Fisher Consistency of AM-Estimates of the Autoregression Parameter Using Hard Rejection Filter Cleaners

Abstract

In recent years several classes of robust estimates of ARMA model parameters have been proposed. The AM-estimates seem most appealing: They are based in on an intuitively appealing robust filter cleaner which cleans the data by replacing outliners with interpolates based on previous cleaned data. They have proved quite useful in a variety of applications. On the other hand, the AM-estimates are sufficiently complicated functions of the data that it has proven difficult to establish even the most basic asymptotic properties such as consistency. This paper considers only a special case of AM-estimates based on a so-called hard-rejection filter cleaner. The importance of hard-rejection filter-cleaners, which are described for the first-order autoregressive (AR(1)) model, is that engineers often use a similar intuitively appealing modification of the Kalman filter for dealing with outliers in tracking problems. Under certain assumptions these special AM-estimates are Fisher consistent for the parameter Phi sub 0 of an AR(1) model, Fisher consistency being the first property one usually establishes along the way to proving consistency.

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Document Details

Document Type
Technical Report
Publication Date
Feb 04, 1987
Accession Number
ADA200632

Entities

People

  • R. D. Martin
  • Victor J. Yohai

Organizations

  • University of Washington

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Consistency
  • Data Science
  • Distribution Functions
  • Engineers
  • Filters
  • Information Science
  • Intervals
  • Kalman Filters
  • Mathematical Filters
  • New York
  • Probability
  • Random Variables
  • Stationary
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.