This fitting method provides a link to the gradient descent for convolution smoothed quantile regression problem implemented in the conquer package of He et al (2020).
rq.fit.conquer (x, y, tau=0.5, kernel = c("Gaussian", "uniform",
"parabolic", "triangular"), h = 0, standardize = TRUE, tol = 1e-04,
iteMax = 5000, ci = FALSE, alpha = 0.05, B = 1000)design matrix usually supplied via rq(), expected to have a intercept as the first column
response vector usually supplied via rq()
quantile of interest
A character string specifying the choice of kernel function. Default is "Gaussian". Other choices are "uniform", "parabolic" or "triangular".
The bandwidth parameter for kernel smoothing of the QR objective function. Default is max((log(n) + p) / n)^0.4, 0.05. The default is used if the input value is less than 0.05.
A logical flag, when TRUE, the design matrix will be standardized so that each column has mean zero and standard deviation one.
Tolerance level of the gradient descent algorithm. The gradient descent algorithm terminates when the maximal entry of the gradient is less than "tol". Default is 1e-05.
Maximum number of iterations. Default is 5000.
A logical flag. Default is FALSE. If "ci =
TRUE", then three types of confidence intervals (percentile,
pivotal and normal) will be constructed via multiplier
bootstrap. This option is subsumed in normal use by the
summary.rq functionality.
Nominal level for confidence intervals, may be passed
via the call to summary
Number of bootstrap replications. May be passed via summary.
Returns an object of class "rq".
See documentation in the conquer package.
Xuming He and Xiaoou Pan and Kean Ming Tan and Wen-Xin Zhou, (2020) conquer: Convolution-Type Smoothed Quantile Regression, https://CRAN.R-project.org/package=conquer