Publication Cover
Sequential Analysis
Design Methods and Applications
Volume 22, 2003 - Issue 1-2
33
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

On Uniform Asymptotic Normality of Sequential Estimators for the Parameters in a Stable AR(1)

&
Pages 31-54 | Received 01 Apr 2001, Published online: 17 Aug 2006

References

  • Lai , T.L. and Siegmund , D. 1983 . Fixed-accuracy estimation of an autoregressive parameter . Ann. Statist. , 11 : 478 – 485 .
  • Greenwood , P.E. and Shiryaev , A.N. 1992 . Asymptotic minimaxity of a sequential estimator for a first order autoregressive model . Stochastic and Stochastics Rep. , 38 : 49 – 65 .
  • Konev , V.V. and Pergamenshchikov , S.M. 1996 . Guaranteed parameter estimation on the basis of a generalized least-squares method . Theory Probab. Appl. , 41 : 765 – 784 .
  • Shiryaev , A.N. and Spokoiny , V.G. 1997 . On sequential estimation of an autoregressive parameter . Stochastic and Stochastics Rep. , 60 : 219 – 240 .
  • Sriram , T.N. 1987 . Sequential estimation of the mean of a first order stationary autoregressive process . Ann. Statist. , 15 : 1079 – 1090 .
  • Sriram , T.N. 1988 . Sequential estimation of the autoregressive parameter in a first order autoregressive process . Sequential Anal. , 7 : 53 – 74 .
  • Aras , G. 1990 . Sequential estimation of the mean of a first-order autoregressive process . Commun. Statist. Theory Methods , 19 : 1639 – 1652 .
  • Lee , S. 1994 . Sequential estimation for the parameters of a stationary autoregressive model . Sequential Anal. , 13 : 301 – 307 .
  • Borisov , V.Z. and Konev , V.V. 1977 . On sequential parameters estimation in discrete time processes . Automat. Remote Control , 6 : 58 – 64 .
  • Konev , V.V. and Lai , T.J. 1995 . Estimation with prescribed precision in stochastic regression models . Sequential Anal. , 14 : 179 – 192 .
  • Konev , V.V. and Pergamenshchikov , S.M. 1997 . On guaranteed estimation of the mean of the autoregressive process . Ann. Statist. , 25 : 2127 – 2163 .
  • Anscombe , F.J. 1952 . Large sample theory of sequential estimation . Proc. Camb. Phil. Soc. , 48 : 600 – 607 .
  • Anderson , T.W. 1959 . On asymptotic distributions of estimates of parameters of stochastic difference equations . Ann. Math. Statist. , 30 : 676 – 687 .
  • Rao , M.M. 1978 . Asymptotic distribution of an estimator of the boundary parameter of an unstable process . Ann. Statist. , 6 : 185 – 190 .
  • Dickey , D.A. and Fuller , W.A. 1979 . Distribution of estimators for autoregressive time series with a unit root . J. Amer. Statist. Assoc. , 74 : 427 – 431 .
  • Lai , T.L. and Wei , C.Z. 1982 . Least squares estimates in stochastic regression models with applications to identification and control of dynamical systems . Ann. Statist. , 10 : 154 – 166 .
  • Lai , T.L. and Wei , C.Z. 1983 . Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters . J. Multivariate Anal. , 13 : 1 – 23 .
  • Rowlands , R.J. and Wetherill , G.B. 1991 . “ Quality control ” . In Handbook of Sequential Analysis Edited by: Ghosh , B.K. and Sen , P.K. 563 – 580 . New York : Marcel Dekker .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.