Applications of a Kullback-Leibler Divergence for Comparing Non-nested Models.

Area of Science:

• Statistics
• Econometrics

Background:

• The Kullback-Leibler divergence (KLD) is a key measure in information theory and statistics.
• Wang and Ghosh (2011) introduced a KLD asymptotically equivalent to Goutis and Robert (1998) under specific conditions.
• Prior research has examined the properties of Wang and Ghosh's KLD within the Bayesian framework.

Purpose of the Study:

• To investigate the properties of the Kullback-Leibler divergence (KLD) proposed by Wang and Ghosh (2011) in the frequentist statistical framework.
• To extend the understanding of this KLD beyond the Bayesian context.
• To evaluate the KLD's performance with non-nested models in practical applications.

Main Methods:

• The study employs the Kullback-Leibler divergence (KLD) as proposed by Wang and Ghosh (2011).
• Analysis is conducted within the frequentist statistical framework.
• Four application examples are utilized, each involving two competing non-nested models.

Main Results:

• The paper provides an empirical exploration of the Wang and Ghosh (2011) KLD properties in a frequentist setting.
• The behavior of the KLD is examined across four distinct application scenarios.
• The study demonstrates the utility of this KLD when comparing non-nested models.

Conclusions:

• The Kullback-Leibler divergence (KLD) by Wang and Ghosh (2011) exhibits relevant properties within the frequentist framework.
• The findings support the application of this KLD for model comparison, particularly with non-nested models.
• This research contributes to a broader understanding of KLD in statistical modeling and analysis.