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

the false discovery rate for multiple testing in factorial experiments identifying the important factors and effects is an important goal in the analysis of two level fractional factorial experiments in moderate and large experiments the large number of potential effects presents problems of multiple statistical inference in this work we apply the false discovery rate fdr idea in multiple inference to effect identification in factorial experiments the fdr is the expected proportion of inert effects among those declared active which we believe is a more relevant quantity to control than the probability of a single erroneous declaration the criterion that has been adopted in previous studies we show how to combine the control of fdr with popular methods for estimating contrast standard error in unreplicated experiments we present simulations of unreplicated 16 and 32 run experiments that illustrate the improvements in power that can be obtained by controlling the fdr we also analyze data from an actual 128 run experiment with replication in which the fdr identifie

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

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

blind source separation in the time frequency domain based on multiple hypothesis testing this paper considers a time frequency t f based approach for blind separation of nonstationary signals in particular we propose a time frequency point selection algorithm based on multiple hypothesis testing which allows automatic selection of auto or cross source locations in the time frequency plane the selected t f points are then used via a joint diagonalization and off diagonalization algorithm to perform source separation the proposed algorithm is developed assuming deterministic signals with additive white complex gaussian noise a performance comparison of the proposed and existing approaches is provided

the empirical distribution of a large number of correlated normal variables motivated by the advent of high dimensional highly correlated data this work studies the limit behavior of the empirical cumulative distribution function ecdf of standard normal random variables under arbitrary correlation first we provide a necessary and sufficient condition for convergence of the ecdf to the standard normal distribution next under general correlation we show that the ecdf limit is a random possible infinite mixture of normal distribution functions that depends on a number of latent variables and can serve as an asymptotic approximation to the ecdf in high dimensions we provide conditions under which the dimension of the ecdf limit defined as the smallest number of effective latent variables is finite estimates of the latent variables are provided and their consistency proved we demonstrate these methods in a real high dimensional data example from brain imaging where it is shown that while the study exhibits apparently strongly significant results they can be entirely explained by correlation as captured by the asymptotic approximation developed here

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

simultaneous testing of grouped hypotheses finding needles in multiple haystacks in large scale multiple testing problems data are often collected from heterogeneous sources and hypotheses form into groups that exhibit different characteristics conventional approaches including the pooled and separate analyses fail to efficiently utilize the external grouping information we develop a compound decision theoretic framework for testing grouped hypotheses and introduce an oracle procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate it is shown that both the pooled and separate analyses can be uniformly improved by the oracle procedure we then propose a data driven procedure that is shown to be asymptotically optimal simulation studies show that our procedures enjoy superior performance and yield the most accurate results in comparison with both the pooled and separate procedures a real data example with grouped hypotheses is studied in detail using different methods both theoretical and numerical results demonstrate that exploit

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

sequential selection procedures and false discovery rate control summary we consider a multiple hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block of hypotheses a rejection rule in this setting amounts to a procedure for choosing the stopping point k this setting is inspired by the sequential nature of many model selection problems where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter we propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting we also show how the methods can be applied to model selection by using recent results on p values in sequential model selection settings

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

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

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

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

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

a multiscale derivation of a new parabolic equation which includes density variations abstract a new parabolic equation is obtained from the acoustic equation by the multiscale method the new equation incorporates the effects of a variable ocean density the density can be smooth or piecewise smooth thus the new formulation alleviates the need for interfacial conditions when the density is stratified in a piecewise constant fashion it also reduces to the standard p e when the density is constant the new equation has the same conservation law as the p e a difference equation is presented which has a discrete version of the same law

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

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

local spectral analysis of the cerebral cortex new gyrification indices gyrification index gi is an appropriate measure to quantify the complexity of the cerebral cortex there is however no universal agreement on the notion of surface complexity and there are various methods in literature that evaluate different aspects of cortical folding in this paper we give two intuitive interpretations on folding quantification based on the magnitude and variation of the mean curvature of the cortical surface we then present a local spectral analysis of the mean curvature to introduce two local gyrification indices that satisfy our interpretations for this purpose the graph windowed fourier transform is extended to the framework of surfaces discretized with triangular meshes an adaptive window function is also proposed to deal with the intersubject cortical size variability the intrinsic nature of the method allows us to compute the degree of folding at different spatial scales our experiments show that while more classical surface area based gis may fail at differentiating deep folds from very convoluted ones our spectral gis overcome this issue the method is applied to the cortical surfaces of 124 healthy adult subjects of oasis database and average gyrification maps are computed and compared with other gi definitions in order to illustrate the capacity of our method to capture and quantify important aspects of gyrification we study the relationship between brain volume and cortical complexity and design a scaling analysis with a power law model results indicate an allometric relation and confirm the well known observations that larger brains are more folded we also perform the scaling analysis at the vertex level to investigate how the degree of folding varies locally with the brain volume results reveal that in our healthy adult brain database cortical regions which are the least folded on average show an increased folding complexity when brain size increases

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

a method for determining groups in multiple survival curves survival analysis includes a wide variety of methods for analyzing time to event data one basic but important goal in survival analysis is the comparison of survival curves between groups several nonparametric methods have been proposed in the literature to test for the equality of survival curves for censored data when the null hypothesis of equality of curves is rejected leading to the clear conclusion that at least one curve is different it can be interesting to ascertain whether curves can be grouped or if all these curves are different from each other a method is proposed that allows determining groups with an automatic selection of their number the validity and behavior of the proposed method was evaluated through simulation studies the applicability of the proposed method is illustrated using real data software in the form of an r package has been developed implementing the proposed method

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

properties of higher criticism under strong dependence the problem of signal detection using sparse faint information is closely related to a variety of contemporary statistical problems including the control of false discovery rate and classification using very high dimensional data each problem can be solved by conducting a large number of simultaneous hypothesis tests the properties of which are readily accessed under the assumption of independence in this paper we address the case of dependent data in the context of higher criticism methods for signal detection short range dependence has no first order impact on performance but the situation changes dramatically under strong dependence there although higher criticism can continue to perform well it can be bettered using methods based on differences of signal values or on the maximum of the data the relatively inferior performance of higher criticism in such cases can be explained in terms of the fact that under strong dependence the higher criticism statistic behaves as though the data were partitioned into very large blocks with all but a single representative of each block being eliminated from the dataset

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

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

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

testing multivariate economic restrictions using quantiles the example of slutsky negative semidefiniteness abstract this paper is concerned with testing a core economic restriction negative semidefiniteness of the slutsky matrix we consider a system of nonseparable structural equations with infinite dimensional unobservables and employ quantile regression methods because they allow us to utilize the entire distribution of the data difficulties arise because the restriction involves several equations while the quantile is a univariate concept we establish that we may use quantiles of linear combinations of the dependent variable develop a new empirical process based test that applies kernel quantile estimators and investigate its finite and large sample behavior finally we apply all concepts to canadian microdata

positive solution of a singular nonlinear third order periodic boundry value problem abstract the singular nonlinear third order periodic boundary value problem u 3 u f t u 0 t 2 with u i 0 u i 2 i 0 1 2 is studied where 0 and f is singular at u 0 under suitable conditions on f it is proved by employing a priori estimates perturbation technique and schauder fixed point theorem that the problem has at least one positive solution if 0 1 3

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

simultaneous factor selection and collapsing levels in anova when performing an analysis of variance the investigator often has two main goals to determine which of the factors have a significant effect on the response and to detect differences among the levels of the significant factors level comparisons are done via a post hoc analysis based on pairwise differences this article proposes a novel constrained regression approach to simultaneously accomplish both goals via shrinkage within a single automated procedure the form of this shrinkage has the ability to collapse levels within a factor by setting their effects to be equal while also achieving factor selection by zeroing out entire factors using this approach also leads to the identification of a structure within each factor as levels can be automatically collapsed to form groups in contrast to the traditional pairwise comparison methods these groups are necessarily nonoverlapping so that the results are interpretable in terms of distinct subsets of levels the proposed procedure is shown to have the oracle property in that asymptotically it performs as well as if the exact structure were known beforehand a simulation and real data examples show the strong performance of the method

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

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

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 discoveries in lasso the lasso method estimates coefficients by minimizing the residual sum of squares plus a penalty term the regularization parameter in lasso controls the trade off between data fitting and sparsity we derive relationship between and the false discovery proportion fdp of lasso estimator and show how to select so as to achieve a desired fdp our estimation is based on the asymptotic distribution of lasso estimator in the limit of both sample size and dimension going to infinity with fixed ratio we use a factor analysis model to describe the dependence structure of the design matrix an efficient majorization minimization based algorithm is developed to estimate the fdp at fixed value of the analytic results are compared with those of numerical simulations on finite size systems and are confirmed to be correct an application to the high throughput genomic riboavin data set also demonstrates the usefulness of our method

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

group comparison of eigenvalues and eigenvectors of diffusion tensors diffusion tensor imaging dti data differ from most medical images in that values at each voxel are not scalars but 3 3 symmetric positive definite matrices called diffusion tensors dts the anatomic characteristics of the tissue at each voxel are reflected by the dt eigenvalues and eigenvectors in this article we consider the problem of testing whether the means of two groups of dt images are equal at each voxel in terms of the dt s eigenvalues eigenvectors or both because eigendecompositions are highly nonlinear existing likelihood ratio statistics lrts for testing differences in eigenvalues or eigenvectors of means of gaussian symmetric matrices assume an orthogonally invariant covariance structure between the matrix entries while retaining the form of the lrts we derive new approximations to their true distributions when the covariance between the dt entries is arbitrary and possibly different between the two groups the approximate distributions are those of similar lrt statistics comput