Breakdown-Point for Spatially and Temporally Correlated Observations

Summary

In this paper, we implement a new definition of breakdown in both finite and asymptotic samples with correlated observations arising from spatial statistics and time series. In such situations, existing definitions typically fail because parameters can sometimes breakdown to zero, i.e. the center of the parameter space. The reason is that these definitions center around defining an explicit critical region for either the parameter or the objective function. If for a particular outlier constellation the critical region is entered, breakdown is said to occur. In contrast to the traditional approach, we use a definition that leaves the critical region implicit but still encompasses all previous definitions of breakdown in linear and nonlinear regression settings. We provide examples involving simultaneously specified spatial autoregressive models, as well as autoregressions from time series, for illustration. In particular, we show that in this context the least median of squares estimator has a breakdown-point much lower than the familiar 50%.