Applicability of Central Limit Theorem on Machine-generated Random Variables for Regression Model
Apolinar T. Paulican · 2014
Time series literatures assume that central limit theorem will still holds evenif the random errors are replaced by pseudo random numbers generated bya computer. The study focused on the asymptotic characteristics of the leastsquaresestimates of the parameters of regressionmodels when the errortermsweregenerated bythe usual machine congruentialgenerator and byusing known chaoticdynamical system. The study also consideredthe normal approximation error |P(tn≤t)-φ(t)| , where φ is the cdf of the standard normal distribution.The magnitude of this error provides a measure on how the central limit theoremapplies for machine-generated errors. The result of the study showed that theestimate of the parameters of the regression model were distributed normal whenthe error terms were generated by congruential generator and by a tent map. Keywords: Mathematics, central limit theorem, machine-generated random variables,regression model, congruential generator, descriptive design, Philippines