Rfit (version 0.09)

jaeckel: Function to Minimize Jaeckel's Dispersion Function

Description

Uses the built-in function optim to minimize Jaeckel's dispersion function. Alternates between CG and BFGS steps and initially takes a number of IRLS steps.

Usage

jaeckel(x, y, beta0 = rq(y ~ x)$coef[2:(ncol(x) + 1)], scores = wscores)

Arguments

x

n by p design matrix

y

n by 1 response vector

beta0

intial estimate

scores

object of class 'scores'

Value

• Results of optim are returned.

Details

This function is meant to mimic the minization algorithm implemented in RGLM (Kapenga, et. al. 1988). The main loop of the function alternates between CG and BFGS estimation methods. To speed up convergence, it first takes a number of iterated reweighted least squares (IRLS) steps which generally gets close to the solution in a small number of steps. Using IRLS for rank regression was first considered by Cheng and Hettmansperger (1983). See also Sievers and Abebe (2004).

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.

Hettmansperger, T.P. and McKean J.W. (1998), Robust Nonparametric Statistical Methods, London: Arnold.

Jaeckel, L. A. (1972), Estimating regression coefficients by minimizing the dispersion of residuals. Annals of Mathematical Statistics, 43, 1449 - 1458.

Kapenga, J. A., McKean, J. W., and Vidmar, T. J. (1988), RGLM: Users Manual, Statist. Assoc. Short Course on Robust Statistical Procedures for the Analysis of Linear and Nonlinear Models, New Orleans.

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

optim, rfit

Examples

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

## The function is currently defined as
function (x, y, beta0 = rq(y ~ x - 1)$coef, scores = wscores, 
    maxiter = 100, irls0 = 10, BFGS0 = 20, stepCG = 5, stepBFGS = 2) 
{
    x <- x - outer(rep(1, nrow(x)), apply(x, 2, mean))
    beta0 <- irls(x, y, beta0, max.iter = irls0)
    if (BFGS0 < 1) 
        BFGS0 <- 1
    fit <- optim(beta0, disp, method = "BFGS", x = x, y = y, 
        scores = scores, control = list(maxit = BFGS0))
    iter <- 0
    while (fit$convergence && iter < maxiter) {
        iter <- iter + 1
        fit <- optim(fit$par, disp, method = "CG", x = x, y = y, 
            scores = scores, control = list(maxit = stepCG))
        fit <- optim(fit$par, disp, method = "BFGS", x = x, y = y, 
            scores = scores, control = list(maxit = stepBFGS))
    }
    optim(fit$par, disp, method = "BFGS", x = x, y = y, scores = scores)
  }