regaep {AEP}R Documentation

Robust linear regression analysis when error term follows AEP distribution

Description

Estimates parameters of the multiple linear regression model through EM algorithm when error term follows AEP distribution. The regression model is given by

y_{i}=β_{0}+β_{1} x_{i1}+\cdots+ β_{k} x_{ik}+ν_{i},~~ i=1,\cdots,n,

where β_{0},β_{1},\cdots,β_{k} are the regression coefficients and ν is the error term follows a zero-location AEP distibution with pdf given by

f_{X}(x|Θ)=≤ft\{\begin{array}{*{20}c} \frac{1}{2σ Γ\bigl(1+\frac{1}{α}\bigr)}\exp\biggl\{-\Big|\frac{-x}{σ(1-ε)}\Big|^{α}\biggr\},~~{}~x ≤q 0,\\ \frac{1}{2σ Γ\bigl(1+\frac{1}{α}\bigr)}\exp\biggl\{-\Big|\frac{x}{σ(1+ε)}\Big|^{α}\biggr\},~~{}~x> 0, \end{array} \right.

where -∞<x<+∞, Θ=(α,σ,ε)^T with 0<α ≤q 2, σ> 0, -1<ε<1, and

Γ(u)=\int_{0}^{+∞} x^{u-1}\exp\bigl\{-x\bigr\}dx,

for u>0.

Usage

regaep(y, x)

Arguments

y

Vector of response observations of length n.

x

A n\times k array of covariate(s).

Value

A list of estimated regression coefficients, estimated parameters of error term, F statistic, R-square, and adjusted R-square.

Author(s)

Mahdi Teimouri

References

A. P. Dempster, N. M. Laird, and D. B. Rubin, 1977. Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B, 39, 1-38.

Examples

x <- seq(-5, 5, 0.1)
y <- 2 + 2*x + raep( length(x), alpha = 1, sigma = 0.5, mu = 0, epsilon = 0.5)
regaep(y, x)

[Package AEP version 0.1.2 Index]