jaeckel function

Function to Minimize Jaeckel's Dispersion Function

Uses the built-in function optim to minimize Jaeckel's dispersion function with respect to beta.

jaeckel(x, y, beta0 = lm(y ~ x)$coef[2:(ncol(x) + 1)], 
  scores = Rfit::wscores, control = NULL,...)

Arguments

• x: n by p design matrix
• y: n by 1 response vector
• beta0: initial estimate of beta
• scores: object of class 'scores'
• control: control passed to fitting routine
• ...: addtional arguments to be passed to fitting routine

Details

Jaeckel's dispersion function (Jaeckel 1972) is a convex function which measures the distance between the observed responses $y$ and the fitted values $x \beta$. The dispersion function is a sum of the products of the residuals, $y - x \beta$, and the scored ranks of the residuals. A rank-based fit minimizes the dispersion function; see McKean and Schrader (1980) and Kloke and McKean (2012) for discussion. jaeckel uses optim with the method set to BFGS to minimize Jaeckel's dispersion function. If control is not specified at the function call, the relative tolerance (reltol) is set to .Machine$double.eps^(3/4) and maximum number of iterations is set to 200.

jaeckel is intended to be an internal function. See rfit for a general purpose function.

Returns

Results of optim are returned.

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

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.

Author(s)

John Kloke

See Also

optim, rfit

Examples

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