Outlier-resistant algorithms for detecting a change in a stochastic process

Outlier-resistant algorithms that detect a change from a given nominal stationary process to another such process are given. The nominal processes are assumed to be mutually independent and to satisfy some general regularity conditions. The outlier sequences are assumed to be independently and identically distributed and independent of the nominal processes. The proposed algorithms are sequential and consist of uniformly bounded steps. The asymptotic performance of the algorithms is analyzed, both in the absence and the presence of outliers. Breakdown points and influence functions are defined and analyzed. The algorithms are studied in more detail for Gaussian autoregressive nominal processes