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

摘要

In recent years several classes of robust estimates of ARMA model parameters have been proposed. The AM-estimates seem most appealing: They are based on an intuitively appealing robust filter cleaner which cleans the data by replacing outliners with interpolates based on previous cleaned data. They have proven 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. (jhd)