skewtreg: Robust multiple linear regression modelling when error term...

In ForestFit: Statistical Modelling for Plant Size Distributions

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,{Θ}) = \frac{2}{σ} t\bigl(z;ν\bigr) T\biggl(λ z√{\frac{ν+1}{ν+z^2}};ν+1\biggr),

where z=(x-μ)/σ, -∞<μ<∞ is the location parameter, σ>0 is the scale parameter, and -∞<λ<∞ is the skewness parameter. Also, t(u,ν) and T(u,ν) denote the density and distribution functions of the Student's t distribution with ν degrees of freedom at point u, respectively. If λ=0, then the skew Student's t distribution turns into the ordinary Student's t distribution that is symmetric around μ. 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)

ForestFit documentation built on March 7, 2023, 8:27 p.m.