Effects of non-normality on confidence intervals in linear models

A. H. POOI

Research Report No. 6/2003

Abstract

A type of non-normal distribution is obtained by a non-linear transformation of the normally distributed random variable. The severity of non-normality is measured by the deviation of the normalized third central moment (skewness) from zero and the deviation of the normalized fourth central moment (kurtosis) from three. The coverage probability of the confidence intervals in the simple linear regression models with non-normal errors is then obtained by using simulation.   It is found that the effects of severe non-normality on the coverage probability are not always large. The effects depend on the sample size n and the values x₁,x₂,..., x_n  of the explanatory variable. To examine the effects of non-normality on the coverage probability, we may first fit the residuals with the non-normal distribution and then use simulation to estimate the severity of the deviation of the coverage probability from the target value.