Estimate weights for elliptical symmetry

This function estimate weights to apply to the rows of a data matrix to make the resulting weighted matrix as close to elliptically symmetric as possible.

dr.weights(formula, data = list(), subset, na.action = na.fail, 
    sigma=1, nsamples=NULL, ...)

Arguments

formula: A one-sided or two-sided formula. The right hand side is used to define the design matrix.
data: An optional data frame.
subset: A list of cases to be used in computing the weights.
na.action: The default is na.fail, to prohibit computations. If set to na.omit, the function will return a list of weights of the wrong length for use with dr.
nsamples: The weights are determined by random sampling from a data-determined normal distribution. This controls the number of samples. The default is 10 times the number of cases.
sigma: Scale factor, set to one by default; see the paper by Cook and Nachtsheim for more information on choosing this parameter.
...: Arguments are passed to cov.rob to compute a robust estimate of the covariance matrix.

Details

The basic outline is: (1) Estimate a mean m and covariance matrix S using a possibly robust method; (2) For each iteration, obtain a random vector from N(m,sigma*S). Add 1 to a counter for observation i if the i-th row of the data matrix is closest to the random vector; (3) return as weights the sample faction allocated to each observation. If you set the keyword weights.only to T on the call to dr, then only the list of weights will be returned.

Value

Returns a list of \(n\) weights, some of which may be zero.

References

R. D. Cook and C. Nachtsheim (1994), Reweighting to achieve elliptically contoured predictors in regression. Journal of the American Statistical Association, 89, 592–599.

Author

Sanford Weisberg, sandy@stat.umn.edu

Examples

data(ais)
w1 <- dr.weights(~ Ht +Wt +RCC, data = ais)
m1 <- dr(LBM~Ht+Wt+RCC,data=ais,weights=w1)