Bootstrap Tests for Nonlinear Simplex Models

ABSTRACT We provide important contributions regarding hypothesis tests on the class of nonlinear simplex regression models. The performance of traditional asymptotic tests based on the maximum likelihood estimation (MLE) tends to exhibit considerable size distortions in finite samples. Therefore, we propose corrections for these asymptotic MLE tests using bootstrap and fast double bootstrap methods. We present a wide range of Monte Carlo simulation scenarios to evaluate the performance of both asymptotic MLE tests and their bootstrap‐corrected versions. A major motivation behind this paper is the data set from the fluid catalytic cracking (FCC) process, one of the world's largest gasoline production processes, for which we performed the statistical modeling. This involved constructing the nonlinear predictor for the mean submodel, followed by local influence and residual analysis, confidence interval estimation and finally, hypothesis testing. Both the Monte Carlo simulations and the FCC application strongly favoured tests based on bootstrap methods.