Decomposable pseudodistances and applications in statistical estimation

Abstract

The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools imbedding the most classical ones, such as maximum likelihood, Chi-square or Kullback Leibler. General pseudodistances with decomposable structure are considered, they allowing to define minimum pseudodistance estimators, without using nonparametric density estimators. A special class of pseudodistances indexed by α > 0, leading for α ↓ 0 to the Kulback Leibler divergence, is presented in detail. Corresponding estimation criteria are developed and asymptotic properties are studied. The estimation method is then extended to regression models. Finally, some examples based on Monte Carlo simulations are discussed.

Pseudodistance Methods Using Simultaneously Sample Observations and Nearest Neighbour Distance Observations for Continuous Multivariate Models

“…g and f are density functions. The property given by (6) Broniatowski et al [12] for more notions and properties of pseudodistances.…”

Existence, consistency and computer simulation for selected variants of minimum distance estimators

“…Barron [2]), or restrict ourselves to only decomposable divergences avoiding the numerical difficulties such as in Frýdlová et al [8], cf. Broniatowski et al [5]. Also, the kernel-based minimum dual φ-divergence estimator (MD φ DE) is newly proposed in Al Mohamad [1] (for symmetric and asymmetric kernels), where its asymptotic properties are proved and the efficiency versus robustness is treated through a comprehensive simulation study for two component Gaussian mixture, Weibull mixture, and generalized Pareto distribution.…”

Robust Model Selection Criteria Based on Pseudodistances

“…The pseudodistances that we use in the present paper were originally introduced in [13], where they are called "type-0" divergences, and corresponding minimum divergence estimators have been studied. They are also presented and extensively studied in [14] where they are called γ-divergences, as well as in [15] in the context of decomposable pseudodistances. Like divergences, the pseudodistances are not mathematical metrics in the strict sense of the term.…”