  The Akaike information criterion (AIC) is a model selection criterion widely
used in practical applications. The AIC is an estimator of the log-likelihood
expected value, and measures the discrepancy between the true model and the
estimated model. In small samples the AIC is biased and tends to select
overparameterized models. To circumvent that problem, we propose two new
selection criteria, namely: the bootstrapped likelihood quasi-CV (BQCV) and its
632QCV variant. We use Monte Carlo simulation to compare the finite sample
performances of the two proposed criteria to those of the AIC and its
variations that use the bootstrapped log-likelihood in the class of varying
dispersion beta regressions. The numerical evidence shows that the proposed
model selection criteria perform well in small samples. We also present and
discuss and empirical application.
