A Prediction Interval for M Estimators*

*This research was supported in part by NSF Grant DMS-8706044

Abstract

There has been much work in the area of estimating the center of a symmetric population. If one allows for the possibility that the population may be heavy-tailed then robust procedures, and in particular M estimators, have proven quite popular. In this paper we consider the following problem: given a random sample, produce an interval such that the M estimator derived from a future random sample (from the same population) will lie in that interval with some preassigned probability. Clearly such an interval is of use, especially in quality control where prediction is vital. In this paper such an interval is proposed based on asymptotic theory. A simulation study was run for a variety of sample sizes (the sizes of the observed and future samples need not be equal) and distributions. The particular M estimator of choice is that based on the biweight ψ function. The proposed interval performs reasonably well relative to the best that can be achieved asymptotically.

Keywords:

• Forecast
• Quality Control
• Robustness

*This research was supported in part by NSF Grant DMS-8706044

*This research was supported in part by NSF Grant DMS-8706044

Notes

*This research was supported in part by NSF Grant DMS-8706044