sBF (version 1.1.1)

sBF: Smooth Backfitting Estimator

Description

Smooth Backfitting for additive models using Nadaraya-Watson estimator.

Usage

sBF(dat, depCol = 1, m = 100, windows = rep(20, ncol(dat) - 1),
bw = NULL, method = "gaussian", mx = 100, epsilon = 1e-04,
PP = NULL, G = NULL)

Arguments

dat

matrix of data.

depCol

column of dat matrix in which the dependent variable is positioned.

m

number of grid points. Higher values of m imply better estimates and loger computational time.

windows

number of windows. (covariate range width)/windows provide the bandwidths for the kernel regression smoother.

bw

bandwidths for the kernel regression smoother.

method

kernel method. See function K.

mx

maximum iterations number.

epsilon

convergence limit of the iterative algorithm.

PP

matrix of joint probabilities.

G

grid on which univariate functions are estimated.

Value

• mxhat
  estimated univariate functions on the grid points.
• m0
  estimated constant value in the additive model.
• grid
  the grid.
• conv
  boolean variable indicating whether the convergence has been achieved.
• nit
  number of iterations performed.
• PP
  matrix of joint probabilities.
• bw
  bandwidths used for the kernel regression smoother.

Details

Bandwidth can be chosen in two different ways: through the argument bw or defining the number of windows into the range of the values of any independent variable through the argument windows (equal to 20 by default). Bandwidth is the width of the windows. Both the parameters bw and windows can be single values, then every smoother has the same bandwidth, or they can be vectors of length equal tu the covariates number to specify different bandwidths for any direction. Higher values of the bandwidth provide smoother estimates. In applications it could be useful using the same PP matrix for different estimates, e.g. to evaluate the impact of different bandwidths and develop algorithms to select optimal bandwidths (see, for example Nielsen and Sperlich, 2005, page 52). This reasoning applies also to the grid G. This is why the possibility to input matrices G and PP as parameters is given. The program creates G and PP if they are not inserted.

See Also

sBF-package, K.

Examples

X <- matrix(rnorm(1000), ncol=2)
MX1 <- X[,1]^3
MX2 <- sin(X[,2])
Y <- MX1 + MX2
data <- cbind(Y, X)
  
est <- sBF(data)

par(mfrow=c(1, 2))
plot(est$grid[,1],est$mxhat[,1], type="l",
     ylab=expression(m[1](x[1])), xlab=expression(x[1]))
curve(x^3, add=TRUE, col="red")
plot(est$grid[,2],est$mxhat[,2], type="l",
     ylab=expression(m[2](x[2])), xlab=expression(x[2]))
curve(sin(x), add=TRUE, col="red")
par(mfrow=c(1, 1))