M-estimates of autoregression with random coefficients

Asymptotic normality of the M-estimates of the autoregression parameters of the autoregression equation with random coefficients was proved. A method to calculate the asymptotic relative efficiency of the M-estimate with $\rho$-function relative to the least squares estimate was presented for the first-order equation. The method is based on the expansion of the asymptotic variance of the M-estimate into a converging series. The M-estimate was shown to be superior to the least-squares estimate if the regenerative process has a contaminated Gaussian distribution.