skewtreg {ForestFit}

Robust multiple linear regression modelling when error term follows a skew Student's t distribution

Description

Robust multiple linear regression modelling with skew Student's t error term. The density function of skew Student's t is given by

f(x,{\Theta}) = \frac{2}{\sigma} t\bigl(z;\nu\bigr) T\biggl(\lambda z\sqrt{\frac{\nu+1}{\nu+z^2}};\nu+1\biggr),

where z=(x-\mu)/\sigma, -\infty<\mu<\infty is the location parameter, \sigma>0 is the scale parameter, and -\infty<\lambda<\infty is the skewness parameter. Also, t(u,\nu) and T(u,\nu) denote the density and distribution functions of the Student's t distribution with \nu degrees of freedom at point u, respectively. If \lambda=0, then the skew Student's t distribution turns into the ordinary Student's t distribution that is symmetric around \mu. Since Student's t is a heavy tailed distribution, it is so useful for regression analysis in presence of outliers.

Usage

skewtreg(y, x, Fisher=FALSE)

Arguments

y

vector of response variable.

x

vector or matrix of explanatory variable(s).

Fisher

Either TRUE or FALSE. By default Fisher==FALSE; otherwise the observed Fisher information matrix and asymptotic standard errors for estimated regression coefficients are evaluated.

Value

A list of estimated regression coefficients, asymptotic standard error, corresponding p-values, estimated parameters of error term (skew Student's t), F statistic, R-square and adjusted R-square, and observed Fisher information matrix is given.

Author(s)

Mahdi Teimouri

Examples

n<-100
x<-rnorm(n)
y<-2+2*x+rt(n,df=2)
skewtreg(y,x,Fisher=FALSE)