SPEAKER: Hira L. Koul, Department of Statistics & Probability,
                    Michigan State University, E. Lansing, MI

TITLE: Asymptotic Distributions of Some Scale Estimators in Nonlinear Models

ABSTRACT:

Often in the robust analysis of regression and time series models there is a need for having a robust scale estimator of a scale parameter of the errors. One often used scale estimator is the median of the absolute residuals. It is of interest to know its limiting distribution and the
consistency rate. Its limiting distribution generally depends on the estimator of the regression and/or autoregressive parameter vector unless the errors are symmetrically distributed around zero. To overcome this difficulty it is then natural to use the median of the absolute differences of pairwise residuals as a scale estimator. This talk will discusses the asymptotic distributions of these two estimators for a large class of nonlinear regression and autoregressive models when the errors are independent and identically distributed, and for nonlinear regression models with long memory moving average errors.

An interesting finding in the case of long memory marginally symmetric errors is that not only is the limiting distribution of a suitably
standardized median of the absolute residuals free of the regression estimator, but it is degenerate at zero.  On the other hand a similarly
standardized median of the absolute differences of pairwise residuals converges in distribution to a normal distribution, regardless of the
errors being symmetric or not.  One striking conclusion is that under the symmetry of the long memory moving average errors, the rate of consistency of the first estimator is faster than that of the second.

COFFEE: 3:45 p.m., 104 Snedecor Hall