Qlm.fit {Qest}

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(), ...)

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.

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

Author(s)

Gianluca Sottile <[e-mail]>, Paolo Frumento <[e-mail]>

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>

See Also

Qlm

Examples

# 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))