perron frobenius theorem for matrices with some negative entries abstract we extend the classical perron frobenius theorem to matrices with some negative entries we study the cone of matrices that has the matrix of 1 s ee t as the central ray and such that any matrix inside the cone possesses a perron frobenius eigenpair we also find the maximum angle of any matrix with ee t that guarantees this property

ray solvable linear systems and ray s2ns matrices abstract ray solvable linear systems and ray s 2 ns matrices are complex generalizations of the sign solvable linear systems and s 2 ns matrices we use the determinantal ray unique matrices instead of ray nonsingular matrices as a generalization of sns matrices to generalize some fundamental results of s 2 ns matrices from the real case to complex case such as the graph theoretical characterization the inverse ray patterns and the upper bound of the number of nonzero entries of s 2 ns matrices the well known characterization of the sign solvable linear systems in terms of the l matrices and s matrices is also generalized to ray solvable linear systems and the relationships between the ray s matrices and real s matrices are investigated some examples are also given to illustrate that some results such as the characterization of the sign inconsistent linear systems do not carry over to the complex case

on estimating a density using hellinger distance and some other strange facts on s interesse ici aux possibles vitesses d estimation d une densite a support compact dans m sous des hypotheses de regularite lorsque la perte est mesuree par le carre de la distance de hellinger on regardera aussi le cas connu des normes mathbb l q pour 1 q 2 et le risque est le risque minimax sur la famille on donne une methode generale permettant de traiter les problemes dans le cadre de la theorie de l approximation sous des conditions concernant l entropie metrique et l e capacite des familles a estimer les rapports entre regularite et entropie metrique etant bien connus nous pourrons aussi traiter les cas classiques et d autres qui le sont moins sous des conditions de bornes inferieures les vitesses sont celles observees pour la norme mathbb l q mais elles different dans le cas general on montre aussi que les restrictions sur la compacite du support ou la regularite sont indispensables et que leur absence mene a l impossibilite d obtenir une estimation raisonnable en ce sens que n importe quelle suite d estimateurs sera arbitrairement mauvaise en un point au moins un resultat analogue est vrai sous des conditions de regularite

information theoretic lower bounds on the oracle complexity of stochastic convex optimization relative to the large literature on upper bounds on complexity of convex optimization lesser attention has been paid to the fundamental hardn4516420ess of these problems given the extensive use of convex optimization in machine learning and statistics gaining an understanding of these complexity theoretic issues is important in this paper we study the complexity of stochastic convex optimization in an oracle model of computation we introduce a new notion of discrepancy between functions and use it to reduce problems of stochastic convex optimization to statistical parameter estimation which can be lower bounded using information theoretic methods using this approach we improve upon known results and obtain tight minimax complexity estimates for various function classes

learning by mirror averaging given a collection of m different estimators or classifiers we study the problem of model selection type aggregation i e we construct a new estimator or classifier called aggregate which is nearly as good as the best among them with respect to a given risk criterion we define our aggregate by a simple recursive procedure which solves an auxiliary stochastic linear programming problem related to the original non linear one and constitutes a special case of the mirror averaging algorithm we show that the aggregate satisfies sharp oracle inequalities under some general assumptions the results allow one to construct in an easy way sharp adaptive nonparametric estimators for several problems including regression classification and density estimation

density estimation by wavelet thresholding density estimation is a commonly used test case for nonparametric estimation methods we explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients minimax rates of convergence are studied over a large range of besov function classes b pq and for a range of global l p error measures 1 p p some form of nonlinearity is essential since the minimax linear estimators are suboptimal by polynomial powers of n a second approach using an approximation of a gaussian white noise model in a mallows metric is used to attain exactly optimal rates of convergence for quadratic error p 2

on adaptive minimax density estimation on r d we address the problem of adaptive minimax density estimation on mathbb r d with mathbb l p loss on the anisotropic nikol skii classes we fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk in particular we show that there are four different regimes with respect to the behavior of the minimax risk we develop a single estimator which is nearly optimal in order over the complete scale of the anisotropic nikol skii classes our estimation procedure is based on a data driven selection of an estimator from a fixed family of kernel estimators

a personalized auxiliary material recommendation system based on learning style on facebook applying an artificial bee colony algorithm facebook is currently the most popular social networking site in the world providing an interactive platform that enables users to contact friends and other social groups as well as post a large number of photos videos and links recently many studies have investigated the effects of using facebook on various aspects of education and it has been used as a learning platform for sharing auxiliary materials however not all of the auxiliary materials posted may conform to the individual learning styles and abilities of each user this study thus proposes a personalized auxiliary material recommendation system based on the degree of difficulty of the auxiliary materials individual learning styles and the specific course topics an artificial bee colony algorithm is implemented to optimize the system the results indicate that this method is superior to other schemes and improves the execution time and accuracy of the recommendation system in an efficient manner

adaptive estimation of and oracle inequalities for probability densities and characteristic functions the theory of adaptive estimation and oracle inequalities for the case of gaussian shift finite interval experiments has made significant progress in recent years in particular sharp minimax adaptive estimators and exact exponential type oracle inequalities have been suggested for a vast set of functions including analytic and sobolev with any positive index as well as for efromovich pinsker and stein blockwise shrinkage estimators is it possible to obtain similar results for a more interesting applied problem of density estimation and or the dual problem of characteristic function estimation the answer is yes in particular the obtained results include exact exponential type oracle inequalities which allow to consider for the first time in the literature a simultaneous sharp minimax estimation of sobolev densities with any positive index not necessarily larger than 1 2 infinitely differentiable densities including analytic entire and stable as well as of not absolutely integrable characteristic functions the same adaptive estimator is also rate minimax over a familiar class of distributions with bounded spectrum where the density and the characteristic function can be estimated with the parametric rate

a novel parallel hybrid intelligence optimization algorithm for a function approximation problem a novel parallel hybrid intelligence optimization algorithm phioa is proposed based on combining the merits of particle swarm optimization with genetic algorithms the phioa uses the ideas of selection crossover and mutation from genetic algorithms gas and the update velocity and situation of particle swarm optimization pso under the independence of pso and gas the proposed algorithm divides the individuals into two equation groups according to their fitness values the subgroup of the top fitness values is evolved by gas and the other subgroup is evolved by the pso algorithm the optimal number is selected as a global optimum at every circulation which shows better results than both pso and gas then improves the overall performance of the algorithm the phioa is used to optimize the structure and parameters of the fuzzy neural network finally the experimental results have demonstrated the superiority of the proposed phioa to search the global optimal solution the phioa can improve the error accuracy while speeding up the convergence process and effectively avoid the premature convergence to compare with the existing methods

asymptotic equivalence of density estimation and gaussian white noise signal recovery in gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation having all the essential traits in a pure form the equivalence has mostly been stated informally but an approximation in the sense of le cam s deficiency distance would make it precise the models are then asymptotically equivalent for all purposes of statistical decision with bounded loss in nonparametrics a first result of this kind has recently been established for gaussian regression we consider the analogous problem for the experiment given by n i i d observations having density f on the unit interval our basic result concerns the parameter space of densities which are in a holder ball with exponent 1 2 and which are uniformly bounded away from zero we show that an i i d sample of size n with density f is globally asymptotically equivalent to a white noise experiment with drift f l 2 and variance 1 4n l this represents a nonparametric analog of le cam s heteroscedastic gaussian approximation in the finite dimensional case the proof utilizes empirical process techniques related to the hungarian construction white noise models on f and log f are also considered allowing for various automatic asymptotic risk bounds in the i i d model from white noise

some inequalities for information divergence and related measures of discrimination inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics ergodic theory and other scientific fields we suggest new inequalities of this type often based on underlying identities as a consequence we obtain certain improvements of the well known pinsker inequality our study depends on two measures of discrimination called capacitory discrimination and triangular discrimination the discussion contains references to related research and comparison with other measures of discrimination e g ali silvey csiszar 1996 1966 divergences and in particular the hellinger distance

rates of convergence for minimum contrast estimators we shall present here a general study of minimum contrast estimators in a nonparametric setting although our results are also valid in the classical parametric case for independent observations these estimators include many of the most popular estimators in various situations such as maximum likelihood estimators least squares and other estimators of the regression function estimators for mixture models or deconvolution the main theorem relates the rate of convergence of those estimators to the entropy structure of the space of parameters optimal rates depending on entropy conditions are already known at least for some of the models involved and they agree with what we get for minimum contrast estimators as long as the entropy counts are not too large but under some circumstances large entropies or changes in the entropy structure due to local perturbations the resulting the rates are only suboptimal counterexamples are constructed which show that the phenomenon is real for non parametric maximum likelihood or regression this proves that under purely metric assumptions our theorem is optimal and that minimum contrast estimators happen to be suboptimal

a new lower bound for multiple hypothesis testing the purpose of this correspondence is to give a new easily tractable and sharp lower bound for the maximal error in multiple hypothesis testing with an application to nonasymptotic lower bounds for the minimax risk of estimators

pso sfdd defense against syn flooding dos attacks by employing pso algorithm a dos attack can be regarded as an attempt of attackers to prevent legal users from gaining a normal network service the tcp connection management protocol sets a position for a classic dos attack namely the syn flood attack in this attack some sources send a large number of tcp syn segments without completing the third handshake step to quickly exhaust connection resources of the under attack system this paper models the under attack server by using the queuing theory in which attack requests are recognized based on their long service time then it proposes a framework in which the defense issue is formulated as an optimization problem and employs the particle swarm optimization pso algorithm to optimally solve this problem pso tries to direct the server to an optimum defense point by dynamically setting two tcp parameters namely maximum number of connections and maximum duration of a half open connection the simulation results show that the proposed defense strategy improves the performance of the under attack system in terms of rejection probability of connection requests and efficient consumption of buffer space

data compression and histograms in this paper the relationship between code length and the selection of the number of bins for a histogram density is considered for a sequence of iid observations on 0 1 first we use a shortest code length criterion to select the number of bins for a histogram a uniform almost sure asymptotic expansion for the code length is given and it is used to prove the asymptotic optimality of the selection rule in addition the selection rule is consistent if the true density is uniform 0 1 secondly we deal with the problem what is the best achievable average code length with underlying density functionf minimax lower bounds are derived for the average code length over certain smooth classes of underlying densitiesf for the smooth class with bounded first derivatives the rate in the lower bound is shown to be achieved by a code based on a sequence of histograms whose number of bins is changed predictively moreover this best code can be modified to ensure that the almost sure version of the code length has asymptotically the same behavior as its expected value i e the average code length

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

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

adaptive minimax regression estimation over sparse l q hulls given a dictionary of mn predictors in a random design regression setting with n observations we construct estimators that target the best performance among all the linear combinations of the predictors under a sparse lq norm 0 q 1 constraint on the linear coefficients besides identifying the optimal rates of convergence our universal aggregation strategies by model mixing achieve the optimal rates simultaneously over the full range of 0 q 1 for any mn and without knowledge of the lq norm of the best linear coefficients to represent the regression function to allow model misspecification our upper bound results are obtained in a framework of aggregation of estimates a striking feature is that no specific relationship among the predictors is needed to achieve the upper rates of convergence hence permitting basically arbitrary correlations between the predictors therefore whatever the true regression function assumed to be uniformly bounded our estimators automatically exploit any sparse representation of the regression function if any to the best extent possible within the lq constrained linear combinations for any 0 q 1 a sparse approximation result in the lq hulls turns out to be crucial to adaptively achieve minimax rate optimal aggregation it precisely characterizes the number of terms needed to achieve a prescribed accuracy of approximation to the best linear combination in an lq hull for 0 q 1 it offers the insight that the minimax rate of lq aggregation is basically determined by an effective model size which is a sparsity index that depends on q mn n and the lq norm bound in an easily interpretable way based on a classical model selection theory that deals with a large number of models

sparse pca optimal rates and adaptive estimation principal component analysis pca is one of the most commonly used statistical procedures with a wide range of applications this paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting under mild technical conditions we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters thus providing a complete characterization of the difficulty of the estimation problem in term of the convergence rate the lower bound is obtained by calculating the local metric entropy and an application of fano s lemma the rate optimal estimator is constructed using aggregation which however might not be computationally feasible we then introduce an adaptive procedure for estimating the principal subspace which is fully data driven and can be computed efficiently it is shown that the estimator attains the optimal rates of convergence simultaneously over a large collection of the parameter spaces a key idea in our construction is a reduction scheme which reduces the sparse pca problem to a high dimensional multivariate regression problem this method is potentially also useful for other related problems

rates of contraction for posterior distributions in lr metrics 1 r the frequentist behavior of nonparametric bayes estimates more specifically rates of contraction of the posterior distributions to shrinking lr norm neighborhoods 1 r of the unknown parameter are studied a theorem for nonparametric density estimation is proved under general approximation theoretic assumptions on the prior the result is applied to a variety of common examples including gaussian process wavelet series normal mixture and histogram priors the rates of contraction are minimax optimal for 1 r 2 but deteriorate as r increases beyond 2 in the case of gaussian nonparametric regression a gaussian prior is devised for which the posterior contracts at the optimal rate in all lr norms 1 r

minimax nonparametric classification i rates of convergence this paper studies minimax aspects of nonparametric classification we first study minimax estimation of the conditional probability of a class label given the feature variable this function say f is assumed to be in a general nonparametric class we show the minimax rate of convergence under square l sub 2 loss is determined by the massiveness of the class as measured by metric entropy the second part of the paper studies minimax classification the loss of interest is the difference between the probability of misclassification of a classifier and that of the bayes decision as is well known an upper bound on risk for estimating f gives an upper bound on the risk for classification but the rate is known to be suboptimal for the class of monotone functions this suggests that one does not have to estimate f well in order to classify well however we show that the two problems are in fact of the same difficulty in terms of rates of convergence under a sufficient condition which is satisfied by many function classes including besov sobolev lipschitz and bounded variation this is somewhat surprising in view of a result of devroye gorfi and lugosi see a probabilistic theory of pattern recognition new york springer verlag 1996

lower bounds for the minimax risk using f divergences and applications lower bounds involving f divergences between the underlying probability measures are proved for the minimax risk in estimation problems our proofs just use simple convexity facts special cases and straightforward corollaries of our bounds include well known inequalities for establishing minimax lower bounds such as fano s inequality pinsker s inequality and inequalities based on global entropy conditions two applications are provided a new minimax lower bound for the reconstruction of convex bodies from noisy support function measurements and a different proof of a recent minimax lower bound for the estimation of a covariance matrix

particle swarm algorithm for solving systems of nonlinear equations solving systems of nonlinear equations is one of the most difficult problems in all of numerical computation and in a diverse range of engineering applications newton s method for solving systems of nonlinear equations can be highly sensitive to the initial guess of the solution in this study a new particle swarm optimization algorithm is proposed to solve systems of nonlinear equations some standard systems are presented to demonstrate the efficiency of this method

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

ray pattern matrices requiring perron frobenius properties abstract a ray pattern matrix is a matrix whose nonzero entries are all unimodular an n n ray pattern matrix a is said to require the weak perron frobenius property if for any n n entrywise positive matrix k the spectral radius k a is one of the eigenvalues of k a to require the strong perron frobenius property if k a is an algebraically simple eigenvalue of k a and the left and right eigenvectors associated to k a are strictly nonzero in this paper necessary and sufficient conditions for ray pattern matrices requiring the weak strong perron frobenius property are given

rates of convergence of minimum distance estimators and kolmogorov s entropy on construit des estimateurs robustes et on montre que le taux de convergence resultant depend naturellement d une fonction entropie

estimation of a regression function by maxima of minima of linear functions in this paper estimation of a regression function from independent and identically distributed random variables is considered estimates are defined by minimization of the empirical l2 risk over a class of functions which are defined as maxima of minima of linear functions results concerning the rate of convergence of the estimates are derived in particular it is shown that for smooth regression functions satisfying the assumption of single index models the estimate is able to achieve up to some logarithmic factor the corresponding optimal one dimensional rate of convergence hence under these assumptions the estimate is able to circumvent the so called curse of dimensionality the small sample behavior of the estimates is illustrated by applying them to simulated data

mixing strategies for density estimation general results on adaptive density estimation are obtained with respect to any countable collection of estimation strategies under kullback leibler and squared l 2 losses it is shown that without knowing which strategy works best for the underlying density a single strategy can be constructed by mixing the proposed ones to be adaptive in terms of statistical risks a consequence is that under some mild conditions an asymptotically minimax rate adaptive estimator exists for a given countable collection of density classes that is a single estimator can be constructed to be simultaneously minimax rate optimal for all the function classes being considered a demonstration is given for high dimensional density estimation on 0 1 d where the constructed estimator adapts to smoothness and interaction order over some piecewise besov classes and is consistent for all the densities with finite entropy

probability inequalities for likelihood ratios and convergence rates of sieve mles let y 1 y n be independent identically distributed with density p 0 and let f be a space of densities we show that the supremum of the likelihood ratios i 1 n p y i p 0 y i where the supremum is over p f with p l 2 p 0 1 2 2 e is exponentially small with probability exponentially close to 1 the exponent is proportional to ne 2 the only condition required for this to hold is that e exceeds a value determined by the bracketing hellinger entropy of f a similar inequality also holds if we replace f by f n and p 0 by q n where q n is an approximation to p 0 in a suitable sense these results are applied to establish rates of convergence of sieve mles furthermore weak conditions are given under which the optimal rate e n defined by h e n f ne n 2 where h f is the hellinger entropy of f is nearly achievable by sieve estimators

on maximum likelihood estimation in infinite dimensional parameter spaces an approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions in this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter we provide conditions under which the rate of convergence can be established this rate is essentially governed by the size of the space of score functions as measured by an entropy index we also show that for a large class of smooth functionals the plug in maximum likelihood estimate is asymptotically efficient that is it achieves the minimal fisher information bound the theory is illustrated by several nonparametric or semiparametric examples

cryptanalysis of the cho et al protocol a hash based rfid tag mutual authentication protocol radio frequency identification systems need secure protocols to provide confidentiality privacy protection mutual authentication etc these protocols should resist active and passive attacks such as forgery traceability replay and de synchronization attacks cho et al recently proposed a hash based mutual authentication protocol cho et al 2012 and claimed that their scheme addresses all privacy juels 2006 and forgery concerns dimitriou 2005 yang et al 2005 linked to rfid technology however we show in the following that the protocol fails to bear out many of the authors security claims which renders the protocol useless more precisely we present the following attacks on this protocol 1 de synchronization attack the success probability of the attack is 1 while the attack complexity is one run of the protocol 2 tag impersonation attack the success probability of the attack is 14 for two runs of the protocol 3 reader impersonation attack the success probability of the attack is 18 for two runs of the protocol we also show an additional and more general attack which is still possible when the conditions needed for the ones above do not hold and that highlights the poor design of the group id rid i t additionally we show how all the above mentioned attacks are applicable against another protocol highly reminiscent of that of cho et al 2012 and designed in cho et al 2011 and also against an enhanced version of the cho et al protocol proposed by kim 2012 finally we end up by showing how slight modifications in the original protocol can prevent the aforementioned security faults

covering numbers for bounded variation functions abstract in this paper we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to l 1 distance

on perron frobenius property of matrices having some negative entries we extend the theory of nonnegative matrices to the matrices that have some negative entries we present and prove some properties which give us information when a matrix possesses a perron frobenius eigenpair we apply also this theory by proposing the perron frobenius splitting for the solution of the linear system ax b by classical iterative methods perron frobenius splittings constitute an extension of the well known regular splittings weak regular splittings and nonnegative splittings convergence and comparison properties are given and proved

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

metalearners for estimating heterogeneous treatment effects using machine learning there is growing interest in estimating and analyzing heterogeneous treatment effects in experimental and observational studies we describe a number of metaalgorithms that can take advantage of any supervised learning or regression method in machine learning and statistics to estimate the conditional average treatment effect cate function metaalgorithms build on base algorithms such as random forests rfs bayesian additive regression trees barts or neural networks to estimate the cate a function that the base algorithms are not designed to estimate directly we introduce a metaalgorithm the x learner that is provably efficient when the number of units in one treatment group is much larger than in the other and can exploit structural properties of the cate function for example if the cate function is linear and the response functions in treatment and control are lipschitz continuous the x learner can still achieve the parametric rate under regularity conditions we then introduce versions of the x learner that use rf and bart as base learners in extensive simulation studies the x learner performs favorably although none of the metalearners is uniformly the best in two persuasion field experiments from political science we demonstrate how our x learner can be used to target treatment regimes and to shed light on underlying mechanisms a software package is provided that implements our methods

the minimum description length principle in coding and modeling we review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling stochastic complexity is formulated as the solution to optimum universal coding problems extending shannon s basic source coding theorem the normalized maximized likelihood mixture and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms we assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference context tree modeling density estimation and model selection in gaussian linear regression serve as examples

multivariate two sample tests based on nearest neighbors abstract a new class of simple tests is proposed for the general multivariate two sample problem based on the possibly weighted proportion of all k nearest neighbor comparisons in which observations and their neighbors belong to the same sample large values of the test statistics give evidence against the hypothesis h of equality of the two underlying distributions asymptotic null distributions are explicitly determined and shown to involve certain nearest neighbor interaction probabilities simple infinite dimensional approximations are supplied the unweighted version yields a distribution free test that is consistent against all alternatives optimally weighted statistics are also obtained and asymptotic efficiencies are calculated each of the tests considered is easily adapted to a permutation procedure that conditions on the pooled sample power performance for finite sample sizes is assessed in simulations

short term scheduling of cascade reservoirs using an immune algorithm based particle swarm optimization this paper presents a new approach for short term hydropower scheduling of reservoirs using an immune algorithm based particle swarm optimization ia pso ia pso is employed by coupling the immune information processing mechanism with the particle swarm optimization algorithm in order to achieve a better global solution with less computational effort with the ia pso technique the hydro electrical optimization model of reservoirs is formulated as a high dimensional dynamic nonlinear and stochastic global optimization problem of a multi reservoir hydropower system the purpose of the proposed methodology is to maximize total hydropower production here it is applied to a reservoir system on the qingjiang river in the yangtze watershed that consists of two reservoirs the results are compared with the results obtained through conventional operation method the dynamic programming and the standard pso algorithm from the comparative results it is found that the ia pso approach provides the most globally optimum solution at a faster convergence speed

an asymptotic property of model selection criteria probability models are estimated by use of penalized log likelihood criteria related to akaike 1973 information criterion aic and minimum description length mdl the accuracies of the density estimators are shown to be related to the tradeoff between three terms the accuracy of approximation the model dimension and the descriptive complexity of the model classes the asymptotic risk is determined under conditions on the penalty term and is shown to be minimax optimal for some cases as an application we show that the optimal rate of convergence is simultaneously achieved for log densities in sobolev spaces w sub 2 sup s u without knowing the smoothness parameter s and norm parameter u in advance applications to neural network models and sparse density function estimation are also provided

covering numbers for convex functions in this paper we study the covering numbers of the space of convex and uniformly bounded functions in multidimension we find optimal upper and lower bounds for the epsilon covering number of cal c a b d b in the l p metric 1 leq p in terms of the relevant constants where d geq 1 a b 0 and cal c a b d b denotes the set of all convex functions on a b d that are uniformly bounded by b we summarize previously known results on covering numbers for convex functions and also provide alternate proofs of some known results our results have direct implications in the study of rates of convergence of empirical minimization procedures as well as optimal convergence rates in the numerous convexity constrained function estimation problems

shadow detecting using particle swarm optimization and the kolmogorov test an algorithm combining both gray level information and geometric features is introduced to detect cast shadows in gray level images a simply connected candidate shadow region and a corresponding region are segmented by setting gray level thresholds and neighbor matching regions are constructed with a mathematical morphological algorithm a shadow non shadow region pair is obtained from the result of kolmogorov test for statistical features of both candidate neighbor matching regions shadow regions are obtained by selecting the region with relatively lower average gray level from the matched region pair the particle swarm optimization pso algorithm is used to facilitate the feature extraction during the matching process experimental results showed the effectiveness of the proposed algorithm for cast shadow detecting in a single gray level image

lower bounds in pattern recognition and learning lower bounds are derived for the performance of any pattern recognition algorithm which using training data selects a discrimination rule from a certain class of rules the bounds involve the vapnik chervonenkis dimension of the class and l the minimal error probability within the class we provide lower bounds when l 0 the usual assumption in valiant s theory of learning and l 0

resampling consistency of substitution estimators on the basis of n i i d random variables with a common unknown distribution p we wish to estimate a functional n p an obvious and very general approach to this problem is to find an estimator p n of p first and then construct a so called substitution estimator n p n of n p in this paper we investigate how to choose the estimator p n so that the substitution estimator n p n will be consistent

minimax estimation in sparse canonical correlation analysis canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables this paper considers the problem of estimating the leading canonical correlation directions in high dimensional settings recently under the assumption that the leading canonical correlation directions are sparse various procedures have been proposed for many high dimensional applications involving massive data sets however there has been few theoretical justification available in the literature in this paper we establish rate optimal nonasymptotic minimax estimation with respect to an appropriate loss function for a wide range of model spaces two interesting phenomena are observed first the minimax rates are not affected by the presence of nuisance parameters namely the covariance matrices of the two sets of random variables though they need to be estimated in the canonical correlation analysis problem second we allow the presence of the residual canonical correlation directions however they do not influence the minimax rates under a mild condition on eigengap a generalized sin theta theorem and an empirical process bound for gaussian quadratic forms under rank constraint are used to establish the minimax upper bounds which may be of independent interest

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

convergence rates of posterior distributions for non i i d observations we consider the asymptotic behavior of posterior distributions and bayes estimators based on observations which are required to be neither independent nor identically distributed we give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion we then specialize our results to independent nonidentically distributed observations markov processes stationary gaussian time series and the white noise model we apply our general results to several examples of infinite dimensional statistical models including nonparametric regression with normal errors binary regression poisson regression an interval censoring model whittle estimation of the spectral density of a time series and a nonlinear autoregressive model

data fusion of multi sensor for iot precise measurement based on improved pso algorithms this work proposes an improved particle swarm optimization pso method to increase the measurement precision of multi sensors data fusion in the internet of things iot system critical iot technologies consist of a wireless sensor network rfid various sensors and an embedded system for multi sensor data fusion computing systems data aggregation is a main concern and can be formulated as a multiple dimensional based on particle swarm optimization approaches the proposed improved pso method can locate the minimizing solution to the objective cost function in multiple dimensional assignment themes which are considered in particle swarm initiation cross rules and mutation rules the optimum seclusion can be searched for efficiently with respect to reducing the search range through validated candidate measures experimental results demonstrate that the proposed improved pso method for multi sensor data fusion is highly feasible for iot system applications

model selection for density estimation with mathbb l _2 loss we consider here estimation of an unknown probability density s belonging to mathbb l 2 mu where mu is a probability measure we have at hand n i i d observations with density s and use the squared mathbb l 2 norm as our loss function the purpose of this paper is to provide an abstract but completely general method for estimating s by model selection allowing to handle arbitrary families of finite dimensional possibly non linear models and any s in mathbb l 2 mu we shall in particular consider the cases of unbounded densities and bounded densities with unknown mathbb l infty norm and investigate how the mathbb l infty norm of s may influence the risk we shall also provide applications to adaptive estimation and aggregation of preliminary estimators one major technical tool of our approach is a proof of the existence of suitable tests between mathbb l 2 balls with centers belonging to mathbb l infty although of a purely theoretical nature our method leads to results that cannot presently be reached by more concrete ones

estimating the intensity of a random measure by histogram type estimators the purpose of this paper is to estimate the intensity of some random measure n on a set mathcal x by a piecewise constant function on a finite partition of mathcal x given a possibly large family mathcal m of candidate partitions we build a piecewise constant estimator histogram on each of them and then use the data to select one estimator in the family choosing the square of a hellinger type distance as our loss function we show that each estimator built on a given partition satisfies an analogue of the classical squared bias plus variance risk bound moreover the selection procedure leads to a final estimator satisfying some oracle type inequality with as usual a possible loss corresponding to the complexity of the family mathcal m when this complexity is not too high the selected estimator has a risk bounded up to a universal constant by the smallest risk bound obtained for the estimators in the family for suitable choices of the family of partitions we deduce uniform risk bounds over various classes of intensities our approach applies to the estimation of the intensity of an inhomogenous poisson process among other counting processes or the estimation of the mean of a random vector with nonnegative components