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Stochastic processes in estimation theory
IEEE Transactions on Information Theory, 1976We describe the role of various stochastic processes, especially martingales and related concepts, in estimation theory. It is shown, in the simplest context, that in nonlinear estimation theory martingales play the same fundamental role as uncorrelation and white noise do in linear estimation.
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2015
We know from our basic knowledge of statistics that one of the objectives in statistics is to better understand and model the underlying process which generates data. This is known as statistical inference: we infer from information contained in sample properties of the population from which the observations are taken.
Wolfgang Karl Härdle, Zdeněk Hlávka
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We know from our basic knowledge of statistics that one of the objectives in statistics is to better understand and model the underlying process which generates data. This is known as statistical inference: we infer from information contained in sample properties of the population from which the observations are taken.
Wolfgang Karl Härdle, Zdeněk Hlávka
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MULTI-ΒAYESIAN ESTIMATION THEORY
Statistics & Risk Modeling, 1986This paper presents a general theory of multi-Bayesian estimation. The authors consider a class of non-randomized procedures D which is essentially B-complete (equivalent to essential completeness in Wald's theory). Through a series of lemmas and theorems, the authors give necessary and sufficient conditions for D to be essentially B-complete.
de Waal, D. J. +3 more
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1974
We first superficially sketch the problem we will treat in this chapter. In the previous chapter we dealt with the question of how one can acquire more precise information on the value of an unknown parameter on the basis of a sample. Although one tries to construct confidence sets which are “as small as possible”, one cannot be guided in such a ...
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We first superficially sketch the problem we will treat in this chapter. In the previous chapter we dealt with the question of how one can acquire more precise information on the value of an unknown parameter on the basis of a sample. Although one tries to construct confidence sets which are “as small as possible”, one cannot be guided in such a ...
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State decoupling in estimation theory
1995 International Conference on Acoustics, Speech, and Signal Processing, 2002When a system is unobservable, the error covariance associated with a Kalman filter will be nearly singular. As a consequence, an optimum estimation does not exist. In this paper, we show that this system can be transformed into a nonlinear system with a linear measurement equation.
Pan-Tai Liu, Hui Fang, Fu Li, Heng Xiao
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Interpretation and Estimation in Ranking Theory
Biometrika, 1985SUMMARY A simple probabilistic interpretation is given to the expected ranks of k objects ordered by randomly generated observers. The result is shown to yield naturally an estimation procedure in a parametric model for the distribution of permutations.
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On the Theory of Equivariant Estimation on Groups
Theory of Probability & Its Applications, 1987See the review in Zbl 0615.62024.
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An estimation in the theory of diophantine approximations
Acta Mathematica Academiae Scientiarum Hungaricae, 1958Originally he found that (1) is satisfied by A 2 4 e -~ and later in a paper written with VE~A T. SOs [4] it is shown that A = 2el+4/~ too, satisfies the inequality (1). They remark that the lessening of the constant A plays an important role at certain applications and the question was raised to find the least numerical constant A* for which M ~ , n >
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