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Limits of conditional expectations
IEEE Transactions on Information Theory, 1993Summary: If \((X^ N, Y^ N)\) on a probability space \((\Omega^ N, {\mathcal F}^ N, P^ N)\) converge in distribution to \((X,Y)\) on \((\Omega, {\mathcal F}, P)\), it is not necessarily true that the conditional expectations \(E^{P^ N} \{F(X^ N)\mid Y^ N\}\) converge in distribution to \(E^ P \{F(X)\mid Y\}\), even for bounded, continuous functions \(F\)
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IMA Journal of Numerical Analysis, 1985
The author presents a stochastic analysis for condition numbers of square matrices. The expected condition analysis has desirable properties under scaling transformations, which enables the equilibration of a matrix to be carried out. An optimal scaling enables the best conditioned of all the possible equilibrated matrices to be determined.
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The author presents a stochastic analysis for condition numbers of square matrices. The expected condition analysis has desirable properties under scaling transformations, which enables the equilibration of a matrix to be carried out. An optimal scaling enables the best conditioned of all the possible equilibrated matrices to be determined.
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A theorem on conditional expectation
IEEE Transactions on Information Theory, 1970A statistic often encountered in various estimation problems is the conditional ensemble average of the time derivative of a random signal given the signal. It turns out that for a very large class of random signals this statistic is equal to zero. This is a rather surprising result and as far as can be determined has not been precisely stated and ...
James E. Mazo, Jack Salz
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On Characterizations of Conditional Expectation
Canadian Mathematical Bulletin, 1973In the following (Ω, α, μ) is a totally σ-finite measure space except where noted. For a sub-σ-algebra β ⊂ α, the conditional expectation E{f|β} off given β is a function measurable relative to β, such thatIn [5] R.G.Douglas proved, among other things the following, in the finite case:Suppose μ(Ω)=l.
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Physica A: Statistical Mechanics and its Applications, 2001
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Alstrøm, Preben +1 more
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Alstrøm, Preben +1 more
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The specification of conditional expectations
Journal of Empirical Finance, 1991Abstract This paper explores different specifications of conditional expectations. The most common specification, linear least squares, is contrasted with nonparametric techniques that make no assumptions about the distribution of the data. Nonparametric regression is successful in capturing some nonlinearities in financial data, in particular ...
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On characterization of distribution by conditional expectation
Communications in Statistics, 1975We show that, under mild conditions on h(1), E(h(X)∣X>y) charactarizes the distribution function of K, and exhibit a method of obtainig the distribution whenever E(h(X)∣X>y) is known, in the continuos and in the discrete case The results of Shenbhag (1970) aad Hamdan (1972) follow immediately.
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