Probability A Graduate Course

By S. Lowe. 2016

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Breaking the curse of dimensionality in regression (2017, background): “By Theorem 5.4 on p.220 of Gut (2013), E [ sup x∈R ∣∣∣P ( ‖S̃Ψn ‖∞ > x | Gn ) − P ( ‖S̃Ψ̂n ‖∞ > x | Gn )∣∣∣ ] → 0.”
On weighted cumulative residual entropy (2017, background): “Some general results regarding this measure have been studied by Rao (2005) and Drissi et al.”
Scaling limits of random planar maps with a unique large face (2012, positive): “ note that the random variables Yv are independent. By [41], Lemma 1, there exists a constant C2(p)>0 such that for every v (2.18) E|Yv|p ≤C2(p)|Av|p/2. Thus, by Rosenthal’s inequality (see, e.g., [27], Theorem 3.9.1), E|Sτn l −S τn k | p =E v X v∈V • Y v p ≤C3(p) X v∈V • E|Y |p +C4(p) X v∈V • E|”