phase transitions for high dimensional clustering and related problems consider a two class clustering problem where we observe x i ell i mu z i z i stackrel mathit i i d sim n 0 i p 1 leq i leq n the feature vector mu in r p is unknown but is presumably sparse the class labels ell i in 1 1 are also unknown and the main interest is to estimate them we are interested in the statistical limits in the two dimensional phase space calibrating the rarity and strengths of useful features we find the precise demarcation for the region of impossibility and region of possibility in the former useful features are too rare weak for successful clustering in the latter useful features are strong enough to allow successful clustering the results are extended to the case of colored noise using le cam s idea on comparison of experiments we also extend the study on statistical limits for clustering to that for signal recovery and that for global testing we compare the statistical limits for three problems and expose some interesting insight we propose classical pca and important features pca if pca for clustering for a threshold t 0 if pca clusters by applying classical pca to all columns of x with an l 2 norm larger than t we also propose two aggregation methods for any parameter in the region of possibility some of these methods yield successful clustering we discover a phase transition for if pca for any threshold t 0 let xi t be the first left singular vector of the post selection data matrix the phase space partitions into two different regions in one region there is a t such that cos xi t ell rightarrow 1 and if pca yields successful clustering in the other cos xi t ell leq c 0 0 our results require delicate analysis especially on post selection random matrix theory and on lower bound arguments

some subclasses of analytic functions involving the generalized noor integral operator abstract in this paper we define the generalized noor integral operator i p n a b c by using convolution by applying this operator we introduce some subclasses k p n a 1 b c a b kk p n a b c a b and s p n a b c a b of analytic functions and study their subordinate relations inclusion relations the integral operator the sufficient conditions for a function to be in the class s p n a b c and the radius problems

gene identification using true discovery rate degree of association sets and estimates corrected for regression to the mean analyses intended to identify genes with expression that is associated with some clinical outcome or state are often based on ranked p values from tests of point null hypotheses of no association van de wiel and kim take the innovative approach of testing the interval null hypotheses that the degree of association for a gene is less than some value of interest against the alternative that it is greater combining this idea with the false discovery rate controlling methods of storey taylor and siegmund gives a computationally simple way to identify true discovery rate degree of association tdrda sets of genes among which a specified proportion are expected to have an absolute association of a specified degree or more this leads to a gene ranking method that uses the maximum lower bound degree of association for which each gene belongs to a tdrda set estimates of each gene s actual degree of association with approximate correction for selection bias due to regression to the mean rm can be derived using simple bivariate normal theory and efron and tibshirani s empirical bayes approach for a given data set all possible tdrda sets can be displayed along with the gene ranking and the rm corrected estimates of degree of association in a concise graphical summary

multiple testing of general contrasts powerful improvements are possible for multiple testing procedures when the hypotheses are logically related closed testing with exhaustive tests provides a unifying framework for developing such procedures but can be computationally difficult and can be nonmonotonic in p values royen introduced a truncated closed testing method for the case of all pairwise comparisons in the analysis of variance that is monotonic in p values shaffer developed a similar truncated procedure for more general comparisons but using bonferroni tests rather than exhaustive tests and westfall extended shaffer s method to allow exhaustive tests this article extends royen s method to general contrasts and proves that it is equivalent to the extended shaffer procedure for k contrasts the method generally requires evaluation of o 2k critical values that correspond to subset intersection hypotheses and is computationally infeasible for large k the set of intersections is represented using a tree structure and a

adjustments to zatsiorsky seluyanov s segment inertia parameters zatsiorsky et al in contemporary problems in biomechanics pp 272 291 crc press massachusetts 1990a obtained by means of a gamma ray scanning technique the relative body segment masses center of mass cm positions and radii of gyration for samples of college aged caucasian males and females although these data are the only available and comprehensive set of inertial parameters regarding young adult caucasians they have been rarely utilized for biomechanical analyses of subjects belonging to the same or a similar population the main reason is probably that zatsiorsky et al used bony landmarks as reference points for locating segment cms and defining segment lengths some of these landmarks were markedly distant from the joint centers currently used by most researchers as reference points the purpose of this study was to adjust the mean relative cm positions and radii of gyration reported by zatsiorsky et al in order to reference them to the joint centers or other commonly used landmarks rather than the original landmarks the adjustments were based on a number of carefully selected sources of anthropometric data

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

on the regularity of solutions to a class of nonlinear dispersive equations we shall study special regularity properties of solutions to some nonlinear dispersive models the goal is to show how regularity on the initial data is transferred to the solutions this will depend on the spaces where regularity is measured

the effect of metric selection on the analysis of diffusion tensor mri data the measurement of the distance between diffusion tensors is the foundation on which any subsequent analysis or processing of these quantities such as registration regularization interpolation or statistical inference is based in recent years a family of riemannian tensor metrics based on geometric considerations has been introduced for this purpose in this work we examine the properties one would use to select metrics for diffusion tensors diffusion coefficients and diffusion weighted mr image data we show that empirical evidence supports the use of a euclidean metric for diffusion tensors based upon monte carlo simulations our findings suggest that affine invariance is not a desirable property for a diffusion tensor metric because it leads to substantial biases in tensor data rather the relationship between distribution and distance is suggested as a novel criterion for metric selection

the interval testing procedure a general framework for inference in functional data analysis we introduce in this work the interval testing procedure itp a novel inferential technique for functional data the procedure can be used to test different functional hypotheses e g distributional equality between two or more functional populations equality of mean function of a functional population to a reference itp involves three steps i the representation of data on a possibly high dimensional functional basis ii the test of each possible set of consecutive basis coefficients iii the computation of the adjusted p values associated to each basis component by means of a new strategy here proposed we define a new type of error control the interval wise control of the family wise error rate particularly suited for functional data we show that itp is provided with such a control a simulation study comparing itp with other testing procedures is reported itp is then applied to the analysis of hemodynamical features involved with cerebral aneurysm pathology itp is implemented in the fdatest r package

false discovery control for random fields this article extends false discovery rates to random fields for which there are uncountably many hypothesis tests we develop a method for finding regions in the field s domain where there is a significant signal while controlling either the proportion of area or the proportion of clusters in which false rejections occur the method produces confidence envelopes for the proportion of false discoveries as a function of the rejection threshold from the confidence envelopes we derive threshold procedures to control either the mean or the specified tail probabilities of the false discovery proportion an essential ingredient of this construnction is a new algorithm to compute a confidence superset for the set of all true null locations we demonstrate our method with applications to scan statistics and functional neuroimaging

stepup procedures controlling generalized fwer and generalized fdr in many applications of multiple hypothesis testing where more than one false rejection can be tolerated procedures controlling error rates measuring at least k false rejections instead of at least one for some fixed k 1 can potentially increase the ability of a procedure to detect false null hypotheses the k fwer a generalized version of the usual familywise error rate fwer is such an error rate that has recently been introduced in the literature and procedures controlling it have been proposed a further generalization of a result on the k fwer is provided in this article in addition an alternative and less conservative notion of error rate the k fdr is introduced in the same spirit as the k fwer by generalizing the usual false discovery rate fdr a k fwer procedure is constructed given any set of increasing constants by utilizing the kth order joint null distributions of the p values without assuming any specific form of dependence among all the p values procedures controlling the k fdr are also developed by using the kth order joint null distributions of the p values first assuming that the sets of null and nonnull p values are mutually independent or they are jointly positively dependent in the sense of being multivariate totally positive of order two mtp2 and then discarding that assumption about the overall dependence among the p values

outlier detection using nonconvex penalized regression this article studies the outlier detection problem from the standpoint of penalized regression in the regression model we add one mean shift parameter for each of the n data points we then apply a regularization favoring a sparse vector of mean shift parameters the usual l1 penalty yields a convex criterion but fails to deliver a robust estimator the l1 penalty corresponds to soft thresholding we introduce a thresholding denoted by based iterative procedure for outlier detection ipod a version based on hard thresholding correctly identifies outliers on some hard test problems we describe the connection between ipod and m estimators our proposed method has one tuning parameter with which to both identify outliers and estimate regression coefficients a data dependent choice can be made based on the bayes information criterion the tuned ipod shows outstanding performance in identifying outliers in various situations compared with other existing approaches in addition ipod is much

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

operator norm consistent estimation of large dimensional sparse covariance matrices estimating covariance matrices is a problem of fundamental importance in multivariate statistics in practice it is increasingly frequent to work with data matrices x of dimension n x p where p and n are both large results from random matrix theory show very clearly that in this setting standard estimators like the sample covariance matrix perform in general very poorly in this large n large p setting it is sometimes the case that practitioners are willing to assume that many elements of the population covariance matrix are equal to 0 and hence this matrix is sparse we develop an estimator to handle this situation the estimator is shown to be consistent in operator norm when for instance we have p n as n oo in other words the largest singular value of the difference between the estimator and the population covariance matrix goes to zero this implies consistency of all the eigenvalues and consistency of eigenspaces associated to isolated eigenvalues we also propose a notion of sparsity for matrices that is compatible with spectral analysis and is independent of the ordering of the variables

synchrony and complexity in state related eeg networks an application of spectral graph theory the brain may be considered as a synchronized dynamic network with several coherent dynamical units however concerns remain whether synchronizability is a stable state in the brain networks if s

model sparsity and brain pattern interpretation of classification models in neuroimaging interest is increasing in applying discriminative multivariate analysis techniques to the analysis of functional neuroimaging data model interpretation is of great importance in the neuroimaging context and is conventionally based on a brain map derived from the classification model in this study we focus on the relative influence of model regularization parameter choices on both the model generalization the reliability of the spatial patterns extracted from the classification model and the ability of the resulting model to identify relevant brain networks defining the underlying neural encoding of the experiment for a support vector machine logistic regression and fisher s discriminant analysis we demonstrate that selection of model regularization parameters has a strong but consistent impact on the generalizability and both the reproducibility and interpretable sparsity of the models for both 2 and 1 regularization importantly we illustrate a trade off between model spatial reproducibility and prediction accuracy we show that known parts of brain networks can be overlooked in pursuing maximization of classification accuracy alone with either 2 and or 1 regularization this supports the view that the quality of spatial patterns extracted from models cannot be assessed purely by focusing on prediction accuracy our results instead suggest that model regularization parameters must be carefully selected so that the model and its visualization enhance our ability to interpret the brain

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

on the propagation of regularities in solutions of the fifth order kadomtsev petviashvili ii equation abstract in this paper we study special properties of solutions of the initial value problem ivp associated to the fifth order kadomtsev petviashvili ii equation mainly for initial data h 1 r 2 whose restriction belongs to h m x 0 r for some m z m 2 and x 0 r we prove that the restriction of the corresponding solution u t belongs to h m b r for any b r and any t 0 in other words the extra regularity on the data propagates in the solutions in the direction of the dispersion

variance component tests of multivariate mediation effects under composite null hypotheses mediation effects of multiple mediators are determined by two associations one between an exposure and mediators s m and the other between the mediators and an outcome conditional on the exposure m y the test for mediation effects is conducted under a composite null hypothesis that is either one of the s m and m y associations is zero or both are zeros without accounting for the composite null the type 1 error rate within a study containing a large number of multimediator tests may be much less than the expected we propose a novel test to address the issue for each mediation test j j 1 j we examine the s m and m y associations using two separate variance component tests assuming a zero mean working distribution with a common variance for the element wise s m and m y associations score tests for the variance components are constructed we transform the test statistics into two normally distributed statistics under the null using a recently developed result we conduct j hypothesis tests accounting for the composite null hypothesis by adjusting for the variances of the normally distributed statistics for the s m and m y associations advantages of the proposed test over other methods are illustrated in simulation studies and a data application where we analyze lung cancer data from the cancer genome atlas to investigate the smoking effect on gene expression through dna methylation in 15 114 genes

high dimensional variable selection via tilting the paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations high dimensionality of the data brings in many complications such as possibly spurious high correlations between the variables which result in marginal correlation being unreliable as a measure of association between the variables and the response we propose a new way of measuring the contribution of each variable to the response which takes into account high correlations between the variables in a data driven way the proposed tilting procedure provides an adaptive choice between the use of marginal correlation and tilted correlation for each variable where the choice is made depending on the values of the hard thresholded sample correlation of the design matrix we study the conditions under which this measure can successfully discriminate between the relevant and the irrelevant variables and thus be used as a tool for variable selection finally an iterative variable screening algorithm is constructed to exploit the theoretical properties of tilted correlation and its good practical performance is demonstrated in a comparative simulation study

one shot detection with laplacian object and fast matrix cosine similarity one shot generic object detection involves searching for a single query object in a larger target image relevant approaches have benefited from features that typically model the local similarity patterns in this paper we combine local similarity encoded by local descriptors with a global context i e a graph structure of pairwise affinities among the local descriptors embedding the query descriptors into a low dimensional but discriminatory subspace unlike principal components that preserve global structure of feature space we actually seek a linear approximation to the laplacian eigenmap that permits us a locality preserving embedding of high dimensional region descriptors our second contribution is an accelerated but exact computation of matrix cosine similarity as the decision rule for detection obviating the computationally expensive sliding window search we leverage the power of fourier transform combined with integral image to achieve superior runtime efficiency that allows us to test multiple hypotheses for pose estimation within a reasonably short time our approach to one shot detection is training free and experiments on the standard data sets confirm the efficacy of our model besides low computation cost of the proposed codebook free object detector facilitates rather straightforward query detection in large data sets including movie videos

properties of certain subclasses of multivalent analytic functions involving the dziok srivastava operator abstract in this paper the authors introduce and investigate the various properties of two subclasses s p k l m 1 h and k p k l m 1 h of multivalent analytic functions in particular some sufficient conditions for the subclass s p k l m 1 1 z 1 z of analytic functions argument properties the growth theorems distortion theorems and covering theorems are obtained some of the results presented in this paper would generalize and extend the corresponding results of earlier authors

significance testing for small microarray experiments summary which signicance test is carried out when the number of repeats is small in microarray experiments can dramatically inuence the results when in two sample comparisons both conditions have fewer than say ve repeats traditional test statistics require extreme results before a gene is considered statis tically signicant dierentially expressed after a multiple comparisons correction in the literature many approaches to circumvent this problem have been proposed some of these proposals use empirical bayes arguments to moderate the variance estimates for individual genes other proposals try to stabilize these variance estimate by combining groups of genes or similar experiments in this paper we compare several of these approaches both on data sets where both experimental conditions are the same and thus few statistically signicant dierentially expressed genes should be identied and on experiments where both conditions do dier this allows us to identify which approaches are most powerful without identifying many false positives we conclude that after balancing the numbers of false positives and true positives an empirical bayes approach and an approach which combines experiments perform best standard t tests are inferior and oer almost no power when the sample size is small copyright 2005 john wiley sons ltd

nonparametric bayes modeling of multivariate categorical data modeling of multivariate unordered categorical nominal data is a challenging problem particularly in high dimensions and cases in which one wishes to avoid strong assumptions about the dependence structure commonly used approaches rely on the incorporation of latent gaussian random variables or parametric latent class models the goal of this article is to develop a nonparametric bayes approach which defines a prior with full support on the space of distributions for multiple unordered categorical variables this support condition ensures that we are not restricting the dependence structure a priori we show this can be accomplished through a dirichlet process mixture of product multinomial distributions which is also a convenient form for posterior computation methods for nonparametric testing of violations of independence are proposed and the methods are applied to model positional dependence within transcription factor binding motifs

corner height influences center of mass kinematics and path trajectory during turning despite the prevalence of directional changes during every day gait relatively little is known about turning compared to straight gait while the center of mass com movement during straight gait is well characterized the com trajectory and the factors that influence it are less established for turning this study investigated the influence of a corner s height on the com trajectory as participants walked around the corner ten participants 25 3 3 74 years performed both 90 step and spin turns to the left at self selected slow normal and fast speeds while walking inside a marked path a pylon was placed on the inside corner of the path four different pylon heights were used to correspond to heights of everyday objects 0 cm no object 63 cm box crate 104 cm desk table counter 167 cm shelf cabinet obstacle height was found to significantly affect the com trajectory taller obstacles resulted in more distance between the corner and the com and between the corner and the cop taller obstacles also were associated with greater curvature in the com trajectory indicating a smaller turning radius despite the constant 90 corner taller obstacles correlated to an increased required coefficient of friction rcof due to the smaller turning radii taller obstacles also tended towards greater mediolateral ml com cop angles contrary to the initial hypothesis additionally the com was found to remain outside the base of support bos for the entire first half of stance phase for all conditions indicating a high risk of falls resulting from slips

semiparametric detection of significant activation for brain fmri functional magnetic resonance imaging fmri aims to locate activated regions in human brains when specific tasks are performed the conventional tool for analyzing fmri data applies some variant of the linear model which is restrictive in modeling assumptions to yield more accurate prediction of the time course behavior of neuronal responses the semiparametric inference for the underlying hemodynamic response function is developed to identify significantly activated voxels under mild regularity conditions we demonstrate that a class of the proposed semiparametric test statistics based on the local linear estimation technique follow x 2 distributions under null hypotheses for a number of useful hypotheses furthermore the asymptotic power functions of the constructed tests are derived under the fixed and contiguous alternatives simulation evaluations and real fmri data application suggest that the semiparametric inference procedure provides more efficient detection of activated brain areas than the popular imaging analysis tools afni and fsl

multiple tests based on a gaussian approximation of the unitary events method with delayed coincidence count the unitary events ue method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons the detection of coincidences is usually based on binned coincidence count grun 1996 which is known to be subject to loss in synchrony detection grun diesmann grammont riehle aertsen 1999 this defect has been corrected by the multiple shift coincidence count grun et al 1999 the statistical properties of this count have not been further investigated until this work the formula being more difficult to deal with than the original binned count first we propose a new notion of coincidence count the delayed coincidence count which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains moreover it generalizes this notion to nondiscretized point processes allowing us to propose a new gaussian approximation of the count since unknown parameters are involved in the approximation we perform a plug in step where unknown parameters are replaced by estimated ones leading to a modification of the approximating distribution finally the method takes the multiplicity of the tests into account via a benjamini and hochberg approach benjamini hochberg 1995 to guarantee a prescribed control of the false discovery rate we compare our new method mtgaue multiple tests based on a gaussian approximation of the unitary events and the ue method proposed in grun et al 1999 over various simulations showing that mtgaue extends the validity of the previous method in particular mtgaue is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model furthermore mtgaue is applied on real data

a high dimensional nonparametric multivariate test for mean vector this work is concerned with testing the population mean vector of nonnormal high dimensional multivariate data several tests for high dimensional mean vector based on modifying the classical hotelling t2 test have been proposed in the literature despite their usefulness they tend to have unsatisfactory power performance for heavy tailed multivariate data which frequently arise in genomics and quantitative finance this article proposes a novel high dimensional nonparametric test for the population mean vector for a general class of multivariate distributions with the aid of new tools in modern probability theory we proved that the limiting null distribution of the proposed test is normal under mild conditions when p is substantially larger than n we further study the local power of the proposed test and compare its relative efficiency with a modified hotelling t2 test for high dimensional data an interesting finding is that the newly proposed test can have even more substantial power gain with l

optimizing methods for linking cinematic features to fmri data abstract one of the challenges of naturalistic neurosciences using movie viewing experiments is how to interpret observed brain activations in relation to the multiplicity of time locked stimulus features as previous studies have shown less inter subject synchronization across viewers of random video footage than story driven films new methods need to be developed for analysis of less story driven contents to optimize the linkage between our fmri data collected during viewing of a deliberately non narrative silent film at land by maya deren 1944 and its annotated content we combined the method of elastic net regularization with the model driven linear regression and the well established data driven independent component analysis ica and inter subject correlation isc methods in the linear regression analysis both ic and region of interest roi time series were fitted with time series of a total of 36 binary valued and one real valued tactile annotation of film features the elastic net regularization and cross validation were applied in the ordinary least squares linear regression in order to avoid over fitting due to the multicollinearity of regressors the results were compared against both the partial least squares pls regression and the un regularized full model regression non parametric permutation testing scheme was applied to evaluate the statistical significance of regression we found statistically significant correlation between the annotation model and 9 ics out of 40 ics regression analysis was also repeated for a large set of cubic rois covering the grey matter both ic and roi based regression analyses revealed activations in parietal and occipital regions with additional smaller clusters in the frontal lobe furthermore we found elastic net based regression more sensitive than pls and un regularized regression since it detected a larger number of significant ics and rois along with the isc ranking methods our regression analysis proved a feasible method for ordering the ics based on their functional relevance to the annotated cinematic features the novelty of our method is in comparison to the hypothesis driven manual pre selection and observation of some individual regressors biased by choice in applying data driven approach to all content features simultaneously we found especially the combination of regularized regression and ica useful when analyzing fmri data obtained using non narrative movie stimulus with a large set of complex and correlated features

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

on certain subclasses of close to convex and quasi convex functions with respect to k symmetric points abstract in the present paper the authors introduce two new subclasses s s k of close to convex functions and c s k of quasi convex functions the integral representations for functions belonging to these classes are provided the convolution conditions growth theorems distortion theorems and covering theorems for these classes are also provided the results obtained generalize some known results and some other new results are obtained

nonlinear denoising and analysis of neuroimages with kernel principal component analysis and pre image estimation we investigate the use of kernel principal component analysis pca and the inverse problem known as pre image estimation in neuroimaging i we explore kernel pca and pre image estimation as a means for image denoising as part of the image preprocessing pipeline evaluation of the denoising procedure is performed within a data driven split half evaluation framework ii we introduce manifold navigation for exploration of a nonlinear data manifold and illustrate how pre image estimation can be used to generate brain maps in the continuum between experimentally defined brain states classes we base these illustrations on two fmri bold data sets one from a simple finger tapping experiment and the other from an experiment on object recognition in the ventral temporal lobe

inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators abstract by making use of a general linear operator i p a c the authors introduce several new subclasses of multivalent functions and investigate various inclusion relationships and argument properties associated with these subclasses some interesting applications involving such and other families of linear operators are also considered the results presented here include a number of known results as their special cases

estimating the false discovery rate using nonparametric deconvolution summary given a set of microarray data the problem is to detect differentially expressed genes using a false discovery rate fdr criterion as opposed to common procedures in the literature we do not base the selection criterion on statistical significance only but also on the effect size therefore we select only those genes that are significantly more differentially expressed than some f fold e g f 2 this corresponds to use of an interval null domain for the effect size based on a simple error model we discuss a naive estimator for the fdr interpreted as the probability that the parameter of interest lies in the null domain e g log2 2 1 given that the test statistic exceeds a threshold we improve the naive estimator by using deconvolution that is the density of the parameter of interest is recovered from the data we study performance of the methods using simulations and real data

familywise robustness criteria for multiple comparison procedures a criticism of multiple comparison procedures is that the family of inferences over which an error rate is controlled is often arbitrarily selected yet the conclusion may depend heavily on the choice of the family such ambiguity is most likely in large exploratory studies requiring numerous simultaneous inferences in ambiguous situations it is desirable that results of multiple comparison procedures depend little on the chosen family to assess this we propose several familywise robustness criteria to evaluate such procedures and we find some of their properties theoretically and by simulation procedures that control the false discovery rate seem to be familywise robust

structural similarity and difference testing on multiple sparse gaussian graphical models we present a new framework on inferring structural similarities and differences among multiple high dimensional gaussian graphical models ggms corresponding to the same set of variables under distinct experimental conditions the new framework adopts the partial correlation coefficients to characterize the potential changes of dependency strengths between two variables a hierarchical method has been further developed to recover edges with different or similar dependency strengths across multiple ggms in particular we first construct two sample test statistics for testing the equality of partial correlation coefficients and conduct large scale multiple tests to estimate the substructure of differential dependencies after removing differential substructure from original ggms a follow up multiple testing procedure is used to detect the substructure of similar dependencies among ggms in each step false discovery rate is controlled asymptotically at a desired level power results are proved which demonstrate that our method is more powerful on finding common edges than the common approach that separately estimates ggms the performance of the proposed hierarchical method is illustrated on simulated datasets

statistical discoveries and effect size estimation abstract current methods of statistical inference are correct but incomplete small probability of wrong null hypothesis rejections can be misunderstood definitive rejections of null hypotheses as well as interval assessments of effect sizes are impossible in single cases with significance probabilities like 05 sufficiently large sets of independent experiments and attained significance levels p values should be registered from such data it is possible to calculate least upper bounds for proportions of fallacies in sets of null hypothesis rejections or effect size assessments a provisional rejection of a null hypothesis in a one tailed test or a one sided confidence interval showing a nonzero effect is here called a discovery consider a large number n of independent experiments with r discoveries for r rejections of null hypotheses the proportion of fallacies q has least upper bound q max n r 1 1 1 for r confidence intervals the proportion of fallacies is e n r assumi

rotating horizontal ground reaction forces to the body path of progression when studying the biomechanics of a transient turn the orientation of the body will change relative to the orientation of the force plates over the progression of the turn to express ground reaction forces relative to the body this study investigated possible origin locations and axis alignments of body reference frames the gait patterns of 10 subjects were recorded as subjects negotiated a 90 hallway corner body reference frames were chosen whose origins were the center of mass com and the pelvis origin pel a finite difference method was used to align the axes of the reference frames according to the horizontal paths of the com and pel the ground reaction impulses gris were calculated relative to the com and pel reference frames gri differences were small between the pel and com frames suggesting that either is acceptable for turning studies based on an investigation of finite difference parameters the com frame should be used when using a kinematic sampling rate of 60 hz either frame is acceptable when sampling at higher rates

subordinations for analytic functions defined by the dziok srivastava linear operator in the present investigation we obtain certain sufficient conditions for a normalized analytic function f z defined by the dziok srivastava linear operator h l a1 to satisfy the certain subordination our results extend corresponding previously known results on starlikeness convexity and close to convexity

comparison of lower limb joint moment and power during turning gait between young and old adults using hierarchical bayesian inference age related differences in lower limb joint moment jm and joint power jp during turning remain unclear the present study investigated age related differences in lower limb jm and jp during turning between young adults yas and old adults oas we introduced the hierarchical bayesian inference for comparing and identifying differences in jm angular velocity and jp at each stance phase in the two age groups this study included 16 healthy yas and 16 healthy oas 8 men and 8 women in each group participants performed 90 step turns to the right at a self selected natural speed on comparing the age groups during 90 step turning the oa group exhibited larger extention hip jm and jp to control brake the upper body in the sagittal plane exhibited larger abductor moment in each lower limb joint for preventing the body from leaning in the frontal plane during the mid stance phase and exhibited larger hip jp and and smaller ankle jm in the transverse plane to rotate the body during the mid stance phase our findings suggested that the overall reliance on the hip joint to control body motion in each anatomical plane during step turning is higher in the oa group than in the ya group in addition the hierarchical bayesian inference is useful for comparing the time courses of jm and jp

certain properties of the dziok srivastava operator the main object of the present paper is to investigate several interesting properties and characteristics of a linear operator h p q s a 1 which was recently introduced and studied in a series of papers by dziok and srivastava appl math comput 103 1999 1 13 adv stud contemp math 5 2002 115 125 integral transform spec funct 14 2003 7 18 the various properties and characteristics of the linear operator h p q s a 1 which are considered in this paper are associated with for example the principle of differential subordination between analytic functions and a certain one parameter family of integral operators

support vector machines for dyadic data we describe a new technique for the analysis of dyadic data where two sets of objects row and column objects are characterized by a matrix of numerical values that describe their mutual relationships the new technique called potential support vector machine p svm is a large margin method for the construction of classifiers and regression functions for the column objects contrary to standard support vector machine approaches the p svm minimizes a scale invariant capacity measure and requires a new set of constraints as a result the p svm method leads to a usually sparse expansion of the classification and regression functions in terms of the row rather than the column objects and can handle data and kernel matrices that are neither positive definite nor square we then describe two complementary regularization schemes the first scheme improves generalization performance for classification and regression tasks the second scheme leads to the selection of a small informative set of row support objects and can be applied to feature selection benchmarks for classification regression and feature selection tasks are performed with toy data as well as with several real world data sets the results show that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as true dyadic data sets in addition a theoretical justification is provided for the new approach

quality assessment of sharpened images challenges methodology and objective metrics most of the effort in image quality assessment qa has been so far dedicated to the degradation of the image however there are also many algorithms in the image processing chain that can enhance the quality of an input image these include procedures for contrast enhancement deblurring sharpening up sampling denoising transfer function compensation and so on in this paper possible strategies for the qa of sharpened images are investigated this task is not trivial because the sharpening techniques can increase the perceived quality as well as introduce artifacts leading to the quality drop over sharpening here the framework specifically adapted for the qa of sharpened images and objective metrics comparison in this context is introduced however the framework can be adopted in other qa areas as well the problem of selecting the correct procedure for subjective evaluation was addressed and a subjective test on blurred sharpened and over sharpened images was performed in order to demonstrate the use of the framework the obtained ground truth data were used for testing the suitability of the state of the art objective quality metrics for the assessment of sharpened images the comparison was performed by novel procedure using rank order correlation analyses which is found more appropriate for the task than standard methods furthermore seven possible augmentations of the no reference s3 metric adapted for sharpened images are proposed the performance of the metric is significantly improved and also superior over the rest of the tested quality criteria with respect to the subjective data

joint mean and covariance estimation with unreplicated matrix variate data abstractit has been proposed that complex populations such as those that arise in genomics studies may exhibit dependencies among observations as well as among variables this gives rise to the challenging problem of analyzing unreplicated high dimensional data with unknown mean and dependence structures matrix variate approaches that impose various forms of inverse covariance sparsity allow flexible dependence structures to be estimated but cannot directly be applied when the mean and covariance matrices are estimated jointly we present a practical method utilizing generalized least squares and penalized inverse covariance estimation to address this challenge we establish consistency and obtain rates of convergence for estimating the mean parameters and covariance matrices the advantages of our approaches are i dependence graphs and covariance structures can be estimated in the presence of unknown mean structure ii the mean structure becomes more efficiently estimated when accounting for

on the generalized benjamin ono equation we study well posedness of the initial value problem for the generalized benjamin ono equation tu ukdxu 0 k e in sobolev spaces hs r for small data and higher nonlinearities k 2 new local and global including scattering results are established our method of proof is quite general it combines several estimates concerning the associated linear problem with the contraction principle hence it applies to other dispersive models in particular it allows us to extend the results for the generalized benjamin ono to nonlinear schrodinger equations or systems of the form atu i2u p u oxu ui axi 0

factor selection and structural identification in the interaction anova model when faced with categorical predictors and a continuous response the objective of an analysis often consists of two tasks finding which factors are important and determining which levels of the factors differ significantly from one another often times these tasks are done separately using analysis of variance anova followed by a post hoc hypothesis testing procedure such as tukey s honestly significant difference test when interactions between factors are included in the model the collapsing of levels of a factor becomes a more difficult problem when testing for differences between two levels of a factor claiming no difference would refer not only to equality of main effects but also to equality of each interaction involving those levels this structure between the main effects and interactions in a model is similar to the idea of heredity used in regression models this article introduces a new method for accomplishing both of the common analysis tasks simultaneously in an interaction model while also adhering to the heredity type constraint on the model an appropriate penalization is constructed that encourages levels of factors to collapse and entire factors to be set to zero it is shown that the procedure has the oracle property implying that asymptotically it performs as well as if the exact structure were known beforehand we also discuss the application to estimating interactions in the unreplicated case simulation studies show the procedure outperforms post hoc hypothesis testing procedures as well as similar methods that do not include a structural constraint the method is also illustrated using a real data example

a linear non gaussian acyclic model for causal discovery in recent years several methods have been proposed for the discovery of causal structure from non experimental data such methods make various assumptions on the data generating process to facilitate its identification from purely observational data continuing this line of research we show how to discover the complete causal structure of continuous valued data under the assumptions that a the data generating process is linear b there are no unobserved confounders and c disturbance variables have non gaussian distributions of non zero variances the solution relies on the use of the statistical method known as independent component analysis and does not require any pre specified time ordering of the variables we provide a complete matlab package for performing this lingam analysis short for linear non gaussian acyclic model and demonstrate the effectiveness of the method using artificially generated data and real world data

accumulation tests for fdr control in ordered hypothesis testing abstractmultiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses with relatively few true signals in this article we consider the multiple testing problem where prior information is available for instance from an earlier study under different experimental conditions that can allow us to test the hypotheses as a ranked list to increase the number of discoveries given an ordered list of n hypotheses the aim is to select a data dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate fdr generalizing several existing methods we develop a family of accumulation tests to choose a cutoff k that adapts to the amount of signal at the top of the ranked list we introduce a new method in this family the hingeexp method which offers higher power to detect true signals compared to existing techniques our theoretical results prove that these metho

estimating the false discovery rate using the stochastic approximation algorithm testing of multiple hypotheses involves statistics that are strongly dependent in some applications but most work on this subject is based on the assumption of independence we propose a new method for estimating the false discovery rate of multiple hypothesis tests in which the density of test scores is estimated parametrically by minimizing the kullback leibler distance between the unknown density and its estimator using the stochastic approximation algorithm and the false discovery rate is estimated using the ensemble averaging method our method is applicable under general dependence between test statistics numerical comparisons between our method and several competitors conducted on simulated and real data examples show that our method achieves more accurate control of the false discovery rate in almost all scenarios

nonlocal models for nonlinear dispersive waves abstract considered herein are model equations for the unidirectional propagation of small amplitude nonlinear dispersive long waves such as those governed by the classical korteweg de vries equation of special interest are physical situations in which the linear dispersion relation is not appropriately approximated by a polynomial so that the operator modelling dispersive effect is nonlocal particular cases in view here are the benjamin ono equation and the intermediate long wave equation which arise in internal wave theory and smith s equation which governs certain types of continental shelf waves the initial value problem for these equations is shown to be globally well posed in the classical sense including continuous dependence upon the initial data and in certain cases upon the modelling of nonlinear and dispersive effects whilst the results are stated for the specific equations listed above the techniques utilized are seen to have a considerable range of generality as regards application to nonlinear dispersive evolution equations particularly worthy of note is our theorem implying that solutions of the intermediate long wave equation converge strongly to solutions of the korteweg de vries equation or to solutions of the benjamin ono equation in appropriate asymptotic limits

on the propagation of regularity for solutions of the fractional korteweg de vries equation abstract we consider the initial value problem ivp for the fractional korteweg de vries equation fkdv 0 1 t u d x x u u x u 0 x t r 0 1 u x 0 u 0 x it has been shown that the solutions to certain dispersive equations satisfy the propagation of regularity phenomena more precisely it deals in determine whether regularity of the initial data on the right hand side of the real line is propagated to the left hand side by the flow solution this property was found originally in solutions of korteweg de vries kdv equation and it has been also verified in other dispersive equations as the benjamin ono bo equation recently it has been shown that the solutions of the dispersive generalized benjamin ono dgbo equation this is 2 3 in 0 1 also satisfy the propagation of regularity phenomena this is achieved by introducing a commutator decomposition to handle the dispersive part in the equation following the approach used in the dgbo we prove that the solutions of the fkdv also satisfies the propagation of regularity phenomena consequently this type of regularity travels with infinite speed to its left as time evolves

on the convex combination of the dziok srivastava operator in the paper we obtain the extreme points of some class defined by the dziok srivastava linear operator by using the krein milman theorem some extremal problems in the class are determined

on the propagation of regularities in solutions of the benjamin ono equation abstract we shall deduce some special regularity properties of solutions to the ivp associated to the benjamin ono equation mainly for datum u 0 h 3 2 r whose restriction belongs to h m b for some m z m 2 and b r we shall prove that the restriction of the corresponding solution u t belongs to h m for any r and any t 0 therefore this type of regularity of the datum travels with infinite speed to its left as time evolves

optimal sample size for multiple testing the case of gene expression microarrays we consider the choice of an optimal sample size for multiple comparison problems the motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression however the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests we discuss two decision problems in the context of this setup the sample size selection and the decision about the multiple comparisons we adopt a decision theoretic approach using loss functions that combine the competing goals of discovering as many differentially expressed genes as possible while keeping the number of false discoveries manageable for consistency we use the same loss function for both decisions the decision rule that emerges for the multiple comparison problem takes the exact form of the rules proposed in the recent literature to control the posterior expected falsediscovery rate for the sample size selection we combine the expe

classes of analytic functions associated with the generalized hypergeometric function using the generalized hypergeometric function we introduce and study a class of analytic functions with negative coefficients coefficients estimates distortion theorems extreme points and the radii of convexity and starlikeness for this class are given relevant connections of these results with those in several earlier investigations are indicated

the ivp for the benjamin ono equation in weighted sobolev spaces abstract in this work we continue our study initiated in fonseca and ponce 2011 11 on the uniqueness properties of real solutions to the ivp associated to the benjamin ono bo equation in particular we shall show that the uniqueness results established in fonseca and ponce 2011 11 do not extend to any pair of non vanishing solutions of the bo equation also we shall prove that the uniqueness result established in fonseca and ponce 2011 11 under a hypothesis involving information of the solution at three different times cannot be relaxed to two different times

differential subordinations and inequalities in the complex plane abstract let p be analytic in the unit disc u and let q be univalent in u in addition let be a set in c and let c3 u c the authors determine conditions on so that p z zp z z 2 p z z z u p u q u applications of this result to differential inequalities differential subordinations and integral inequalities are presented

type ii generalized family wise error rate formulas with application to sample size determination multiple endpoints are increasingly used in clinical trials the significance of some of these clinical trials is established if at least r null hypotheses are rejected among m that are simultaneously tested the usual approach in multiple hypothesis testing is to control the family wise error rate which is defined as the probability that at least one type i error is made more recently the q generalized family wise error rate has been introduced to control the probability of making at least q false rejections for procedures controlling this global type i error rate we define a type ii r generalized family wise error rate which is directly related to the r power defined as the probability of rejecting at least r false null hypotheses we obtain very general power formulas that can be used to compute the sample size for single step and step wise procedures these are implemented in our r package rpowersamplesize available on the cran making them directly available to end users complexities of the formulas are presented to gain insight into computation time issues comparison with monte carlo strategy is also presented we compute sample sizes for two clinical trials involving multiple endpoints one designed to investigate the effectiveness of a drug against acute heart failure and the other for the immunogenicity of a vaccine strategy against pneumococcus copyright 2016 john wiley sons ltd

outlier detection and false discovery rates for whole genome dna matching we define a statistic called the matching statistic for locating regions of the genome that exhibit excess similarity among cases when compared to controls such regions are reasonable candidates for harboring disease genes we find the asymptotic distribution of the statistic while accounting for correlations among sampled individuals we then use the benjamini and hochberg false discovery rate fdr method for multiple hypothesis testing to find regions of excess sharing the p values for each region involve estimated nuisance parameters under appropriate conditions we show that the fdr method based on p values and with estimated nuisance parameters asymptotically preserves the fdr property finally we apply the method to a pilot study on schizophrenia

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

a sequentially rejective test procedure based on a modified bonferroni inequality summary a sharper bonferroni procedure for multiple tests of significance is derived this procedure is an improvement of hochberg s 1988 procedure which contrasts the individual p values with corresponding critical points it is shown that hochberg s original procedure is conservative and can be made more powerful by enlarging the rejection region so that the type one error is exactly at the nominal level it is also shown that the modified procedure retains all the desired properties of the original procedure

on false discovery rate thresholding for classification under sparsity we study the properties of false discovery rate fdr thresholding viewed as a classification procedure the 0 class null is assumed to have a known density while the 1 class alternative is obtained from the 0 class either by translation or by scaling furthermore the 1 class is assumed to have a small number of elements w r t the 0 class sparsity we focus on densities of the subbotin family including gaussian and laplace models nonasymptotic oracle inequalities are derived for the excess risk of fdr thresholding these inequalities lead to explicit rates of convergence of the excess risk to zero as the number m of items to be classified tends to infinity and in a regime where the power of the bayes rule is away from 0 and 1 moreover these theoretical investigations suggest an explicit choice for the target level alpha m of fdr thresholding as a function of m our oracle inequalities show theoretically that the resulting fdr thresholding adapts to the unknown sparsity regime contained in the data this property is illustrated with numerical experiments

on the propagation of regularity and decay of solutions to the benjamin equation in this paper we investigate some special regularities and decay properties of solutions to the initial value problem of the benjamin equation the main result shows that for initial datum u0 hs r with s 3 4 if the restriction of u0 belongs to hl x0 for some l z and x0 r then the restriction of the corresponding solution u t belongs to hl for any r and any t 0 t consequently this type of regularity travels with infinite speed to its left as time evolves

on well posedness for the benjamin ono equation we prove existence and uniqueness of solutions for the benjamin ono equation with data in h s mathbb r s 1 4 moreover the flow is holder continuous in weaker topologies