Then the first-order derivative of f(cj(Θ0; y)) with respect to cj(Θ0; y) is: − 1 n ∑n i=1 1 νj0 φ( cj(Θ0;y)−Wij(Θ0) νj0 ) < 0. Thus it ensures uniqueness of the root of f(cj(Θ0; y)) = 0 in the entire domain of cj(y). Note that, ĉj(Θ0; y) satisfied (S.1), hence f(ĉj(Θ0; y)) = 0. On the other hand, f(cj0(y)) → 0 (given the uniform law of large numbers). By the standard inverse function theorem, ...

If for a ‘permissible’ family of functions F and an i.i.d. process {Xi} ∞ i=0 lim n→∞ sup f∈F ∣ ∣ ∣ ∣ ∣ 1 n n−1 ∑ i=0 f(Xi)− Ef(X0) ∣ ∣ ∣ ∣ ∣ = 0 with probability one, then the same holds for every absolutely regular (weakly Bernoulli) process having the same marginal distribution. In particular, for any class of sets C having finite V-C dimension and any absolutely regular process {Xi} ∞ i=0 l...

3 Software Application: ALL microarray dataset 4 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 ALL data package and initial gene filtering . . . . . . . . . . 5 3.3 Association of expression measures and cytogenetic test status: two-sample t-statistics . . . . . . . . . . . . . . . . . . . 7 3.4 Augmentation procedures for gFWER, TPPFP, and FDR control . . . . ...

In their paper, Peter Bickel and Bo Li give an interesting unified view of regularization methods in statistics. The literature on this subject is immense, so they outline a general conceptual approach, and then focus on some selected problems where regularization is used, such as regression and classification, or more generally, prediction. In this context, they discuss in detail a number of r...

This package provides facilities for performing and reporting different types of univariate goodness-of-fit statistical tests. Overview This package contains tools for performing univariate goodness-of-fit (GOF) statistical tests. Static methods for computing (or approximating) the distribution function F (x) of certain GOF test statistics, as well as their complementary distribution function ¯...

Overview This package contains tools for performing univariate goodness-of-fit (GOF) statistical tests. Static methods for computing (or approximating) the distribution function F (x) of certain GOF test statistics, as well as their complementary distribution function ¯ F (x) = 1 − F (x), are implemented in classes FDist and FBar. Tools for computing the GOF test statistics and the correspondin...

Highly degenerate incoherent radiation has a Gaussian density matrix and a large occupation number of modes f. If it is passed through a weakly transmitting barrier, its counting statistics is close to Poissonian. We show that a second identical barrier, in series with the first, drastically modifies the statistics. The variance of the photocount is increased above the mean by a factor f times ...

We consider the sample paths of the order statistics of independent and identically distributed random variables with common distribution function F . If F is strictly increasing but possibly having discontinuities, we prove that the sample paths of the order statistics satisfy the large deviation principle in the Skorokhod M1 topology. Sanov’s theorem is deduced in the SkorokhodM ′ 1 topology ...

Youngser Park Center for Imaging Science Johns Hopkins University Baltimore, MD, 21218 [email protected] Heng Wang Dept. of Applied Mathematics & Statistics Johns Hopkins University Baltimore, MD, 21218 [email protected] Tobias Nöbauer Research Institute of Molecular Pathology (IMP) Max. F. Perutz Laboratories (MFPL) & Research Platform for Quantum Phenomena and Nanoscale Biological Systems (QuNaB...

Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spectral density S(f) scaling as a power of the frequency f. Furthermore, we anal...