minimax rates in permutation estimation for feature matching the problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation we address this problem from a statistical point of view and provide a theoretical analysis of the accuracy of several natural estimators to this end the minimax rate of separation is investigated and its expression is obtained as a function of the sample size noise level and dimension of the features we consider the cases of homoscedastic and heteroscedastic noise and establish in each case tight upper bounds on the separation distance of several estimators these upper bounds are shown to be unimprovable both in the homoscedastic and heteroscedastic settings interestingly these bounds demonstrate that a phase transition occurs when the dimension d of the features is of the order of the logarithm of the number of features n for d o log n the rate is dimension free and equals log n 1 2 where is the noise level in contrast when d is larger than c log n for some constant c 0 the minimax rate increases with d and is of the order of d log n 1 4 we also discuss the computational aspects of the estimators and provide empirical evidence of their consistency on synthetic data finally we show that our results extend to more general matching criteria

a pocket calculator algorithm for the shapiro francia test for non normality an application to medicine an easy to calculate approximation to the shapiro francia w test and its p value is proposed its accuracy is sufficient for practical application in samples of size 5 or larger

on subalgebras of the car algebra abstract every nuclear unital separable c algebra a is unitally and completely isometrically ismorphic to the range of a unital completely positive projection on the car algbra b m 2 m 2 let c be a nuclearly imbeddable separable unital c algebra in the sense of voiculescu vo13 then there exists a c subalgebra e of the car algebra b such that c is isomorphic to a quotient c algebra of e we include one of the possible proofs that exact c algebras are nuclearly imbeddable proofs of g covariant analogs are outlined for compact g some related results are obtained on non selfadjoint operator algebras the unital separable nuclear c algebras not of type i are mutually cb isomorphic and have cb distance 256 separable lindenstrauss spaces are isometric to quotients of the car algebra by a sum of closed left and a closed right ideal

asymptotic distribution of the shapiro wilk w for testing for normality abstract twenty years have elapsed since the shapiro wilk statistic w for testing the normality of a sample first appeared in that time a number of statistics which are close relatives of w have been found to have a common known asymptotic distribution it was assumed therefore that w must have that asymptotic distribution the authors show this to be the case and examine the norming constants that are used with all the statistics in addition the consistency of the w test is established keywords goodness of fit normal order scores

on ii1 factors arising from 2 cocycles of w rigid groups we consider ii1 factors l g arising from 2 cocyles h2 g t on groups g containing infinite normal subgroups h g with the relative property t i e g w rigid we prove that given any separable ii1 factor m the set of 2 cocycles h h2 h t with the property that l g is embeddable into m is at most countable we use this result the relative property t of z2 z2 for sl 2 z non amenable and the fact that every cocycle h2 z2 t t extends to a cocycle on z2 sl 2 z to show that the one parameter family of ii1 factors m l z2 t are mutually non isomorphic modulo countable sets and cannot all be embedded into the same separable ii1 factor other examples and applications are discussed

some prime factorization results for type ii1 factors we prove several unique prime factorization results for tensor products of type ii1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected lie groups of real rank 1 in particular we show that if mathcal r overline otimes mathcal l mathbb f r 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f r m is isomorphic to a subfactor in mathcal r overline otimes mathcal l mathbb f s 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f s n for some 2 ri sj then m n

unique prime factorization for infinite tensor product factors abstract in this article we investigate a unique prime factorization property for infinite tensor product factors we provide several examples of type ii and iii factors which satisfy this property including all free product factors with diffuse free product components in the type iii setting this is the first classification result for infinite tensor product non amenable factors our proof is based on popa s intertwining techniques and a characterization of relative amenability on the continuous cores

sparse sign consistent johnson lindenstrauss matrices compression with neuroscience based constraints johnson lindenstrauss jl matrices implemented by sparse random synaptic connections are thought to be a prime candidate for how convergent pathways in the brain compress information however to date there is no complete mathematical support for such implementations given the constraints of real neural tissue the fact that neurons are either excitatory or inhibitory implies that every so implementable jl matrix must be sign consistent i e all entries in a single column must be either all nonnegative or all nonpositive and the fact that any given neuron connects to a relatively small subset of other neurons implies that the jl matrix should be sparse we construct sparse jl matrices that are sign consistent and prove that our construction is essentially optimal our work answers a mathematical question that was triggered by earlier work and is necessary to justify the existence of jl compression in the brain and emphasizes that inhibition is crucial if neurons are to perform efficient correlation preserving compression

overweight tails are inefficient test statistics which are almost determined by o n tail order statistics are shown to provide tests of asymptotic relative efficiency 0 against the usual type of contiguous alternative the result is applied to several goodness of fit tests the variance weighted kolmogorov smirnov statistic the kolmogorov smirnov statistic in the stabilized probability plot and the correlation coefficient in a q q plot for a variety of distributions with exponential tails

adaptive estimation of a quadratic functional by model selection we consider the problem of estimating s 2 when s belongs to some separable hilbert space and one observes the gaussian process y t langles t rangle sigmal t for all t epsilon mathbb h where l is some gaussian isonormal process this framework allows us in particular to consider the classical gaussian sequence model for which mathbb h l 2 mathbb n and l t sum lambda geq1 t lambda varepsilon lambda where varepsilon lambda lambda geq1 is a sequence of i i d standard normal variables our approach consists in considering some at most countable families of finite dimensional linear subspaces of mathbb h the models and then using model selection via some conveniently penalized least squares criterion to build new estimators of s 2 we prove a general nonasymptotic risk bound which allows us to show that such penalized estimators are adaptive on a variety of collections of sets for the parameter s depending on the family of models from which they are built in particular in the context of the gaussian sequence model a convenient choice of the family of models allows defining estimators which are adaptive over collections of hyperrectangles ellipsoids l p bodies or besov bodies we take special care to describe the conditions under which the penalized estimator is efficient when the level of noise sigma tends to zero our construction is an alternative to the one by efroimovich and low for hyperrectangles and provides new results otherwise

weak exactness for c algebras and application to condition ao abstract kirchberg introduced weak exactness for von neumann algebras as an analogue of exactness for c algebras ozawa found useful characterizations of weak exactness and he proved that weak exactness for group von neumann algebras is equivalent to exactness of the groups we generalize this concept to inclusions of c algebras in von neumann algebras and study some fundamental properties and relationship to kirchberg s weak exactness we then give some permanence properties which are similar to those of exact groups in the last section we study a similar condition to ozawa s condition ao with our weak exactness and generalize ozawa s theorem for bi exact groups as a corollary we give new examples of prime factors

maximum likelihood ratio tests for comparing the discriminatory ability of biomarkers subject to limit of detection in this article we consider comparing the areas under correlated receiver operating characteristic roc curves of diagnostic biomarkers whose measurements are subject to a limit of detection lod a source of measurement error from instruments sensitivity in epidemiological studies we propose and examine the likelihood ratio tests with operating characteristics that are easily obtained by classical maximum likelihood methodology

high dimensional analysis of semidefinite relaxations for sparse principal components principal component analysis pca is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix however pca is well known to behave poorly in the large p small n setting in which the problem dimension p is comparable to or larger than the sample size n this paper studies pca in this high dimensional regime but under the additional assumption that the maximal eigenvector is sparse say with at most k nonzero components we consider a spiked covariance model in which a base matrix is perturbed by adding a k sparse maximal eigenvector and we analyze two computationally tractable methods for recovering the support set of this maximal eigenvector as follows a a simple diagonal thresholding method which transitions from success to failure as a function of the rescaled sample size dia n p k n k 2 log p k and b a more sophisticated semidefinite programming sdp relaxation which succeeds once the rescaled sample size sdp n p k n klog p k is larger than a critical threshold in addition we prove that no method including the best method which has exponential time complexity can succeed in recovering the support if the order parameter sdp n p k is below a threshold our results thus highlight an interesting trade off between computational and statistical efficiency in high dimensional inference

approximation dans les espaces metriques et theorie de l estimation we investigate the relations between the speed of estimation and the metric structure of the parameter space especially in the case when its metric dimension is infinite given some distance d on generally hellinger distance in the case of n i i d variables we consider the minimax risk for n observations r n q mathop inf sup limits t n theta in theta text ie theta d q theta t n t n being any estimate of we shall look for functions r such that for positive constants c 1 q and c 2 q c 1 r q n r n q c2 r q n r n is the speed of estimation and we shall show under fairly general conditions including i i d variables and regular cases of markov chains and stationnary gaussian processes that r n is determined up to multiplicative constants by the metric structure of we shall also give a construction for some sort of universal estimates the risk of which is bounded by c 2 r q n in all cases where the preceding theory applies

on the structural theory of ii1 factors of negatively curved groups ii actions by product groups abstract this paper contains a series of structural results for von neumann algebras arising from measure preserving actions by product groups on probability spaces expanding upon the methods used earlier by the first two authors we obtain new examples of strongly solid factors as well as von neumann algebras with unique or no cartan subalgebra for instance we show that every ii 1 factor associated with a weakly amenable group in the class s of ozawa is strongly solid there is also the following product version of this result any maximal abelian subalgebra of any ii 1 factor associated with a finite product of weakly amenable groups in the class s of ozawa has an amenable normalizing algebra finally pairing some of these results with a cocycle superrigidity result of ioana it follows that compact actions by finite products of lattices in s p n 1 n 2 are virtually w superrigid

estimation of integral functionals of a density let be a smooth function of k 2 variables we shall investigate in this paper the rates of convergence of estimators of t f f f x f x f k x x dx when f belongs to some class of densities of smoothness s we prove that when 2k 1 4 one can define an estimator t n of t f based on n i i d observations of density f on the real line which converges at the semiparametric rate 1 n on the other hand when s 2k 1 4 t f cannot be estimated at a rate faster than n with 4 s k 4s 1 we shall also provide some extensions to the multidimensional case those results extend previous works of levit of bickel and ritov and of donoho and nussbaum on estimation of quadratic functionals

the asymptotic equivalence of some modified shapiro wilk statistics complete and censored sample cases on etablit l equivalence asymptotique d une classe de statistiques basees sur des choix differents de scores normaux

optimal adaptive estimation of a quadratic functional minimax mean squared error estimates of quadratic functionals of smooth functions have been constructed for a variety of smoothness classes in contrast to many nonparametric function estimation problems there are both regular and irregular cases in the regular cases the minimax mean squared error converges at a rate proportional to the inverse of the sample size whereas in the irregular case much slower rates are the rule we investigate the problem of adaptive estimation of a quadratic functional of a smooth function when the degree of smoothness of the underlying function is not known it is shown that estimators cannot achieve the minimax rates of convergence simultaneously over two parameter spaces when at least one of these spaces corresponds to the irregular case a lower bound for the mean squared error is given which shows that any adaptive estimator which is rate optimal for the regular case must lose a logarithmic factor in the irregular case on the other hand we give a rather simple adaptive estimator which is sharp for the regular case and attains this lower bound in the irregular case moreover we explicitly describe a subset of functions where our adaptive estimator loses the logarithmic factor and show that this subset is relatively small

equivalence of normal states on von neumann algebras and the flow of weights abstract let m be a von neumann algebra two positive normal functionals on m are called equivalent if is in the norm closure of the orbit of under the action of inner automorphisms our main result is an isometric characterization of the quotient space m we construct a natural isometry a g4 of m into the set of positive normal functionals on the smooth flow of weights of m where the smooth flow of weights is realized as the center z n of the crossed product n m r for some faithful normal semifinite weight on m as an application we obtain that an automorphism on a factor m with separable predual acts trivially on m if and only if acts trivially on the smooth flow of weights i e the connes takesaki modulus mod of vanishes we also obtain a new proof of the diameter formula diam s n m 2 1 1 for the quotient of the state space of a factor of type iii 0 1

tests of goodness of fit based on the l_2 wasserstein distance we consider the wasserstein distance between a sample distribution and the set of normal distributions as a measure of nonnormality by considering the standardized version of this distance we obtain a version of shapiro wilk s test of normality the asymptotic behavior of the statistic is studied using approximations of the quantile process by brownian bridges this method differs from the ad hoc method of de wet and venter and permits a similar analysis for testing other location scale families

tables and large sample distribution theory for censored data correlation statistics for testing normality abstract plotting order statistics versus some variant of the normal scores is a standard graphical technique for assessing the assumption of normality to obtain an objective evaluation of the normal assumption it is customary to calculate the correlation coefficient associated with this plot the shapiro francia statistic is the square of the correlation between the observed order statistics and the expected values of standard normal order statistics whereas the shapiro wilk statistic also involves the covariances of the standard normal order statistics in a wide variety of applications an investigation of the plausibility of the normal or lognormal model is needed when the observations on strength or life length are right censored the plotting procedure still applies if the observations are censored at a fixed order statistic or a fixed time here the corresponding distribution theory for some modified versions of the shapiro wilk correlation statistic is investigated because the asymptotic th

weak exactness for dual operator spaces we introduce a new tensor product circle times sigma lambda and study the weak condition c which is also called weak exactness for dual operator spaces our definition of weak condition c is equivalent to kirchberg s notion of weak exactness in the case of von neumann algebras we also study the connection of weak exact w tros with their linking von neumann algebras and study the structure of exact respectively nuclear w tros c 2007 elsevier inc all rights reserved

approximation properties and absence of cartan subalgebra for free araki woods factors abstract we show that all the free araki woods factors h r u t have the complete metric approximation property using ozawa popa s techniques we then prove that every nonamenable subfactor n h r u t which is the range of a normal conditional expectation has no cartan subalgebra we finally deduce that the type iii1 factors constructed by connes in the 70s can never be isomorphic to any free araki woods factor which answers a question of shlyakhtenko and vaes

normal scores normal plots tests for normality abstract in this article we develop new plotting positions for normal plots the use of the plots usually centers on detecting irregular tail behavior or outliers along with the normal plot we develop tests for various departures from normality especially for skewness and heavy tails the tests can be considered as components of a shapiro wilk type test that has been decomposed into different sources of nonnormality convergence to the limiting distributions is slow so finite sample corrections are included to make the tests useful for small sample sizes

sparser johnson lindenstrauss transforms we give two different and simple constructions for dimensionality reduction in e2 via linear mappings that are sparse only an o e fraction of entries in each column of our embedding matrices are non zero to achieve distortion 1 e with high probability while still achieving the asymptotically optimal number of rows these are the first constructions to provide subconstant sparsity for all values of parameters improving upon previous works of achlioptas 2003 and dasgupta et al 2010 such distributions can be used to speed up applications where e2 dimensionality reduction is used

the fast johnson lindenstrauss transform and approximate nearest neighbors we introduce a new low distortion embedding of ell 2 d into ell p o log n p 1 2 called the fast johnson lindenstrauss transform fjlt the fjlt is faster than standard random projections and just as easy to implement it is based upon the preconditioning of a sparse projection matrix with a randomized fourier transform sparse random projections are unsuitable for low distortion embeddings we overcome this handicap by exploiting the heisenberg principle of the fourier transform i e its local global duality the fjlt can be used to speed up search algorithms based on low distortion embeddings in ell 1 and ell 2 we consider the case of approximate nearest neighbors in ell 2 d we provide a faster algorithm using classical projections which we then speed up further by plugging in the fjlt we also give a faster algorithm for searching over the hypercube

minimax estimation via wavelet shrinkage we attempt to recover an unknown function from noisy sampled data using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients the shrinkage can be tuned to be nearly minimax over any member of a wide range of triebel and besov type smoothness constraints and asymptotically minimax over besov bodies with p q linear estimates cannot achieve even the minimax rates over triebel and besov classes with p 2 so the method can significantly outperform every linear method e g kernel smoothing spline sieve in a minimax sense variants of our method based on simple threshold nonlinear estimators are nearly minimax our method possesses the interpretation of spatial adaptivity it reconstructs using a kernel which may vary in shape and bandwidth from point to point depending on the data least favorable distributions for certain of the triebel and besov scales generate objects with sparse wavelet transforms many real objects have similarly sparse transforms which suggests that these minimax results are relevant for practical problems sequels to this paper which was first drafted in november 1990 discuss practical implementation spatial adaptation properties universal near minimaxity and applications to inverse problems

measure equivalence rigidity and bi exactness of groups we get three types of results on measurable group theory direct product groups of ozawa s class s groups wreath product groups and amalgamated free products we prove measure equivalence factorization results on direct product groups of ozawa s class s groups as consequences monod shalom type orbit equivalence rigidity theorems follow we prove that if two wreath product groups a g b of non amenable exact direct product groups g with amenable bases a b are measure equivalent then g and are measure equivalent we get bass serre rigidity results on amalgamated free products of non amenable exact direct product groups

recognition of stable distribution with levy index α close to 2 we address the problem of recognizing stable levy distribution with levy index close to 2 from experimental data we are interested in the case when the sample size of available data is not large thus the power law asymptotics of the distribution is not clearly detectable and the shape of the empirical probability density function is close to a gaussian we propose a testing procedure combining a simple visual test based on empirical fourth moment with the anderson darling and jarque bera statistical tests and we check the efficiency of the method on simulated data furthermore we apply our method to the analysis of turbulent plasma density and potential fluctuations measured in the stellarator type fusion device and demonstrate that the phenomenon of the l h transition from low confinement l mode to a high confinement h mode which occurs in this device is accompanied by the transition from levy to gaussian fluctuation statistics

on the superrigidity of malleable actions with spectral gap some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces v rx x are revealed by the study of group measure space von neumann algebras l x x t mvnl and the classification of actions up to orbit equivalence oe i e up to isomorphism of probability spaces carrying the orbits of actions onto each other although one is in von neumann algebras and the other in ergodic theory the two problems are closely related as an oe of actions v rx x a rxy has been shown to implement an algebra isomorphism l x x t l y x a taking l x onto l y and vice versa si dy fm in particular the isomorphism class of l x xi t only depends on the equivalence relation 7 r t gt 1t x g t thus von neumann equivalence vne of group actions requiring isomorphism of their group measure space algebras is weaker than oe since there are exam ples of non oe actions whose associated von neumann algebras are all isomorphic cj1 it is in general strictly weaker on the other hand oe is manifestly weaker than classical conjugacy which for free actions r rx x a rx y requires isomor phism of probability spaces a x p y v satisfying ar a 1 a so in particular r a how much weaker vne and oe can be with respect to conju gacy is best seen in the amenable case where by a celebrated theorem of connes all free ergodic actions of all infinite amenable groups give rise to the same hi factor cl and by dy ow cfw they are undistinguishable under oe as well also any embedding of algebras l x xi t c l y x a with a amenable forces t to be amenable but the non amenable case is extremely complex and for many years progress has been slow mvn2 dy me c2 cw sc even after the discovery of the first rigidity phenomena by connes in von neumann algebras c3 c4 and by zimmer in oe ergodic theory zi z2 this changed dramatically over the last 7 8 years with the advent of a variety of striking rigidity results ful gl g2 mosh h hk p1 p8 see p9 for a survey also sh for a survey on oe rigidity our aim in this paper is to investigate the most extreme such phenomena called strong rigidity which show that for certain classes of source group actions

optimal estimation of genetic relatedness in high dimensional linear models estimating the genetic relatedness between two traits based on the genome wide association data is an important problem in genetics research in the framework of high dimensional linear models we

a variant of the johnson lindenstrauss lemma for circulant matrices we continue our study of the johnson lindenstrauss lemma and its connection to circulant matrices started in hinrichs and vybiral in press 7 we reduce the bound on k from k e 2log3n proven there to k e 2log2n our technique differs essentially from the one used in hinrichs and vybiral in press 7 we employ the discrete fourier transform and singular value decomposition to deal with the dependency caused by the circulant structure

modeling activity times by the parkinson distribution with a lognormal core theory and validation abstract based on theoretical arguments and empirical evidence we advocate the use of the lognormal distribution as a model for activity times however raw data on activity times are often subject to rounding and to the parkinson effect we address those factors in our statistical tests by using a generalized version of the parkinson distribution with random censoring of earliness ultimately validating our model with field data from several sources we also confirm that project activities exhibit stochastic dependence that can be modeled by linear association

model selection for regression on a fixed design we deal with the problem of estimating some unknown regression function involved in a regression framework with deterministic design points for this end we consider some collection of finite dimensional linear spaces models and the least squares estimator built on a data driven selected model among this collection this data driven choice is performed via the minimization of some penalized model selection criterion that generalizes on mallows c p we provide non asymptotic risk bounds for the so defined estimator from which we deduce adaptivity properties our results hold under mild moment conditions on the errors the statement and the use of a new moment inequality for empirical processes is at the heart of the techniques involved in our approach

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem