Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 68, Issue 10, Pages 6774-6789Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2022.3169885
Keywords
Minimum f -divergence estimation; consistency; asymptotic normality; degradation models; robust analysis
Funding
- National Natural Science Foundation of China [12071372, 11528102, 11571282]
- Fundamental Research Funds for the Central Universities of China [JBK2001001, JBK1806002, JBK140507]
- Academic Research Funds [R-155-000-205-114, R-155-000-195-114, A-8000016-00-00, iRIMS 210040-A0001]
- Tier 2 Ministry of Education (MOE) Funds in Singapore [MOE2017-T2-2-082]
- Indirect Research Cost (IRC) [R-155-000-197-113]
- Simons Foundation [709773]
- Direct Cost [R-155-000-197-112]
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This paper proposes a parameter estimation method that minimizes the f-divergence between two probability distributions and explores the statistical properties of the estimator. The effectiveness of the proposed method is demonstrated through a case study on degradation modeling and analysis of real data.
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.
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