Restricted Distance-Type Gaussian Estimators Based on Density Power Divergence and Their Applications in Hypothesis Testing

Ángel Felipe, María Jaenada, Pedro Miranda and Leandro Pardo ()
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Ángel Felipe: Department of Statistics and Operational Research, Complutense University of Madrid, 28040 Madrid, Spain
María Jaenada: Department of Statistics and Operational Research, Complutense University of Madrid, 28040 Madrid, Spain
Pedro Miranda: Department of Statistics and Operational Research, Complutense University of Madrid, 28040 Madrid, Spain
Leandro Pardo: Department of Statistics and Operational Research, Complutense University of Madrid, 28040 Madrid, Spain

Mathematics, 2023, vol. 11, issue 6, 1-41

Abstract: In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in this case constrained estimators to inherent restrictions of the underlying distribution. Furthermore, we derive robust Rao-type test statistics based on the MDPDGE for testing a simple null hypothesis, and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study.

Keywords: Gaussian estimator; minimum density power divergence Gaussian estimator; robustness; influence function; Rao-type tests; elliptical family of distributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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