locCteWeights {locpol}R Documentation

Local Polynomial Weights

Description

Local Constant and local Linear estimator with weight.

Usage

  locCteWeightsC(x, xeval, bw, kernel, weig = rep(1, length(x))) 
  locLinWeightsC(x, xeval, bw, kernel, weig = rep(1, length(x)))
  locWeightsEval(lpweig, y) 
  locWeightsEvalC(lpweig, y) 

Arguments

x x covariate data values.
y y response data values.
xeval Vector with evaluation points.
bw Smoothing parameter, bandwidth.
kernel Kernel used to perform the estimation, see Kernels
weig Vector of weights for observations.
lpweig Local polynomial weights $(X^TWX)^{-1}X^TW$ evaluated at xeval matrix.

Details

locCteWeightsC and locLinWeightsC computes local constant and local linear weights, say any of the entries of the vector $(X^TWX)^{-1}X^TW$ for $p=0$ and $p=1$ resp. locWeightsEvalC and locWeightsEval computes local the estimator for a given vector of responses y

Value

locCteWeightsC and locLinWeightsC returns a list with two components

den Estimation of $(n*bw*f(x))^{p+1}$.
locWeig $(X^TWX)^{-1}X^TW$ evaluated at xeval Matrix.

locWeightsEvalC and locWeightsEval returns the vector with the estimation. It performs the matrix multiplication between locWeig and y to obtain the estimation at given xeval points.

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

Kernels, locpol.

Examples

        size <- 200
        sigma <- 0.25
        deg <- 1
        kernel <- EpaK
        bw <- .25
        xeval <- 0:100/100
        regFun <- function(x) x^3
        x <- runif(size)
        y <- regFun(x) + rnorm(x, sd = sigma)
        d <- data.frame(x, y)
        lcw <- locCteWeightsC(d$x, xeval, bw, kernel)$locWeig
        lce <- locWeightsEval(lcw, y) 
        lceB <- locCteSmootherC(d$x, d$y, xeval, bw, kernel)$beta0
        mean((lce-lceB)^2)
    llw <- locLinWeightsC(d$x, xeval, bw, kernel)$locWeig
        lle <- locWeightsEval(llw, y) 
        lleB <- locLinSmootherC(d$x, d$y, xeval, bw, kernel)$beta0
        mean((lle-lleB)^2)

[Package locpol version 0.2-0 Index]