Assessing Goodness of Approximate Distributions for Inferences about Parameters in Nonlinear Regression Model

Abstract

It is often crucial to make inferences about parameters of a nonlinear regression model due to a dependency of Fisher information on the parameter being estimated. Here, the distribution of the relevant test statistic is not exact, but approximate. Therefore, similar conclusion, based on the values of different test statistics, may not be reached. This study shows, in this circumstance, how to come up with a nonlinear regression model that can be used for forecasting and other related purposes. The goodness of the approximate distributions, F and χ 2 , has been assessed to reach a correct decision. The simulation results show that the simulated probability of committing a type I error is very close to its true value in case of F distribution corresponding to F statistic. However, the χ 2 distribution does not do a similar job for the LRT statistic since the simulated type I error is quite larger.

Dhaka Univ. J. Sci. 71(1): 13-16, 2023 (Jan)