Strong Approximations in Probability and Statistics

By M. D. Burke. International Encyclopedia of Statistical Science, 2011

299 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/3a1eadd97041786adab6b97563d2f70da9dea89f

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Citations in the corpus

Inconsistency of bootstrap: The Grenander estimator (2010, methodology): “Using ideas similar to that in Equation (5) and the following discussion, the process as a function of the process Z 0 n,2 and apply a continuous mapping type argument to find its limiting distribution.”
Komlós–Major–Tusnády approximation under dependence (2014, background): “Due to the powerful consequences of KMT approximation [see, e.g., Csörgő and Hall (1984) or the books of Csörgő and Révész (1981) and Shorack and Wellner (1986) for the scope of its applications], extending these results for dependent random variables would have a great importance, but until…”
A Confidence Corridor for Sparse Longitudinal Data Curves (2011, unknown): “[Theorem 2.6.7 of Csőrgő and Révész (1981)] Suppose that ξi, 1 ≤ i ≤ n are i.i.d. with E ξ1 = 0,E ξ 2 1 = 1 and H (x) > 0 (x ≥ 0) is an increasing continuous function such that x−2−γH (x) is increasing for some γ > 0 and x−1 logH (x) is decreasing with EH (|ξ1”
Extensions of some classical methods in change point analysis (2014, background): “…iterated logarithm, but also rates of convergence and Bahadur–Kiefer representations (with exact rate) can be established if we have a rate in (3.3) and the modulus of continuity of is known [cf. Chapter 1 in Csörgő and Révész (1981) on the modulus of continuity of Wiener and related processes].”
Asymptotic results for the empirical process of stationary sequences (2009, unknown): “Csörgő and Révész [20]).”
Split invariance principles for stationary processes. (2011, methodology): “We now proceed similarly as in Csörgő and Révész [9] for the proof of Step 2 of their Theorem 1.2.1.”
A specification test for nonlinear nonstationary models (2012, unknown): “Indeed, by noting on the richer space that sup 0≤t≤1 ∣∣∣∣∣ 1√ n [nt]∑ j=1 ǫj −W1(t) ∣∣∣∣∣= oP (1)(5.4) [see, e.g., Csörgő and Révész (1981)], and using this result in place of the fact that 1√ n ∑[nt] j=1 ǫj ⇒W (t) on D[0,1], the same technique as in the proof of Phillips (1987) [see also Chan…”