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#' The lambdas for each coavariate for models 2 and 3
#'
#' This function calculates the range of the Beta_hats using B-splines and then
#' using Lamb_grl() it searches for the global smoothing parameter
#'
#' @section Note:
#' Some warning messages are related to the function \code{\link{rq.fit.sfn}}
#' (See http://www.inside-r.org/packages/cran/quantreg/docs/sfnMessage).
#'
#' @section Author(s):
#' Mohammed Abdulkerim Ibrahim
#'
#' @section Refrences:
#' Gijbels, I., Ibrahim, M. A., and Verhasselt, A. (2017). Testing the
#' heteroscedastic error structure in quantile varying coefficient models.
#' {\it Submitted}.
#'
#' Andriyana, Y. (2015). P-splines quantile regression in varying coefficient
#' models. {\it PhD Dissertation}. KU Leuven, Belgium. ISBN 978-90-8649-791-1.
#'
#' Andriyana, Y. and Gijbels, I. & Verhasselt, A. (2014). P-splines quantile
#' regression estimation in varying coefficient models. {\it Test}, 23, 153-194.
#'
#' Andriyana, Y., Gijbels, I. and Verhasselt, A. (2017). Quantile regression
#' in varying-coefficient models: non-crossing quantile curves and
#' heteroscedasticity. {\it Statistical Papers}, to appear.
#' DOI:10.1007/s00362-016-0847-7
#'
#' He, X. (1997). Quantile curves without crossing. {\it The American Statistician},
#' 51, 186-192.
#'
#' @seealso \code{\link{rq.fit.sfn}} \code{\link{as.matrix.csr}}
#'
#' @export
lambdak_grl <- function(times, subj, X, y, d, tau, kn, degree, lambda, gam){
dim = length(subj)
X = matrix(X, nrow = dim)
px = ncol(X)-1
qvc2_indiv = qrvcp_grl(times, subj, y, X, tau, kn = kn,
degree = degree, lambda = 0, d,rep(1,px))$hat_bt
range = NULL
for (k in 1:px) {
range[k] =(max(qvc2_indiv[seq((k - 1) * dim + 1, k * dim)]) -
min(qvc2_indiv[seq((k - 1) * dim + 1, k * dim)]))^(-(gam))
}
lambdasic = Lamb_grl(times, subj, X, y, d, tau, kn, degree,
lambda,range)$lambdasic
out = list(lambdasic = lambdasic, range = range)
return(out)
}
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