# Inference for multiple linear regression model with extended skew normal errors

A. A. Alhamide, Kamarulzaman Ibrahim, M. T. Alodat

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

This paper presents the estimation of the parameters of the multiple linear regression model when errors are assumed to follow the independent extended skew normal distribution. The estimators of the regression parameters are determined using the maximum likelihood and least squares methods. In addition, the asymptotic distributions of the estimators are studied. The properties of the estimators under both approaches are compared based on a simulation study and a real data set is applied for illustration.

Original language English 81-96 16 Pakistan Journal of Statistics 32 2 Published - 1 Mar 2016

### Fingerprint

Multiple Linear Regression
Linear Regression Model
Skew
Estimator
Skew-normal Distribution
Model Error
Least Square Method
Asymptotic distribution
Maximum Likelihood
Regression
Simulation Study

### Keywords

• Asymptotic distribution
• Berry-Esseen theorem
• Extended skew normal distribution
• Least squares estimator
• Maximum likelihood estimates
• Multiple linear regression model
• Simulation

### ASJC Scopus subject areas

• Statistics and Probability

### Cite this

Inference for multiple linear regression model with extended skew normal errors. / Alhamide, A. A.; Ibrahim, Kamarulzaman; Alodat, M. T.

In: Pakistan Journal of Statistics, Vol. 32, No. 2, 01.03.2016, p. 81-96.

Research output: Contribution to journalArticle

@article{85d388d8c3234e3bb425692d5d4e5f9c,
title = "Inference for multiple linear regression model with extended skew normal errors",
abstract = "This paper presents the estimation of the parameters of the multiple linear regression model when errors are assumed to follow the independent extended skew normal distribution. The estimators of the regression parameters are determined using the maximum likelihood and least squares methods. In addition, the asymptotic distributions of the estimators are studied. The properties of the estimators under both approaches are compared based on a simulation study and a real data set is applied for illustration.",
keywords = "Asymptotic distribution, Berry-Esseen theorem, Extended skew normal distribution, Least squares estimator, Maximum likelihood estimates, Multiple linear regression model, Simulation",
author = "Alhamide, {A. A.} and Kamarulzaman Ibrahim and Alodat, {M. T.}",
year = "2016",
month = "3",
day = "1",
language = "English",
volume = "32",
pages = "81--96",
journal = "Pakistan Journal of Statistics",
issn = "1012-9367",
publisher = "Pakistan Journal of Statistics",
number = "2",

}

TY - JOUR

T1 - Inference for multiple linear regression model with extended skew normal errors

AU - Alhamide, A. A.

AU - Ibrahim, Kamarulzaman

AU - Alodat, M. T.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - This paper presents the estimation of the parameters of the multiple linear regression model when errors are assumed to follow the independent extended skew normal distribution. The estimators of the regression parameters are determined using the maximum likelihood and least squares methods. In addition, the asymptotic distributions of the estimators are studied. The properties of the estimators under both approaches are compared based on a simulation study and a real data set is applied for illustration.

AB - This paper presents the estimation of the parameters of the multiple linear regression model when errors are assumed to follow the independent extended skew normal distribution. The estimators of the regression parameters are determined using the maximum likelihood and least squares methods. In addition, the asymptotic distributions of the estimators are studied. The properties of the estimators under both approaches are compared based on a simulation study and a real data set is applied for illustration.

KW - Asymptotic distribution

KW - Berry-Esseen theorem

KW - Extended skew normal distribution

KW - Least squares estimator

KW - Maximum likelihood estimates

KW - Multiple linear regression model

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=84975166625&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975166625&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84975166625

VL - 32

SP - 81

EP - 96

JO - Pakistan Journal of Statistics

JF - Pakistan Journal of Statistics

SN - 1012-9367

IS - 2

ER -