Minimum f-Divergence Estimation With Applications to Degradation Data Analysis

Minimizing the divergence between two probability distributions offers an alternative parameter estimation method. The current literature mainly focuses on minimizing the Kullback-Leibler (K-L) divergence between the true and the proposed models in which the true model is assumed to be known or fixed. In this paper, we propose a parameter estimation method that minimizes the
$f$
-divergence between two probability distributions. The method is suitable for different situations, no matter the true distribution is known or not. The statistical properties of the estimator, including consistency and asymptotic normality, are established. As an illustration, our method is employed to estimate the degradation model, which is a model frequently used to assess the lifetime of highly reliable products. A simulation study and a real degradation data analysis are presented to illustrate the effectiveness of the proposed estimation method.