A hybrid method for density power divergence minimization with application to robust univariate location and scale estimation

Andrews T. Anum and Michael Pokojovy

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 14, 5186-5209

Abstract: We develop a new globally convergent optimization method for solving a constrained minimization problem underlying the minimum density power divergence estimator for univariate Gaussian data in the presence of outliers. Our hybrid procedure combines classical Newton’s method with a gradient descent iteration equipped with a step control mechanism based on Armijo’s rule to ensure global convergence. Extensive simulations comparing the resulting estimation procedure with the more prominent robust competitor, Minimum Covariance Determinant (MCD) estimator, across a wide range of breakdown point values suggest improved efficiency of our method. Application to estimation and inference for a real-world dataset is also given.

Date: 2024
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DOI: 10.1080/03610926.2023.2209347

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