177 research outputs found
Robust quantile estimation and prediction for spatial processes
In this paper, we present a statistical framework for modeling conditional
quantiles of spatial processes assumed to be strongly mixing in space. We
establish the consistency and the asymptotic normality of the kernel
conditional quantile estimator in the case of random fields. We also define a
nonparametric spatial predictor and illustrate the methodology used with some
simulations.Comment: 13 page
Exploring hypergraphs with martingales
Recently, we adapted exploration and martingale arguments of Nachmias and
Peres, in turn based on ideas of Martin-L\"of, Karp and Aldous, to prove
asymptotic normality of the number of vertices in the largest component
of the random -uniform hypergraph throughout the supercritical regime.
In this paper we take these arguments further to prove two new results: strong
tail bounds on the distribution of , and joint asymptotic normality of
and the number of edges of . These results are used in a
separate paper "Counting connected hypergraphs via the probabilistic method" to
enumerate sparsely connected hypergraphs asymptotically.Comment: 32 pages; significantly expanded presentation. To appear in Random
Structures and Algorithm
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