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A Hybrid Method for Density Power Divergence Minimization with Application to Robust Univariate Location and Scale
Andrews T Anum1, Michael Pokojovy1
1Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968, USA.
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.
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