sensitivity analysis for certain permutation inferences in matched observational studies summary in observational studies treatments are not randomly assigned to experimental units so that randomization tests and their associated interval estimates are not generally applicable in an effort to compensate for the lack of randomization treated and control units are often matched on the basis of observed covariates however the possibility remains of bias due to residual imbalances in unobserved covariates a general though simple method is proposed for displaying the sensitivity of permutation inferences to a range of assumptions about unobserved covariates in matched observational studies the sensitivity analysis is applicable to wilcoxon s signed rank test to the mcnemar cox test for paired binary responses and to some matching problems with a variable number of controls

a new general method for constructing confidence sets in arbitrary dimensions with applications let x have a star unimodal distribution p 0 on r p we describe a general method for constructing a star shaped set s with the property p 0 x s 1 where 0 1 is fixed this is done by using the camp meidell inequality on the minkowski functional of an arbitrary star shaped set s and then minimizing lebesgue measure in order to obtain size efficient sets conditions are obtained under which this method reproduces a level high density set the general theory is then applied to two specific examples set estimation of a multivariate normal mean using a multivariate t prior and classical invariant estimation of a location vector for a mixture model in the bayesian example a number of shape properties of the posterior distribution are established in the process these results are of independent interest as well a computer code is available from the authors for automated application the methods presented here permit construction of explicit confidence sets under very limited assumptions when the underlying distributions are calculationally too complex to obtain level sets

an analytical characterization of effective and of irreducible groups inducing cone orderings abstract an analytical characterization of effective and of irreducible groups inducing cone orderings is given the characterization implies easily a necessary condition for a group majorization to be a group induced cone ordering

hyperbolic geometry of complex networks we develop a geometric framework to study the structure and function of complex networks we assume that hyperbolic geometry underlies these networks and we show that with this assumption heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry conversely we show that if a network has some metric structure and if the network degree distribution is heterogeneous then the network has an effective hyperbolic geometry underneath we then establish a mapping between our geometric framework and statistical mechanics of complex networks this mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes while the auxiliary fields coupled to edges are linear functions of these energies or distances the geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures finally we show that targeted transport processes without global topology knowledge made possible by our geometric framework are maximally efficient according to all efficiency measures in networks with strongest heterogeneity and clustering and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

some recent developments on majorization inequalities in probability and statistics abstract we review some recent developments on majorization inequalities in probability and statistics in section 2 we describe some related generalizations including majorization in an integral form multivariate majorization stochastic majorization and other related orderings include the lorentz ordering and arrangement increasing ordering and state some results section 3 concerns partial orderings of probability contents of certain classes of geometric regions in r n via a majorization ordering of their parameter vectors section 4 deals with some applications of majorization theory to dependence and peakedness orderings of random variables in most cases the described results have become available since the publication of marshall and olkin s book 1979 and are directly or indirectly inspired by it

an ordering for positive dependence on introduit une relation d ordre partiel pour des distributions bivariables dependantes positives appelees plus associees

active control trials with binary data a comparison of methods for testing superiority or non inferiority using the odds ratio this paper considers methods for testing for superiority or non inferiority in active control trials with binary data when the relative treatment effect is expressed as an odds ratio three asymptotic tests for the log odds ratio based on the unconditional binary likelihood are presented namely the likelihood ratio wald and score tests all three tests can be implemented straightforwardly in standard statistical software packages as can the corresponding confidence intervals simulations indicate that the three alternatives are similar in terms of the type i error with values close to the nominal level however when the non inferiority margin becomes large the score test slightly exceeds the nominal level in general the highest power is obtained from the score test although all three tests are similar and the observed differences in power are not of practical importance

probability inequalities for multivariate distributions with dependence structures abstract let x 1 xn be a sequence of random variables with a given positive or negative dependence structure in this article we exploit the assumed dependence structure to construct a sequence of bounds for the p xi e ci i 1 n where ci are infinite intervals of the same type these bounds are superior to the well known product bounds that are based solely on the marginal probabilities moreover the new bounds can serve as respectable approximations for the p xi e ci i 1 n

curvature and temperature of complex networks we show that heterogeneous degree distributions in observed scale free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space fermi dirac statistics provides a physical interpretation of hyperbolic distances as energies of links the hidden space curvature affects the heterogeneity of the degree distribution while clustering is a function of temperature we embed the internet into the hyperbolic plane and find a remarkable congruency between the embedding and our hyperbolic model besides proving our model realistic this embedding may be used for routing with only local information which holds significant promise for improving the performance of internet routing

sensitivity of two sample permutation inferences in observational studies abstract in observational studies subjects are not randomly assigned to treatment or control so they may differ in their chances of receiving the treatment a simple method is developed and demonstrated for displaying the sensitivity of conventional two group permutation inferences to departures from random assignment of treatments the unmatched case discussed here differs in certain technical and computational details from the matched case discussed previously however the underlying model and the method for quantifying departures from randomization are the same the method may be applied to wilcoxon s rank sum test the gehan and log rank tests for censored outcomes mantel s test for scored categories and fisher s exact test for binary responses the method embeds the usual randomization reference distribution in a one parameter family of departures involving an unobserved covariate that would have been controlled by adjustments had it been observed as this parameter is varied the sensitivity

group majorization and schur type inequalities abstract the problem of the reduction of a group majorization induced by an infinite group to a finite group majorization is discussed a necessary and sufficient condition for a possibility of the reduction is given the condition generalizes some known inequalities in the matrix theory involving eigenvalues or singular values of a matrix a corresponding result for a skew symmetric matrix is derived

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

a process in a randomly fluctuating environment on considere un processus de markov stationnaire en temps continu et une particule se deplacant a vitesse unitaire le long d une droite reelle sa direction etant completement determinee par celle du processus

is the t test really conservative when the parent distribution is long tailed abstract it is generally believed that the t test is conservative for a sample from a long tailed symmetric distribution yet the probability inequalities expressing this property have not been proved the inequalities are explored here using various criteria for long tailedness and leaning on the geometrical interpretation of the t test it is proved that the t test is conservative but only for large enough critical values examples of a liberal t test for lower values are given the results are used to explain some curiosities in the asymptotic distribution of the t statistic and to study its behavior when the parent distribution is skewed

surface order large deviations for ising potts and percolation models we derive uniform surface order large deviation estimates for the block magnetization in finite volume ising or potts models with plus or free or a combination of both boundary conditions in the phase coexistence regime ford 3 the results are valid up to a limit of slab thresholds conjectured to agree with the critical temperature our arguments are based on the renormalization of the random cluster model withq 1 andd 3 and on corresponding large deviation estimates for the occurrence in a box of a largest cluster with density close to the percolation probability the results are new even for the case of independent percolation q 1 as a byproduct of our methods we obtain further results in the fk model concerning semicontinuity inp andq of the percolation probability the second largest cluster in a box and the tail of the finite cluster size distribution

comparative analysis of two rates in this paper we examine comparative analysis of rates with a view to each of the usual comparative parameters rate difference rd rate ratio rr and odds ratio or and with particular reference to first principles for rd and rr we show the prevailing statistical practices to be rather poor we stress the need for restricted estimation of variance in the chi square function underlying interval estimation and also point estimation and hypothesis testing for rr analysis we propose a chi square formulation analogous to that for rd and thus one which obviates the present practice of log transformation and its associated use of taylor series approximation of the variance as for or analysis we emphasize that the chi square function introduced by cornfield for unstratified data and extended by gart to the case of stratified analysis is based on the efficient score and thus embodies its optimality properties we provide simulation results to evince the better performance of the proposed parameter constrained procedures over the traditional ones

algebraic methods toward higher order probability inequalities ii in work motivated by problems in the analysis of variance kimball 15 proved that if vi qi q0 i 1 n where the q i are mutually independent positive random variables then v 1 v n are positively upper orthant dependent puod p mathop cap limits i 1 n v i geqslant v i geqslant prod limits i 1 n p v i geqslant v i v 1 ldots v n geqslant 0 1 1 and also are positively lower orthant dependent plod p mathop cap limits i 1 n v i leqslant v i geqslant prod limits i 1 n p v i leqslant v i v 1 ldots v n geqslant 0 1 2 these results motivated much research on other inequalities cf 4 10 20 24

comments on active control trials with binary data a comparison of methods for testing superiority or non inferiority using the odds ratio by a l siqueira a whitehead and s todd statistics in medicine 2008 27 353 370

g majorization group induced cone orderings and reflection groups a vector y is g majorized by a vector x if y is an element of the convex hull of the orbit of x under the action of a group g it is known that if g is a finite reflection group then g majorization is equivalent to a group induced cone ordering in this paper it is established that if for a finite subgroup g of the orthogonal group g majorization is equivalent to a group induced cone ordering then g must be a reflection group

inequalities theory of majorization and its applications by albert w marshall and ingram olkin abstract in the years since the appearance of marshall and olkin s masterful survey the influence of this work has been so great that some comments however incomplete and idiosyncratic on subsequent developments will be of value figure 1 an appendix lists minor errata to the first printing of the book

inequalities of fkg type abstract in 1971 fortuin kasteleyn and ginibre proved a correlation inequality for monotone functions on certain partially ordered sets this inequality has become a standard tool in the rigorous analysis of diverse stochastic models such as those arising in percolation theory statistical mechanics of spin systems and combinatorics several generalizations of the fkg inequality have appeared in the literature notably by holley in 1974 and by ahlswede daykin in 1978 we review the three inequalities present simplified proofs and list a few major applications we also prove chains of intermediate inequalities stronger than the fkg and holley inequalities which may be useful for understanding and for future development

soft communities in similarity space the mathbb s 1 model has been central in the development of the field of network geometry it places nodes in a similarity space and connects them with a likelihood depending on an effective distance which combines similarity and popularity dimensions with popularity directly related to the degrees of the nodes the mathbb s 1 model has been mainly studied in its homogeneous regime in which angular coordinates are independently and uniformly scattered on the circle we now investigate if the model can generate networks with targeted topological features and soft communities that is inhomogeneous angular distributions to that end hidden degrees must depend on angular coordinates and we propose a method to estimate them we conclude that the model can be topologically invariant with respect to the soft community structure our results expand the scope of the model beyond the independent hidden variables limit and can have an important impact in the embedding of real world networks