locpolSmoothers {locpol}

Local Polynomial estimation.

Description

Computes the local polynomial estimation of the regression function.

Usage

locCteSmootherC(x, y, xeval, bw, kernel, weig = rep(1, length(y)))
locLinSmootherC(x, y, xeval, bw, kernel, weig = rep(1, length(y)))
locCuadSmootherC(x, y, xeval, bw, kernel, weig = rep(1, length(y)))
locPolSmootherC(x, y, xeval, bw, deg, kernel, DET = FALSE,
	weig = rep(1, length(y)))
looLocPolSmootherC(x, y, bw, deg, kernel, weig = rep(1, length(y)),
        DET = FALSE)

Arguments

x

x covariate data values.

y

y response data values.

xeval

Vector of evaluation points.

bw

Smoothing parameter, bandwidth.

kernel

Kernel used to perform the estimation, see Kernels

weig

Vector of weights for observations.

deg

Local polynomial estimation degree (p).

DET

Boolean to ask for the computation of the determinant if the matrix X^TWX.

Details

All these function perform the estimation of the regression function for different degrees. While locCteSmootherC, locLinSmootherC, and locCuadSmootherC uses direct computations for the degrees 0,1 and 2 respectively, locPolSmootherC implements a general method for any degree. Particularly useful can be looLocPolSmootherC(Leave one out) which computes the local polynomial estimator for any degree as locPolSmootherC does, but estimating m(x_i) without using i–th observation on the computation.

Value

A data frame whose components gives the evaluation points, the estimator for the regression function m(x) and its derivatives at each point, and the estimation of the marginal density for x to the p+1 power. These components are given by:

x

Evaluation points.

beta0, beta1, beta2, ...

Estimation of the i-th derivative of the regression function (m^{(i)}(x)) for i=0,1,....

den

Estimation of (n*h*f(x))^{p+1}, being h the bandwidth bw.

Author(s)

Jorge Luis Ojeda Cabrera.

References

Fan, J. and Gijbels, I. Local polynomial modelling and its applications\/. Chapman & Hall, London (1996).

Wand, M.~P. and Jones, M.~C. Kernel smoothing\/. Chapman and Hall Ltd., London (1995).

See Also

locpoly from package KernSmooth, ksmooth and loess in stats (but from earlier package modreg).

Examples

N <- 100
xeval <- 0:10/10
d <- data.frame(x = runif(N))
bw <- 0.125
fx <- xeval^2 - xeval + 1
##	Non random
d$y <- d$x^2 - d$x + 1
cuest <- locCuadSmootherC(d$x, d$y ,xeval, bw, EpaK)
lpest2 <- locPolSmootherC(d$x, d$y , xeval, bw, 2, EpaK)
print(cbind(x = xeval, fx, cuad0 = cuest$beta0,
lp0 = lpest2$beta0, cuad1 = cuest$beta1, lp1 = lpest2$beta1))
##	Random
d$y <- d$x^2 - d$x + 1 + rnorm(d$x, sd = 0.1)
cuest <- locCuadSmootherC(d$x,d$y , xeval, bw, EpaK)
lpest2 <- locPolSmootherC(d$x,d$y , xeval, bw, 2, EpaK)
lpest3 <- locPolSmootherC(d$x,d$y , xeval, bw, 3, EpaK)
cbind(x = xeval, fx, cuad0 = cuest$beta0, lp20 = lpest2$beta0,
lp30 = lpest3$beta0, cuad1 = cuest$beta1, lp21 = lpest2$beta1,
lp31 = lpest3$beta1)