Goryainov

pp. 111-122

pp. 407-415

The process of two-dimensional autoregression of order (1, 1) was considered. Distribution of the innovation field of the autoregressive model is assumed to be unknown. Estimation of the autoregressive model parameters, based on the signs of observation residuals, was constructed. Consistency and asymptotic normality of these estimations was proved. Asymptotic relative efficiency of the estimation in relation to the least squares estimation was calculated. The conclusion was drawn on the advantage of the constructed estimation over the least squares estimation if the innovation field has double exponential distribution or Tukey distribution.

A process of a two-dimensional autoregression of order (1, 1) is considered in this article. Distribution of the innovation field of the autoregressive model is assumed to be unknown. An algorithm for calculating M-estimates of coefficients of the autoregressive field was constructed. The convergence of this algorithm was proved. The algorithm is an iterative version of the weighted least squares method. The weights are recalculated at each step. Each iteration represents the process of solving the system of linear equations. In contrast to the method of Newton (method of tangents) the algorithm converges from any point of the initial approximation.

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.

In this article the process of two-dimensional autoregression of (1,1) order is considered. Distribution of the renovating field of the autoregressive model is assumed to be unknown. The author found the asymptotically locally most powerful tests for verifying the hypotheses about coefficients of the autoregressive field, based on the approximate rank index marks. Estimation of the autoregressive model parameters based on the ranks of observation residuals was build. Consistency and asymptotic normality of these estimations was proved. The conclusion was drawn on the advantage of the constructed estimation over the least squares estimation if the renovating field has normal logistic and double exponential distribution, while rank index marks correspond to Gaussian density.

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.