Improved estimation in a non-Gaussian parametric regression. (English) Zbl 1259.62082
Summary: This paper considers the problem of estimating the parameters in a continuous time regression model with a non-Gaussian noise of pulse type. The vector of unknown parameters is assumed to belong to a compact set. The noise is specified by an Ornstein-Uhlenbeck process driven by the mixture of a Brownian motion and a compound Poisson process. Improved estimates for the unknown regression parameters, based on a special modification of the James-Stein procedure [W. James Ch. Stein, J. Neyman (ed.), Proc. 4th Berkeley Symp. Math. Stat. Probab., Vol. 1, 361–379 (1961)] with smaller quadratic risk than the usual least squares estimates, are proposed. The developed estimation scheme is applied for the improved parameter estimation in the discrete time regression with the autoregressive noise depending on unknown nuisance parameters.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62H12 | Estimation in multivariate analysis |
| 62M05 | Markov processes: estimation; hidden Markov models |
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