Modified estimation methods: properties and aplications

• Grant number: 23/02946-0
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2023
• End date: June 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Agreement: CNPq
• Principal Investigator: Francisco Louzada Neto
• Grantee: Francisco Louzada Neto
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID
• Associated scholarship(s): 23/13249-9 - Modified Estimation Methods: Properties and aplications, BP.JD

Abstract

The purpose of this post-doctoral project is to develop different estimation methods in sta- tistical inference. Considering the classical approach, we will introduce a new estimation pro- cedure based on a modification of the maximum likelihood estimators (MLE) that allow us to obtain closed-form estimators. For this new method sufficient and necessary conditions will be studied to obtain its asymptotic properties. In addition, considering the maximum product spacing (MPS) estimator, we will prove that such method has limitations in its present form, which does not allow the inclusion of censored data, a problem in many areas. Therefore, we will provide a simple modification in this procedure to include random censoring, this general type of censoring has type I and II as special cases. Further, we will prove that both MLEs and MPSs in the presence of censoring are asymptotically equivalent, i.e., they are consistent and asymptotically efficient. On the other hand, under the Bayesian inference, we observed that ob- jective priors have not been used in models that have censoring and cure fraction. This problem is due the complexity in obtaining the Fisher information matrix in closed-form. Therefore in this project we will propose alternative ways to obtain objective priors that are based on formal rules allowing an objective Bayesian analysis in the presence of censored data and cure fraction. At the end, we will present necessary and sufficient conditions in which such objective priors lead to proper posterior distributions. (AU)