357 research outputs found
On an extremal problem for nonoverlapping domains *
The paper considers the problem of finding the range of functional I = J f (z
0), f (z 0), F ( 0), F ( 0) , defined on the class M of pairs
functions (f (z), F ()) that are univalent in the system of the disk and
the interior of the disk, using the method of internal variations. We establish
that the range of this functional is bounded by the curve whose equation is
written in terms of elliptic integrals, depending on the parameters of the
functional I
Improved estimation in a non-Gaussian parametric regression
The paper considers the problem of estimating the parameters in a continuous
time regression model with a non-Gaussian noise of pulse type. The noise is
specified by the 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 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.Comment: arXiv admin note: substantial text overlap with arXiv:1105.503
Adaptive model selection method for a conditionally Gaussian semimartingale regression in continuous time
This paper considers the problem of robust adaptive efficient estimating of a
periodic function in a continuous time regression model with the dependent
noises given by a general square integrable semimartingale with a conditionally
Gaussian distribution. An example of such noise is the non-Gaussian
Ornstein-Uhlenbeck-Levy processes. An adaptive model selection procedure, based
on the improved weighted least square estimates, is proposed. Under some
conditions on the noise distribution, sharp oracle inequality for the robust
risk has been proved and the robust efficiency of the model selection procedure
has been established. The numerical analysis results are given.Comment: 50 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1710.03111, arXiv:1712.0645
El nacionalismo religioso en los países de la antigua URSS. Análisis específico de la realidad rusa
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