\(R\)-estimation of the parameters of autoregressive [AR(\(p\))] models. (English) Zbl 0795.62076

Koul, Hira L.; Saleh, A. K. Md. E.

Ann. Stat. 21, No. 1, 534-551 (1993).

The authors consider \(R\)-estimation of a subset of the parameters of a stationary linear \(\text{AR}(p)\) when the complementary subset may be redundant. They compare the unrestricted and restricted \(R\)-estimators with preliminary-test and shrinkage \(R\)-estimators. Using asymptotic distributional risk as the criterion, the latter two estimators are found to be robust with respect to the complementary subset. The restricted estimator may dominate when this subset actually is redundant but is behaves poorly otherwise. More detailed results are derived.

Reviewer: E.McKenzie (Glasgow)

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05	Nonparametric estimation
62M05	Markov processes: estimation; hidden Markov models
62G10	Nonparametric hypothesis testing

Keywords:

robust estimation; rank-statistics; Stein phenomena; stationary autoregressive processes; preliminary-test estimators; \(R\)-estimation; shrinkage \(R\)-estimators; asymptotic distributional risk