We consider the problem of testing whether the observations X 1; . . . ;X n of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry–Esséen– Zolotarev bounds. The bounds are ex...

In the pharmaceutical industry, a number of tests such as content uniformity and dissolution testing are usually performed at various stages of drug manufacturing process to ensure that the drug product meets standards for identity, strength, quality, purity, and stability of the drug product as specified in the United States Pharmacopedia and National Formulary (USP/NF). The USP/NF provides re...

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

Let A and B be positive semidefinite matrices. We investigate the conditions under which the Lieb-Thirring inequality can be extended to singular values. That is, for which values of p does the majorisation σ(BpAp) ≺w σ((BA) p) hold, and for which values its reversed inequality σ(BpAp) ≻w σ((BA) p).

We give a short proof of the Cwikel–Lieb–Rozenblum (CLR) bound on the number of negative eigenvalues of Schrödinger operators. The argument, which is based on work of Rumin, leads to remarkably good constants and applies to the case of operator-valued potentials as well. Moreover, we obtain the general form of Cwikel’s estimate about the singular values of operators of the form f(X)g(−i∇).

We use `p estimates together with Brascamp-Lieb inequalities to obtain bounds on the variance of the solution u" to the elliptic equation r" a(x="; ')r"u" = r" f . The variance is shown to be O("r) where the exponent r depends on the contrast of a(x; '). In two dimensions, we show that variance of the Greens function of the above elliptic operator is bounded. We also obtain decay rates for the ...

We consider the Brascamp–Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of centred gaussian extremals. For arbitrary extremals we completely address the issue of existence, and partly address the issue of uniqueness. We also analyse th...

We prove global versions of certain known nonlinear Brascamp– Lieb inequalities under a natural homogeneity assumption. We also establish a conditional theorem allowing one to generally pass from local to global nonlinear Brascamp–Lieb estimates under such a homogeneity assumption.

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution f(x, y, z) of continuous random vectors X,Y and Z, we determine whether X ⊥ Y |Z. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifier...

In this work we prove non-trivial impossibility results for perhaps the simplest non-linear estimation problem, that of Group Testing (GT), via the recently developed Madiman-Tetali inequalities. Group Testing concerns itself with identifying a hidden set of d defective items from a set of n items via t disjunctive/pooled measurements (“group tests”). We consider the linear sparsity regime, i.e...