Parametric versus nonparametric: the fitness coefficient

TL;DR

This paper introduces the fitness coefficient, a new measure comparing parametric and nonparametric density estimators, which is easy to compute, interpretable, and useful for model assessment and semiparametric inference.

Contribution

The paper proposes the fitness coefficient as a novel, interpretable metric for model comparison, with theoretical convergence properties and practical applications demonstrated on real and simulated data.

Findings

Fitness coefficient converges to one if the model is correct.

Fitness coefficient converges to zero if the model is false.

Practical utility shown through real and simulated datasets.

Abstract

The fitness coefficient, introduced in this paper, results from a competition between parametric and nonparametric density estimators within the likelihood of the data. As illustrated on several real datasets, the fitness coefficient generally agrees with p-values but is easier to compute and interpret. Namely, the fitness coefficient can be interpreted as the proportion of data coming from the parametric model. Moreover, the fitness coefficient can be used to build a semiparamteric compromise which improves inference over the parametric and nonparametric approaches. From a theoretical perspective, the fitness coefficient is shown to converge in probability to one if the model is true and to zero if the model is false. From a practical perspective, the utility of the fitness coefficient is illustrated on real and simulated datasets.