A normal comparison inequality and its applications

By Wenbo V. Li, Qi-Man Shao. 2002

100 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/89146ab39bba560ff4487f569a8ad88d883bb3a8

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In Management Science and Operations Research

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Level crossings and other level functionals of stationary Gaussian processes (2006, background): “…inequality (2.20) given by Li and Shao in 2002 (see [89]) that provide an upper bound in (2.20), cleared of the term (1− ρ2ij)−1/2: Theorem 2.15 (Li and Shao, 2002) Suppose that (X1i, 1 ≤ i ≤ n) are standard normal random variables with covariance matrix Λ1 = (Λ 1 i,j) and (X2i, 1 ≤ i ≤ n)…”
The first exit time of a Brownian motion from an unbounded convex domain (2003, background): “One is lower tail probabilities which study P (supt∈S(Xt −Xt0) ≤ x) as x → 0, with t0 ∈ S fixed, see Li and Shao (2002a) for details.”
Random polynomials having few or no real zeros (2000, methodology): “Remark. Using a stationary Gaussian process generated from the integrated Brownian motion instead of the Ornstein-Uhlenbeck process in the proof of Lemma 2.5 and applying a new normal comparison inequality, Li and Shao [ LiS ] recently proved that 0:5 <b< 1.”
Lower tail probabilities for Gaussian processes (2004, methodology): “It is shown by developing a new normal comparison inequality in Li and Shao (2002) that in fact lim n→∞ γ n / log n = 1/4.”
Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism (2010, background): “The first result bounds the tail of a bivariate normal distribution and its first part is due to Li and Shao [29].”
Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function (2010, methodology): “efully they will also give an unfamiliar reader some idea of how the method of comparison, as it is referred to by Piterbarg [17], is traditionally employed. Our treatment largely follows Li and Shao [11], although we would also like to draw attention to a 1954 paper of Plackett [18] which contains ”