On Stochastic Limit and Order Relationships

By H. B. Mann, A. Wald. 1943

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Citations in the corpus

Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, background): “According to Lemmas 7 and 8 and the continuous mapping theorem (CMT) (Mann and Wald, 1943), which states that continuous functions are limit-preserving even if their arguments are sequences of random variables, there exists PX , which may depend on n, such that PX · [ψ1(xt), .”
Two-dimensional Poisson Trees converge to the Brownian web (2003, unknown): “For (b), it is straightforward to check that, for any c = (c1 ,...,c m) ∈ C, cδ = (c1 δ ,...,c m δ ) ∈ Cδ, d ∗m(cδ ,c )→ 0 implies d ∗m(fδ(cδ), f (c)) → 0a sδ → 0. Thus, an extended continuous mapping theorem of Mann and Wald [ 11 ], Prohorov [12] (see also Theorem 3.27 of [10]) gives (b).”
Bias reduction in exponential family nonlinear models (2009, unknown): “2 A Monte Carlo simulation study: Bias reduction versus bias correction As it has been demonstrated by the previous complete enumeration studies, the advantage of the BR estimator over the BC estimator of Cordeiro & McCullagh (1991) is that the latter is undefined when the ML estimates are infinite.”
Folklore Theorems, Implicit Maps, and Indirect Inference (2012, background): “Equally important in econometric asymptotics, especially since the uptake of function space limit theory in the 1980s, is the continuous mapping theorem whose history also stretches into antiquity, an early source being the Mann and Wald (1943) article on stochastic order notation.”
Testing for separability of spatial–temporal covariance functions (2006, methodology): “This is a straightforward onsequen e of the delta method (Mann and Wald, 1943).”
The problem of near-multicollinearity revisited: erratic vs systematic volatility (2002, methodology): “This follows from the Mann and Wald (1943) theorem since, under the traditional assumptions, as T → ∞:”