Rfit (version 0.09)

irls: Function for Iterated Reweighted Least Squares R-type estimates

Description

This function is used to get close to the final solution. From our empirical studies it is generally the case that the IRLS estimates get close to the final solution faster than other types of algorithms, however they do not seem to find the exact minimizer of Jaeckel's dispersion. Hence a small number of these steps can be first used to speed up a Newton-type algorithm.

Usage

irls(x, y, b0 = suppressWarnings(rq(y ~ x - 1)$coef), scores , eps = 0.001, max.iter = 20)

Arguments

x

n by p design matrix

y

n by 1 response vector

b0

initial estimate

scores

object of class scores

eps

stop if the relative change in the estimate is less than this value

max.iter

maximum number of IRLS steps to take

Value

• A vector of estimated regression coefficents.

References

Cheng, K. S. and Hettmansperger, T. P. (1983), Weighted Least-Squares Rank Regression, Communications in Statistics, Part A - Theory and Methods, 12, 1069-1086.

Sievers, J. and Abebe, A. (2004), Rank Estimation of Regression Coefficients Using Iterated Reweighted Least Squares, Journal of Statistical Computation and Simulation, 74, 821-831.

See Also

rfit, jaeckel

Examples

##  This is an internal function.  See rfit for user-level examples.

## The function is currently defined as
function (x, y, b0 = suppressWarnings(rq(y ~ x - 1)$coef), scores = wscores,
    eps = 0.001, max.iter = 20)
{
    x <- as.matrix(x)
    n <- length(y)
    p <- ncol(x)
    e0 <- drop(y - x %*% b0)
    w0 <- irlsweights(e0, scores)
    m <- median(e0)
    b1 <- lsfit(x, y - m, wt = w0, intercept = F)$coef
    e1 <- drop(y - x %*% b1)
    m <- median(e1)
    iter <- 0
    while (sum((b0 - b1)^2)/sum(b1^2) > eps && iter < max.iter) {
        iter <- iter + 1
        b0 <- b1
        e0 <- e1
        b1 <- lsfit(x, y - m, wt = irlsweights(e0, scores), intercept = F)$coef
        e1 <- drop(y - x %*% b1)
        m <- median(e1)
    }
    b1
  }