

   QQuuaannttiillee sspplliinnee rreeggrreessssiioonn

        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)

   AArrgguummeennttss::

          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 quan-
             tile function. Default is the unique sorted values
             of x.

   derivative: Specifies whether the function itself of deriva-
             tives 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.

   DDeessccrriippttiioonn::

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

   VVaalluuee::

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

   RReeffeerreenncceess::

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

   SSeeee AAllssoo::

        sreg

   EExxaammpplleess::

