A Robust Estimator of Location Using an Adaptive Spline Model

Abstract

This paper contains a new approach toward the robust estimation of a location parameter. We propose NPS (Normal Pareto Spline) distribution which provides rough fit to density functions for arbitrary unimodal symmetric distributions. The bases of our NPS estimation are Pareto tails and spline constraints. Pareto tails can represent a diversity of tail behavior, and spline constraints ensure the smoothness of the density function. We show that the NPS estimate of location has lower asymptotic variance than Huber's M-estimator in most cases, regardless of how Huber's trimmed constant k is chosen. We also show that the NPS estimate of location can guarantee resistance for outliers. For the generalized two sample location problem, where the scale parameters are unequal, we propose an iterative method to estimate the shift parameter and also have a proof that this iterative method converges to the desired M-estimate for an arbitrary scale location family of symmetric distributions. Keywords include: Pareto tails, Spline, Outlier, Robust adaptive estimation.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1985
Accession Number
ADA153662

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  • D. Y. Kim

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  • Massachusetts Institute of Technology

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  • Materials and Manufacturing Processes

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  • Mathematics

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  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.
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