locpol {locpol}R Documentation

Local Polynomial estimation.

Description

Formula interface for the local polynomial estimation.

Usage

    locpol(formula,data,weig=rep(1,nrow(data)),bw=NULL,kernel=EpaK,deg=1,
            xeval=NULL,xevalLen=100)
    confInterval(x)
    ## S3 method for class 'locpol':
    residuals(object,...)
    ## S3 method for class 'locpol':
    fitted(object,deg=0,...)
    ## S3 method for class 'locpol':
    summary(object,...)
    ## S3 method for class 'locpol':
    print(x,...)
    ## S3 method for class 'locpol':
    plot(x,...)        

Arguments

formula formula as in lm, only first covariate is used.
data data frame with data.
weig Vector of weigths for each observations.
bw Smoothing parameter, bandwidth.
kernel Kernel used to perform the estimation, see Kernels
deg Local polynomial estimation degree($p$).
xeval Vector of evaluation points.
xevalLen Length of xeval if it is NULL
x A locpol object.
object A locpol object.
... Any other required argument.

Details

This is an interface to the local polynomial estimation function that provides basic lm functionality. summary and print methods shows very basic information about the fit, fitted return the estimation of the derivatives if code{deg} is larger than 0, and plot provides a plot of data, local polynomial estimation and the variance estimation.

Variance estimation is carried out by means of the local constant regression estimation of the squared residuals.

confInterval provides confidence intervals for all points in x$lpFit$[,x$X], say those in xeval.

Value

A list containing among other components:

mf Model frame for data and formula.
data data frame with data.
weig Vector of weight for each observations.
xeval Vector of evaluation points.
bw Smoothing parameter, bandwidth.
kernel Kernel used, see Kernels
KName Kernel name, a string with the name of kernel.
deg Local polynomial estimation degree($p$).
X,Y Names in data of the response and covariate. They are also used in lpFit to name the fitted data.
residuals
lpFit

{ Data frame with the local polynomial fit. It contains covariate, response, derivatives estimation, $X$ density estimation, and variance estimation.}

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).

Crist'obal, J. A. and Alcal'a, J. T. (2000). Nonparametric regression estimators for length biased data/. J. Statist. Plann. Inference, 89, pp. 145-168.

Ahmad, Ibrahim A. (1995) On multivariate kernel estimation for samples from weighted distributions/. Statistics & Probability Letters, 22, num. 2, pp. 121-129

See Also

locpoly from package KernSmooth, ksmooth and loess from package modreg.

Examples

    N <- 250
    xeval <- 0:100/100
    ##  ex1
    d <- data.frame(x = runif(N))
    d$y <- d$x^2 - d$x + 1 + rnorm(N, sd = 0.1)
    r <- locpol(y~x,d)
        plot(r)
    ##  ex2
    d <- data.frame(x = runif(N))
    d$y <- d$x^2 - d$x + 1 + (1+d$x)*rnorm(N, sd = 0.1)
    r <- locpol(y~x,d)
        plot(r)
    ##  length biased data !!
    d <- data.frame(x = runif(10*N))
    d$y <- d$x^2 - d$x + 1 + (rexp(10*N,rate=4)-.25)
    posy <- d$y[ whichYPos <- which(d$y>0) ];
    d <- d[sample(whichYPos, N,prob=posy,replace=FALSE),]
    rBiased <- locpol(y~x,d)
    r <- locpol(y~x,d,weig=1/d$y)
    plot(d)
    points(r$lpFit[,r$X],r$lpFit[,r$Y],type="l",col="blue")
    points(rBiased$lpFit[,rBiased$X],rBiased$lpFit[,rBiased$Y],type="l")
    curve(x^2 - x + 1,add=TRUE,col="red")
    ##  add example with real data !!

[Package locpol version 0.2-0 Index]