regaep {AEP}

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}=\beta_{0}+\beta_{1} x_{i1}+\cdots+ \beta_{k} x_{ik}+\nu_{i},~ i=1,\cdots,n,

where {\boldsymbol{\beta}}=\bigl(\beta_{0},\beta_{1},\cdots,\beta_{k}\bigr)^{T} are the regression coefficients and \nu_i is the error term follows a zero-location AEP distibution.

Usage

regaep(y, x)

Arguments

y

Vector of response observations of length n.

x

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

Value

A list of estimated regression coefficients, summary of residuals, F statistic, R-square (R^2), adjusted R-square, and inverted observed Fisher information matrix.

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)