Gaussian processes: Inequalities, small ball probabilities and applications

By Wenbo V. Li, Qi-Man Shao. 2001

485 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/35ae350b57da11ccf1219f4a27317d2b095d0db1

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Citations in the corpus

Comparison and anti-concentration bounds for maxima of Gaussian random vectors (2013, background): “For a survey on the latter problem, called the “small ball problem”, we refer the reader to [15].”
Local linear regression for functional data (2007, background): “Remark 24 Display (22) was proved in Mas (2008a). In the first case (when ρ (s) ≥ Cs4), since the bias term is here O(h4), the rate of convergence of our estimate outperforms the one computed in Ferraty et al.”
Sample path properties of bifractional Brownian motion (2006, methodology): “As applications of small ball probability estimates, Monrad and Rootzén [33], Xiao [44] and Li and Shao [27] established Chung-type laws of the iterated logarithm for fractional Brownian motion and other strongly locally non-deterministic Gaussian processes with stationary increments.”
NONPARAMETRIC REGRESSION ON FUNCTIONAL DATA: INFERENCE AND PRACTICAL ASPECTS (2007, background): “We refer to Li & Shao (2001) for a survey of the main results on small ball probability.”
The Littlewood-Offord problem and invertibility of random matrices (2007, background): “However, rigorous anti-concentration estimates are hard to prove (see [18]), especially for discrete random variables ξk.”
Information Rates of Nonparametric Gaussian Process Methods (2011, background): “(See Kuelbs and Li, 1993 and Li and Shao, 2001and references.)”
Nonparametric modelling for functional data: selected survey and tracks for future (2018, background): “In fact, the exponential expansions discussed in Equation (6) are all statedwhend is ametric (likeHölder or L∞ in [86,87], or like L2 in [89,90]), while the key point in nonparametric functional methodology is that the measure of proximity d between functional elements which is used along the”
Reproducing kernel Hilbert spaces of Gaussian priors (2008, unknown): “[11]).”
Random Fractals and Markov Processes (2005, background): “See Li and Shao (2001) for an extensive survey on small ball probabilities and their applications.”
Lower bounds for posterior rates with Gaussian process priors (2008, background): “Small ball probabilities have been studied in many papers in the probability literature and precise equivalents as ε → 0 of φ(ε) are available for many classes of Gaussian processes, see for instance [11].”