Several Estimation Problems in a Gaussian White Noise

  • I. A. Ibragimov
  • R. Z. Has’minskii
Part of the Applications of Mathematics book series (SMAP, volume 16)


A statistical experiment generated by observing a signal with Gaussian white noise is a very convenient model for investigation. The simple form of the likelihood ratio Z (see formula (2.A.17)) and the normality of the random field ln Z — these facts allow us to avoid many difficulties. At the same time, the model is sufficiently interesting since the signal observed may to a large extent depend arbitrarily on the parameter. Finally, this model is of importance in many applications (see [72]). In this chapter we shall first—in Section 1—study the effects which arise in the case of an unbounded or expanding parameter set Θ, since this case is of special importance in information theory. Next, in Sections 2 and 3 the case when the signal 5 depends on the parameter in a discontinuous manner will be considered. Finally, in Sections 4 and 5 examples of non-parametric problems are given.


Loss Function Gaussian White Noise Estimation Problem Maximum Likelihood Estimator Nonparametric Estimation 
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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • I. A. Ibragimov
    • 1
  • R. Z. Has’minskii
    • 2
  1. 1.LOMILeningradUSSR
  2. 2.Doz., Institut Problem Peredači Inf.MoscowUSSR

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