Qlm.fit: Fitter Functions for Quantile-based Linear Models

Description

This is the basic computing engine called by “Qlm” used to fit quantile-based linear models. This function should only be used directly by experienced users.

Usage

Qlm.fit(y, X, w = rep(1, nobs), start = NULL, wtau = NULL,
  control = Qest.control(), ...)

Value

a “list” with components

coefficients: p vector
std.errs: p vector
covar: p x p matrix
dispersion: estimated dispersion parameter
residuals: n vector
rank: integer, giving the rank
fitted.values: n vector
qr: the QR decomposition, see “qr”
df.residual: degrees of freedom of residuals
obj.function: the minimized loss function
gradient: p vector
hessian: p x p matrix
convergence: logical. The convergence status
n.it: the number of iterations
control: control elements

Arguments

y: vector of observations of length n.
X: design matrix of dimension n * p.
w: an optional vector of weights to be used in the fitting process.
start: starting values for the parameters in the linear predictor.
wtau: an optional function that assigns a different weight to each quantile. By default, all quantiles in (0,1) have the same weight.
control: a list of operational parameters. This is usually passed through Qest.control.
...: additional arguments for wtau.

Author

Gianluca Sottile <gianluca.sottile@unipa.it>, Paolo Frumento <paolo.frumento@unipi.it>

References

Sottile G, and Frumento P (2022). Robust estimation and regression with parametric quantile functions. Computational Statistics and Data Analysis. <doi:10.1016/j.csda.2022.107471>

Examples

Run this code

# Ex. 1 Normal model

set.seed(1234)
n <- 100
x1 <- rnorm(n)
x2 <- runif(n,0,3)
y <- rnorm(n, 4 + x1 + 2*x2, 1)
X <- cbind(1, x1, x2)
w <- rep.int(1, n)

m <- Qlm.fit(y = y, X = X, w = w, control = Qest.control(display = TRUE))

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