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.

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]