A User's Guide to Measure-Theoretic Probability

By R. Taylor. 2003

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

SE(3) diffusion model with application to protein backbone generation (2023, background): “The previous proposition is based on the disintegration of measures (Pollard, 2002).”
Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings (2015, unknown): “The proof is essentially similar to that of lemma 18 in Chapter 10 of [22] with the exception that we employ a compactly supported smoother.”
Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models (2014, unknown): “See, e.g., Section 10.4 of Pollard (2001).”
Jump detection with wavelets for high-frequency financial time series (2014, methodology): “That is, we choose a wavelet filter rather window size to minimize †Following Pollard (2002) and Lee and Mykland (2008), we use Op notation throughout this article to mean that, for random vectors {Xn}, and non-negative random variable {dn}, Xn = Op(dn), if for each δ > 0, there exists a finite…”
Dynamic Mechanism Design: A Myersonian Approach (2014, unknown): “14Existence and uniqueness follows by the Tulcea extension theorem (see, e.g., Pollard, 2002, Ch.4, Theorem 49).”
Testing Models of Low‐Frequency Variability (2006, methodology): “Stock and Watson (2007) document instability in the sizeof the unit root component (corresponding to the value of g in the local level model) over the post-war period, but apparently this instability is not so severe that it leads to rejections based on the tests considered here.”
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors (2012, result): “The existing techniques can also lead to results of the form (4) when p = pn → ∞, but under much stronger conditions on p requiring pc/n→ 0; see Example 17 (Section 10) in [34].”
Normal Approximation by Stein's Method (2010, background): “• BR76 = Bhattacharya and Ranga Rao (1976) • RR96 = Rinott and Rotar (1996) and RR97= Rinott and Rotar (1997) • MT = Meckes (2006) Ph.D. thesis • Alea = Chatterjee and Meckes (2008) • Luminy = Meckes (2009), Luminy paper • PTTM = Pollard (2029) and UGMTP = Pollard (2001).”
Optimized Data Pre-Processing for Discrimination Prevention (2017, unknown): “We use (cid:96) 1 -distance (twice the total variation) (Pollard, 2002) to measure utility, ∆ p X,Y , p ˆ X, ˆ Y = x,y p X,Y ( x, y ) − p ˆ X, ˆ Y ( x, y ) (cid:12)(cid:12)(cid:12) .”
Regret Bounds for Gaussian Process Bandit Problems (2010, unknown): “For T ≥ 2, we have To obtain an equivalent on u T when T goes to inﬁnity, we use the well-known bound on tails of the normal distribution (e.g., see Pollard (2002, Appendix D)): Consequently, we obtain and similarly Finally, elementary computations give Putting together the three last results, we…”
Gaussian approximation of suprema of empirical processes (2012, background): “For textbook treatments of Yurinskii’s and KMT’s couplings, we refer to [16] and Chapter 10 in [49].”
Isotonic regression in general dimensions (2017, unknown): “By Pinsker’s inequality (cf. Pollard, 2002, p. 62), we obtain that d2TV ( PY |X,τ , PY |X,τw ) ≤ 1 2 d2KL(PY |X,τ , PY |X,τw) = n 4 ‖fτ − fτw‖2L2(Pn).”
Intersection bounds: estimation and inference (2009, methodology): “He we shall apply Yurinskii coupling, see Yurinskii (1977) and Pollard (2002) (page 244).”
Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes (2007, methodology): “The book is similar to that of Ash and Doleans-Dade (2000), but different from those by Billingsley (1986) and Pollard (2002), in that measure and probability are studied consecutively and not intertwined.”
Commutative Semantics for Probabilistic Programming (2017, background): “Integration satisﬁes the following properties (e.g. [32, Thm. 12]): for any monotone sequence These properties entirely determine integration, since every measurable function is a limit of a monotone sequence of simple functions [32, Lemma 11].”