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Multiple testing of local maxima for detection of peaks in ChIP-Seq data
False discovery rate kernel smoothing matched filter Poisson sequence topological inference
2013/6/14
A topological multiple testing approach to peak detection is proposed for the problem of detecting transcription factor binding sites in ChIP-Seq data. After kernel smoothing of the tag counts over th...
An almost sure limit theorem for the maxima and sums of stationary Gaussian sequences
Extreme vaiues partial sums almost sure central limit theorem
2009/9/21
Let XI, X,, . . . be some standardized stationary Gaussian
process and let us put:
Our purpose is to prove an almost sure central limit theorem for the
sequence (MkS,t/ sh under suitable normalizat...
Limiting distributions and almost sure limit theorems for the normalized maxima of complete and incomplete samples from Gaussian sequence
complete and incomplete samples limiting distribution maximum stationary Gaussian sequence
2009/9/16
Let ${X_k, kgeqslant 1}$ be a stationary Gaussian sequence with partial maximum $M_n=max{X_{k},1leqslant kleqslant n}$ and sample mean $overline{X}_n=sum_{k=1}^{n}X_{k}/n$. Suppose that some of the ra...
We provide a simple probabilistic proof of a result of J. Král and I. Netuka: If f is a measurable real-valued function on Rd (d> 1) then the set of points at which f has a strict fine local maxim...
Maxima of the cells of an equiprobable multinomial
multinomial random vectors equiprobable cell independent interest
2009/3/23
Consider a sequence of multinomial random vectors with increasing number of equiprobable cells. We show that if the number of trials increases fast enough, the sequence of maxima of the cells after a ...