviour of local polynomials
for random designs was found.
For practical use, we therefore propose local polynomial regression
fitting with ridging, as implemented in the function
lpridge. In lpepa, several parameters described
in SBE&G are fixed either in the fortran
routine or in the R-function. There, you find comments how to change them.
For var=TRUE, the variance of the estimator proportional to the
residual variance is computed, i.e., the exact finite sample variance of the
regression estimator is var(est) = est.var * sigma^2.
a list including used parameters and estimator.
x |
vector of ordered design points. |
y |
vector of observations ordered according to x. |
bandwidth |
vector of bandwidths actually used for nonparametric estimation. |
deriv |
order of derivative of the regression function estimated. |
x.out |
vector of ordered output design points. |
order |
order of the polynomial used for local polynomials. |
mnew |
force to restart the algorithm after mnew updating steps. |
var |
logical flag: whether the variance of the estimator was computed. |
est |
estimator of the derivative of order deriv of the regression function. |
est.var |
estimator of the variance of est (proportional to residual variance). |
See also http://www.unizh.ch/biostat/ under ‘Manuscripts’ etc.
- Numerical stability and computational speed:
B. Seifert, M. Brockmann, J. Engel and T. Gasser (1994)
Fast algorithms for nonparametric curve estimation.
J. Computational and Graphical Statistics 3, 192–213.
- Statistical properties:
Seifert, B. and Gasser, T. (1996)
Finite sample variance of local polynomials: Analysis and solutions.
J. American Statistical Association 91(433), 267–275.
Seifert, B. and Gasser, T. (2000) Data adaptive ridging in local polynomial regression. J. Computational and Graphical Statistics 9, 338–360.
Seifert, B. and Gasser, T. (1998) Ridging Methods in Local Polynomial Regression. in: S. Weisberg (ed), Dimension Reduction, Computational Complexity, and Information, Vol.30 of Computing Science & Statistics, Interface Foundation of North America, 467–476.
Seifert, B. and Gasser, T. (1998) Local polynomial smoothing. in: Encyclopedia of Statistical Sciences, Update Vol.2, Wiley, 367–372.
Seifert, B., and Gasser, T. (1996) Variance properties of local polynomials and ensuing modifications. in: Statistical Theory and Computational Aspects of Smoothing, W. Härdle, M. G. Schimek (eds), Physica, 50–127.
lpridge, and also lowess and
loess which do local linear and quadratic regression
quite a bit differently.
data(cars) attach(cars) epa.sd <- lpepa(speed,dist, bandw=5) # local polynomials plot(speed, dist, main = "data(cars) & lp epanechnikov regression") lines(epa.sd$x.out, epa.sd$est, col="red") lines(lowess(speed,dist, f= .5), col="orange") detach()