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Estimation for the first-order diagonal bilinear time series model. (English) Zbl 0711.62078
The problem of estimation of the parameter b in the simple diagonal bilinear model $\{X\sb t\}$, $$ X\sb t=e\sb t+be\sb{t-1}X\sb{t-1}, $$ is considered, where $\{e\sb t\}$ is Gaussian white noise with zero mean and possibly unknown variance $\sigma\sp 2$. The asymptotic normality of the moment estimator of b is established for the two cases when $\sigma\sp 2$ is known and $\sigma\sp 2$ is unknown. It is noted that the limit distribution of the least-squares cannot easily be derived analytically. A bootstrap comparison of the sampling distributions of the least-squares and moment estimates shows that both are asymptotically normal with the least-squares estimate being the more efficient.

62M10Time series, auto-correlation, regression, etc. (statistics)
62E20Asymptotic distribution theory in statistics
62F10Point estimation
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