Model selection criteria of the standard censored regression model based on the bootstrap sample augmentation mechanism

The statistical regression technique is an extraordinarily essential data fitting tool to explore the potential possible generation mechanism of the random phenomenon. Therefore, the model selection or the variable selection is becoming extremely important so as to identify the most appropriate model with the most optimal explanation effect on the interesting response. In this paper, we discuss and compare the bootstrap-based model selection criteria on the standard censored regression model (Tobit regression model) under the circumstance of limited observation information. The Monte Carlo numerical evidence demonstrates that the performances of the model selection criteria based on the bootstrap sample augmentation strategy will become more competitive than their alternative ones, such as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) etc. under the circumstance of the inadequate observation information. Meanwhile, the numerical simulation experiments further demonstrate that the model identification risk due to the deficiency of the data information, such as the high censoring rate and rather limited number of observations, can be adequately compensated by increasing the scientific computation cost in terms of the bootstrap sample augmentation strategies. We also apply the recommended bootstrap-based model selection criterion on the Tobit regression model to fit the real fidelity dataset.