ForestFit (version 2.4.3)

skewtreg: 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)

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.

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.

Author

Mahdi Teimouri

Examples

# \donttest{
n<-100
x<-rnorm(n)
y<-2+2*x+rt(n,df=2)
skewtreg(y,x,Fisher=FALSE)
# }