Simulation of Errors in Linear Regression: An Approach Based on Fixed Percentage Area

Summary

Recent advances in statistical computation heavily depend on Monte Carlo simulation methods. In many statistical problems, simulated values are used to check or justify any rule whose distributional properties are not known or very difficult to compute. Monte Carlo simulation methods have extensive use in regression analysis. In fact they have formed the basis of regression diagnostics. In linear regression the simulation of a regression model is almost equivalent to simulate the random enors of this model. In the simulation of random errors it is a common practice to generate data from a target distribution with a fixed mean and a fixed variance. We cast our doubt that the fixed variance approach of simulating errors may distort the non-normal shape of any longer-tailed distribution. In this paper we propose a new approach of simulating random errors by fixing the lower percentage area of any target distribution which, we believe, will allow the longer-tailed distribution to be more widely spread than the fixed variance case without doing any harm to a genuine normal case. The usefulness of the proposed approach is investigated through a Monte Carlo power simulation experiment for testing normality of the non-normal errors.