A Simulation Study for the AIC and Likelihood Cross-validation: The Case of Exponential Versus Weibull Distributions
Kunio Takezawa *
Division of Informatics and Inventory, Institute for Agro-Environmental Sciences, National Agriculture and Food Research Organization, Kannondai 3-1-3, Tsukuba, Ibaraki 305-8604, Japan
*Author to whom correspondence should be addressed.
Abstract
Various methods are available for choosing statistical models. It is difficult to know which model selection criterion is the best for specific data. This paper discusses a method for choosing the model selection criterion based on the characteristics of the data and models. As an example, we examined the choice between AIC and likelihood cross-validation as the model selection criterion with the exponential distribution and Weibull distribution as candidate models. First, we examined the characteristics of AIC and likelihood cross-validation using data generated from an exponential distribution or Weibull distribution; AIC and likelihood cross-validation show substantially different natures. Next, from the results of the numerical simulations, we propose an intuitive method for deciding whether to use AIC or likelihood cross-validation.
Keywords: AIC, cross-validation, expected log-likelihood, future data, exponential distribution, maxi-mum likelihood estimator, Weibull distribution