Goryainova

pp. 407-415

In this article the process of two-dimensional autoregression of order (1,1) is considered. Distribution of the innovation field of the autoregressive model was assumed to be unknown. Definitions of the influence functional and the gross error sensitivity coefficient for autoregressive field parameter estimation were given. An explicit expression for the influence functional of sign estimation of the equation coefficients of the autoregressive field was obtained. It was shown that the sign estimation was robust. Sign estimation could be recommended as an alternative to least squares estimation with anomalously large errors when observing an autoregressive field.

Asymptotic normality of M-estimations with not necessarily convex regret function for 2D-autoregression of (1,1) order was recognized. Stability of these estimations when filling observation data with rough upwards excursions was recognized with computer simulation.