qspreg {funfits}R Documentation

Quantile spline regression

Description

This is an experimental function to find the smoothing parameter for a quantile spline using a more appropriate criterion than mean squared error prediction. The quantile spline is found by an iterative algorithm using weighted least squares cubic splines. At convergence the estimate will also be a weighted natural cubic spline but the weights will depend on the estimate. Of course these weights are crafted so that the resulting spline is an estimate of the alpha quantile instead of the mean.

Usage

qspreg(x, y, lam=NA, maxit=50, maxit.cv=10, tol=0.0001, cost=1,
 offset=0, sc=sqrt(var(y)) * 1e-07, alpha=0.5, wt=rep(1, length(x)),
 nstep.cv=50, xgrid=sort(unique(x)), deriv=0, hmin=-35, hmax=-15)

Arguments

x Vector of independent variables
y Vector dependent variables
lam Values of the smoothing parameter. If omitted is found by GCV based on the the quantile criterion
maxit Maximum number of iterations used to estimate each quantile spline.
maxit.cv Maximum number of iterations to find GCV minimum.
tol Tolerance for convergence when computing quantile spline.
cost Cost value used in the GCV criterion. Cost=1 is the usual GCV denominator.
offset Constant added to the effective degrees of freedom in the GCV function.
sc Scale factor for quantile function. Default is a scale on the order of machine precision. Scales on the order of the residuals will result is a robust regression fit using the Huber weight function.
alpha Quantile to be estimated. Default is find the median.
wt Weight vector default is constant values. Passing nonconstant weights is a pretty strange thing to do.
xgrid Grid of x values to evaluate the estimated quantile function. Default is the unique sorted values of x.
derivative Specifies whether the function itself of derivatives should be evaluated at xgrid.
hmin Minimum value of log( lambda) used for GCV grid search.
hmax Maximum value of log( lambda) used for GCV grid search.

Value

Object of class qspreg with many arguments similar to sreg object.

References

Nychka,D. Oconnell, M. (1996) "

See Also

sreg

Examples



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