# locPolWeights: Local Polynomial Weights In locpol: Kernel local polynomial regression

## Description

Local Constant and local Linear estimator with weight.

## Usage

 ```1 2 3 4 5``` ``` locCteWeightsC(x, xeval, bw, kernel, weig = rep(1, length(x))) locLinWeightsC(x, xeval, bw, kernel, weig = rep(1, length(x))) locPolWeights(x, xeval, deg, 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. `deg` Local polynomial estimation degree (p). `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*h*f(x))^{p+1} being h the bandwidth `bw`. `locWeig` (X^TWX)^{-1}X^TW evaluated at `xeval` Matrix.

## 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).

`Kernels`, locpol.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ``` 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) ```