extremes of moving averages of random variables with finite endpoint where zj are iid and nonnegative random variables and c 0 are constants satisfying summability conditions at least sufficient to make the random series above converge we suppose that the distribution of zj is regularly varying near 0 and discuss lower tail behavior of finite and infinite linear combinations the behavior is quite different in the two cases for finite linear combinations the lower tail is again regularly varying but for infinite moving averages the lower tail is f varying i e it is in the domain of attraction of a type i extreme value distribution in the sense of minima convergence of point processes based on the moving averages is shown to hold in both the finite and infinite order cases and suitable conclusions are drawn from such convergences a useful analytic tool is asymptotic normality of the esscher transform of the common distribution of the z s the extreme value results of this paper are in terms of minima of the moving average processes but results can be adapted to study maxima of moving averages of random variables in the domain of attraction of the type iii extreme value distribution for maxima

false discovery rate adjusted charting schemes for multistage process monitoring and fault identification most statistical process control research focuses on single stage processes this article considers the problem of multistage process monitoring and fault identification this problem is formulated as a multiple hypotheses testing problem however as the number of stages increases the detection power of multiple hypotheses testing methods that seek to control the type i error rate decreases dramatically to maintain the detection power we use a false discovery rate fdr control approach which is widely used in microarray research two multistage process monitoring and fault identification schemes an fdr adjusted shewhart chart and an fdr adjusted cumulative sum cusum chart are established to apply the fdr approach the distribution of the cusum statistics are obtained based on markov chain theory and brownian motion with drift models the detection and fault identification power of the new schemes are evaluated by the monte carlo method the results indicate that the novel fdr adjusted approaches

multiple testing for pattern identification with applications to microarray time course experiments in time course experiments it is often desirable to identify genes that exhibit a specific pattern of differential expression over time and thus gain insights into the mechanisms of the underlying biological processes two challenging issues in the pattern identification problem are i how to combine the simultaneous inferences across multiple time points and ii how to control the multiplicity while accounting for the strong dependence we formulate a compound decision theoretic framework for set wise multiple testing and propose a data driven procedure that aims to minimize the missed set rate subject to a constraint on the false set rate the hidden markov model proposed in yuan and kendziorski 2006 is generalized to capture the temporal correlation in the gene expression data both theoretical and numerical results are presented to show that our data driven procedure controls the multiplicity provides an optimal way of combining simultaneous inferences across multiple time points and greatly i

empirical bayes confidence intervals for selected parameters in high dimensional data modern statistical problems often involve a large number of populations and hence a large number of parameters that characterize these populations it is common for scientists to use data to select the most significant populations such as those with the largest t statistics the scientific interest often lies in studying and making inferences regarding these parameters called the selected parameters corresponding to the selected populations the current statistical practices either apply a traditional procedure assuming there were no selection a practice that is not valid or they use the bonferroni type procedure that is valid but very conservative and often noninformative in this article we propose valid and sharp confidence intervals that allow scientists to select parameters and to make inferences for the selected parameters based on the same data this type of confidence interval allows the users to zero in on the most interesting selected parameters without collecting more data the validity of

empirical bayes false coverage rate controlling confidence intervals summary benjamini and yekutieli suggested that it is important to account for multiplicity correction for confidence intervals when only some of the selected intervals are reported they introduced the concept of the false coverage rate fcr for confidence intervals which is parallel to the concept of the false discovery rate in the multiple hypothesis testing problem and they developed confidence intervals for selected parameters which control the fcr their approach requires the fcr to be controlled in the frequentist s sense i e controlled for all the possible unknown parameters in modern applications the number of parameters could be large as large as tens of thousands or even more as in microarray experiments we propose a less conservative criterion the bayes fcr and study confidence intervals controlling it for a class of distributions the bayes fcr refers to the average fcr with respect to a distribution of parameters under such a criterion we propose some confidence intervals which by some analytic and numerical calculations are demonstrated to have the bayes fcr controlled at level q for a class of prior distributions including mixtures of normal distributions and zero where the mixing probability is unknown the confidence intervals are shrinkage type procedures which are more efficient for the is that have a sparsity structure which is a common feature of microarray data more importantly the centre of the proposed shrinkage intervals reduces much of the bias due to selection consequently the proposed empirical bayes intervals are always shorter in average length than the intervals of benjamini and yekutieli and can be only 50 or 60 as long in some cases we apply these procedures to the data of choe and colleagues and obtain similar results

simultaneous confidence intervals for comparing binomial parameters summary to compare proportions with several independent binomial samples we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic it applies to a variety of measures including the difference of proportions odds ratio and relative risk for the odds ratio a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the bonferroni implementation of wald or exact small sample pairwise intervals it performs well even for the problematic but practically common case in which the binomial parameters are relatively small for the difference of proportions the proposed method has performance comparable to a method proposed by piegorsch 1991 biometrics 47 45 52

convergence of neural networks for programming problems via a nonsmooth lojasiewicz inequality this paper considers a class of neural networks nns for solving linear programming lp problems convex quadratic programming qp problems and nonconvex qp problems where an indefinite quadratic objective function is subject to a set of affine constraints the nns are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic which enable to implement an exact penalty method a new method is exploited to address convergence of trajectories which is based on a nonsmooth lstrokojasiewicz inequality for the generalized gradient vector field describing the nn dynamics the method permits to prove that each forward trajectory of the nn has finite length and as a consequence it converges toward a singleton furthermore by means of a quantitative evaluation of the lstrokojasiewicz exponent at the equilibrium points the following results on convergence rate of trajectories are established 1 for nonconvex qp problems each trajectory is either exponentially convergent or convergent in finite time toward a singleton belonging to the set of constrained critical points 2 for convex qp problems the same result as in 1 holds moreover the singleton belongs to the set of global minimizers and 3 for lp problems each trajectory converges in finite time to a singleton belonging to the set of global minimizers these results which improve previous results obtained via the lyapunov approach are true independently of the nature of the set of equilibrium points and in particular they hold even when the nn possesses infinitely many nonisolated equilibrium points

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

exact post selection inference with application to the lasso we develop a general approach to valid inference after model selection in a nutshell our approach produces post selection inferences with the same frequency guarantees as those given by data splitting but are more powerful at the core of our framework is a result that characterizes the distribution of a post selection estimator conditioned on the selection event we specialize the approach to model selection by the lasso to form valid condence intervals for the selected coecients and test whether all relevant variables have been included in the model

extreme value theory for moving average processes this paper studies extreme values in infinite moving average processes x t sum lambda c lambda t z lambda defined from an i i d noise sequence z lambda in particular this includes the arma processes often used in time series analysis a fairly complete extremal theory is developed for the cases when the d f of the z lambda s has a smooth tail which decreases approximately as exp z p as z rightarrow infty for 0 p infty or as a power of z the influence of the averaging on extreme values depends on p and the c lambda s in a rather intricate way for p 2 which includes normal sequences the correlation function r t sum lambda c lambda t c lambda sum lambda c 2 lambda determines extremal behavior while perhaps more surprisingly for p neq 2 correlations have little bearing on extremes further the sample paths of x t near extreme values asymptotically assume a specific nonrandom form which again depends on p and c lambda in an interesting way one use of this latter result is as an informal quantitative check of a fitted moving average or arma model by comparing the sample path behavior predicted by the model with the observed sample paths

simultaneous confidence intervals uniformly more likely to determine signs many studies draw inferences about multiple endpoints but ignore the statistical implications of multiplicity effects inferred to be positive when there is no adjustment for multiplicity can lose their statistical significance when multiplicity is taken into account perhaps explaining why such adjustments are so often omitted we develop new simultaneous confidence intervals that mitigate this problem these are uniformly more likely to determine signs than are standard simultaneous confidence intervals when one or more of the parameter estimates are small the new intervals sacrifice some length to avoid crossing zero but when all the parameter estimates are large the new intervals coincide with standard simultaneous confidence intervals so there is no loss of precision when only a small fraction of the estimates are small the procedure can determine signs essentially as well as one sided tests with prespecified directions incurring only a modest penalty in maximum length the intervals are constructed by inverting level tests to form a 1 confidence set and then projecting that set onto the coordinate axes to get confidence intervals the tests have hyper rectangular acceptance regions that minimize the maximum amount by which the acceptance region protrudes from the orthant that contains the hypothesized parameter value subject to a constraint on the maximum side length of the hyper rectangle copyright 2013 oxford university press

adjusted bayesian inference for selected parameters summary we address the problem of providing inference from a bayesian perspective for parameters selected after viewing the data we present a bayesian framework for providing inference for selected parameters based on the observation that providing bayesian inference for selected parameters is a truncated data problem we show that if the prior for the parameter is non informative or if the parameter is a fixed unknown constant then it is necessary to adjust the bayesian inference for selection our second contribution is the introduction of bayesian false discovery rate controlling methodology which generalizes existing bayesian false discovery rate methods that are only defined in the two group mixture model we illustrate our results by applying them to simulated data and data from a microarray experiment

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

on the lower tail probabilities of some random series the behavior of tail probabilities p s r r 0 is investigated where s is a series s j z j generated by some sequence of positive numbers j and by a sequence z j of independent copies of a positive random variable z we present the exact asymptotic expression for p s r by means of laplace transform eexp s under weak assumptions on the behavior of the tail probabilities of z in the vicinity of zero the bounds of accuracy are also given and under weak supplementary smoothness conditions the asymptotic properties of the density of s are investigated

the benjamini hochberg method with infinitely many contrasts in linear models summary benjamini and hochberg s method for controlling the false discovery rate is applied to the problem of testing infinitely many contrasts in linear models exact easily calculated critical values are derived defining a new multiple comparisons method for testing contrasts in linear models the method is adaptive depending on the data through the f statistic like the waller duncan bayesian multiple comparisons method comparisons with scheffes method are given and the method is extended to the simultaneous confidence intervals of benjamini and yekutieli testing contrasts of a variety of types is a standard practice in the analysis of variance leading to the problem of multiple comparisons and multiple tests this issue is also controversial with much literature that is not completely reviewed here hochberg and tamhane 1987 is a good general reference for multiple comparisons methods that control the familywise error rate benjamini and hochberg 1995 introduced a method to control the false discovery rate and an extension of this method to confidence intervals for selected significant parameters is given by benjamini and yekutieli 2005 a common modem thread in the literature is the small n large k case in which the number of tests k is large and the sample size n is small we provide an exact characterization of the problem of testing infinitely many contrasts k oo in linear models using the benjamini hochberg method for fixed possibly small n the characterization is completely nonparametric without distributional assumptions concerning the data generating process instead we assume that the contrasts tested are a random sample from contrast space the resulting infinite contrasts characterization of the benjamini hochberg method is shown surprisingly to depend on the data

strong control conservative point estimation and simultaneous conservative consistency of false discovery rates a unified approach summary the false discovery rate fdr is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses benjamini and hochberg introduced this quantity and proved that a particular step up p value method controls the fdr storey introduced a point estimate of the fdr for fixed significance regions the former approach conservatively controls the fdr at a fixed predetermined level and the latter provides a conservatively biased estimate of the fdr for a fixed predetermined significance region in this work we show in both finite sample and asymptotic settings that the goals of the two approaches are essentially equivalent in particular the fdr point estimates can be used to define valid fdr controlling procedures in the asymptotic setting we also show that the point estimates can be used to estimate the fdr conservatively over all significance regions simultaneously which is equivalent to controlling the fdr at all levels simultaneously the main tool that we use is to translate existing fdr methods into procedures involving empirical processes this simplifies finite sample proofs provides a framework for asymptotic results and proves that these procedures are valid even under certain forms of dependence

hierarchical false discovery rate controlling methodology we discuss methodology for controlling the false discovery rate fdr in complex large scale studies that involve testing multiple families of hypotheses the tested hypotheses are arranged in a tree of disjoint subfamilies and the subfamilies of hypotheses are hierarchically tested by the benjamini and hochberg fdr controlling bh procedure we derive an approximation for the multiple family fdr for independently distributed test statistics q the level at which the bh procedure is applied times the number of families tested plus the number of discoveries divided by the number of discoveries plus 1 we provide a universal bound for the fdr of the discoveries in the new hierarchical testing approach 2 1 44 q and demonstrate in simulations that when the data has an hierarchical structure the new testing approach can be considerably more powerful than the bh procedure

an analysis of a neural dynamical approach to solving optimization problems recently a neural dynamical approach to solving linearly constrained variational inequality problems is presented and its stability and convergence are conjectured by simulation this technical note analyzes the global stability and convergence of the neural dynamical approach theoretically it is shown that the neural dynamical approach is convergent globally to a solution when the nonlinear mapping is monotone at the solution unlike existing convergence results of neural dynamical methods for solving linearly or nonlinearly variational inequalities our main results don t assume the differentiability condition of the nonlinear mapping therefore the neural dynamical approach can be further guaranteed to solve linearly constrained monotone variational inequality problems with a non smooth mapping comparsions and examples illustrative significance of the obtained results on non smooth mapping

multiple testing of composite null hypotheses in heteroscedastic models in large scale studies the true effect sizes often range continuously from zero to small to large and are observed with heteroscedastic errors in practical situations where the failure to reject small deviations from the null is inconsequential specifying an indifference region or forming composite null hypotheses can greatly reduce the number of unimportant discoveries in multiple testing the heteroscedasticity issue poses new challenges for multiple testing with composite nulls in particular the conventional framework in multiple testing which involves rescaling or standardization is likely to distort the scientific question we propose the concept of a composite null distribution for heteroscedastic models and develop an optimal testing procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate the proposed approach is different from conventional methods in that the effect size statistical significance and multiplicity issues are addressed in

controlling false discoveries in multidimensional directional decisions with applications to gene expression data on ordered categories microarray gene expression studies over ordered categories are routinely conducted to gain insights into biological functions of genes and the underlying biological processes some common experiments are time course dose response experiments where a tissue or cell line is exposed to different doses and or durations of time to a chemical a goal of such studies is to identify gene expression patterns profiles over the ordered categories this problem can be formulated as a multiple testing problem where for each gene the null hypothesis of no difference between the successive mean gene expressions is tested and further directional decisions are made if it is rejected much of the existing multiple testing procedures are devised for controlling the usual false discovery rate fdr rather than the mixed directional fdr mdfdr the expected proportion of type i and directional errors among all rejections benjamini and yekutieli 2005 journal of the american statistical association 100 71 93 proved that an augmentation of the usual benjamini hochberg bh procedure can control the mdfdr while testing simple null hypotheses against two sided alternatives in terms of one dimensional parameters in this article we consider the problem of controlling the mdfdr involving multidimensional parameters to deal with this problem we develop a procedure extending that of benjamini and yekutieli based on the bonferroni test for each gene a proof is given for its mdfdr control when the underlying test statistics are independent across the genes the results of a simulation study evaluating its performance under independence as well as under dependence of the underlying test statistics across the genes relative to other relevant procedures are reported finally the proposed methodology is applied to a time course microarray data obtained by lobenhofer et al 2002 molecular endocrinology 16 1215 1229 we identified several important cell cycle genes such as dna replication repair gene mcm4 and replication factor subunit c2 which were not identified by the previous analyses of the same data by lobenhofer et al 2002 and peddada et al 2003 bioinformatics 19 834 841 although some of our findings overlap with previous findings we identify several other genes that complement the results of lobenhofer et al 2002

operating characteristics and extensions of the false discovery rate procedure summary we investigate the operating characteristics of the benjamini hochberg false discovery rate procedure for multiple testing this is a distribution free method that controls the expected fraction of falsely rejected null hypotheses among those rejected the paper provides a framework for understanding more about this procedure we first study the asymptotic properties of the deciding point d that determines the critical p value from this we obtain explicit asymptotic expressions for a particular risk function we introduce the dual notion of false non rejections and we consider a risk function that combines the false discovery rate and false non rejections we also consider the optimal procedure with respect to a measure of conditional risk

estimating the null distribution to adjust observed confidence levels for genome scale screening summary in a novel approach to the multiple testing problem efron 2004 journal of the american statistical association 99 96 104 2007a journal of the american statistical association 102 93 103 2007b annals of statistics 35 1351 1377 formulated estimators of the distribution of test statistics or nominal p values under a null distribution suitable for modeling the data of thousands of unaffected genes nonassociated single nucleotide polymorphisms or other biological features estimators of the null distribution can improve not only the empirical bayes procedure for which it was originally intended but also many other multiple comparison procedures such estimators in some cases improve the proposed multiple comparison procedure mcp based on a recent non bayesian framework of minimizing expected loss with respect to a confidence posterior a probability distribution of confidence levels the flexibility of that mcp is illustrated with a nonadditive loss function designed for genomic screening rather than for validation the merit of estimating the null distribution is examined from the vantage point of the confidence posterior mcp cpmcp in a generic simulation study of genome scale multiple testing conditioning the observed confidence level on the estimated null distribution as an approximate ancillary statistic markedly improved conditional inference specifically simulating gene expression data however indicates that estimation of the null distribution tends to exacerbate the conservative bias that results from modeling heavy tailed data distributions with the normal family to enable researchers to determine whether to rely on a particular estimated null distribution for inference or decision making an information theoretic score is provided as the sum of the degree of ancillarity and the degree of inferential relevance the score reflects the balance conditioning would strike between the two conflicting terms the cpmcp and other methods introduced are applied to gene expression microarray data

simultaneous confidence intervals that are compatible with closed testing in adaptive designs we describe a general method for finding a confidence region for a parameter vector that is compatible with the decisions of a two stage closed test procedure in an adaptive experiment the closed test procedure is characterized by the fact that rejection or nonrejection of a null hypothesis may depend on the decisions for other hypotheses and the compatible confidence region will in general have a complex nonrectangular shape we find the smallest cross product of simultaneous confidence intervals containing the region and provide computational shortcuts for calculating the lower bounds on parameters corresponding to the rejected null hypotheses we illustrate the method with an adaptive phase ii iii clinical trial

limit theory for moving averages of random variables with regularly varying tail probabilities let z k infty k infty be iid where the z k s have regularly varying tail probabilities under mild conditions on a real sequence c j j geq 0 the stationary process x n sum infty j 0 c jz n j n geq 1 exists a point process based on x n converges weakly and from this a host of weak limit results for functionals of x n ensue we study sums extremes excedences and first passages as well as behavior of sample covariance functions

empirical bayes analysis of a microarray experiment microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels a typical microarray experiment can produce millions of data points raising serious problems of data reduction and simultaneous inference we consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes a simple nonparametric empirical bayes model is introduced which is used to guide the efficient reduction of the data to a single summary statistic per gene and also to make simultaneous inferences concerning which genes were affected by the radiation although our focus is on one specific experiment the proposed methods can be applied quite generally the empirical bayes inferences are closely related to the frequentist false discovery rate fdr criterion

hierarchical control of false discovery rate for phase locking measures of eeg synchrony computing phase locking values plvs between eeg signals is becoming a popular measure for quantifying functional connectivity because it affords a more detailed picture of the synchrony relationships between channels at different times and frequencies however the accompanying increase in data dimensionality incurs a serious multiple testing problem for determining plv significance standard methods for controlling type i error which treat all hypotheses as belonging to a single family can fail to detect any significant discoveries instead we propose a novel application of a hierarchical fdr method which subsumes multiple families for detecting significant plv effects for simulations and experimental data we show that the proposed hierarchical fdr method is most powerful this method revealed significant synchrony effects in the expected regions at an acceptable error rate of 5 where other methods including standard fdr correction failed to reveal any significant effects

generalized fiducial inference for binary logistic item response models generalized fiducial inference gfi has been proposed as an alternative to likelihood based and bayesian inference in mainstream statistics confidence intervals cis can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a bayesian posterior distribution however no prior distribution needs to be specified which renders gfi more suitable when no a priori information about model parameters is available in the current paper we apply gfi to a family of binary logistic item response theory models which includes the two parameter logistic 2pl bifactor and exploratory item factor models as special cases asymptotic properties of the resulting fiducial distribution are discussed random draws from the fiducial distribution can be obtained by the proposed markov chain monte carlo sampling algorithm we investigate the finite sample performance of our fiducial percentile ci and two commonly used wald type cis associated with maximum likelihood ml estimation via monte carlo simulation the use of gfi in high dimensional exploratory item factor analysis was illustrated by the analysis of a set of the eysenck personality questionnaire data

selective inference on multiple families of hypotheses summary in many complex multiple testing problems the hypotheses are divided into families given the data families with evidence for true discoveries are selected and hypotheses within them are tested neither controlling the error rate in each family separately nor controlling the error rate over all hypotheses together can assure some level of confidence about the filtration of errors within the selected families we formulate this concern about selective inference in its generality for a very wide class of error rates and for any selection criterion and present an adjustment of the testing level inside the selected families that retains control of the expected average error over the selected families

optimal confidence sets bioequivalence and the limacon of pascal abstract we begin with a decision theoretic investigation into confidence sets that minimize expected volume at a given parameter value such sets are constructed by inverting a family of uniformly most powerful tests and hence they also enjoy the optimality property of being uniformly most accurate in addition these sets possess bayesian optimal volume properties and represent the first case to our knowledge of a frequentist 1 confidence set that possesses a bayesian optimality property the hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing our sets are optimal for testing bioequivalence in certain settings in the case of the normal distribution the optimal set is a curve known as the limacon of pascal we illustrate the use of these curves with a biopharmaceutical example

a novel recurrent neural network for solving nonlinear optimization problems with inequality constraints this paper presents a novel recurrent neural network for solving nonlinear optimization problems with inequality constraints under the condition that the hessian matrix of the associated lagrangian function is positive semidefinite it is shown that the proposed neural network is stable at a karush kuhn tucker point in the sense of lyapunov and its output trajectory is globally convergent to a minimum solution compared with variety of the existing projection neural networks including their extensions and modification for solving such nonlinearly constrained optimization problems it is shown that the proposed neural network can solve constrained convex optimization problems and a class of constrained nonconvex optimization problems and there is no restriction on the initial point simulation results show the effectiveness of the proposed neural network in solving nonlinearly constrained optimization problems

a coverage theory for least squares summary a sensible use of an estimation method requires that assessment criteria for the quality of the estimate be available we present a coverage theory for the least squares estimate by suitably modifying the empirical costs one constructs statistics that are guaranteed to cover with known probability the cost associated with a next still unseen member of the population all results of this paper are distribution free and can be applied to least squares problems in use across a variety of fields

false discovery rate adjusted multiple confidence intervals for selected parameters often in applied research confidence intervals cis are constructed or reported only for parameters selected after viewing the data we show that such selected intervals fail to provide the assumed coverage probability by generalizing the false discovery rate fdr approach from multiple testing to selected multiple cis we suggest the false coverage statement rate fcr as a measure of interval coverage following selection a general procedure is then introduced offering fcr control at level q under any selection rule the procedure constructs a marginal ci for each selected parameter but instead of the confidence level 1 q being used marginally q is divided by the number of parameters considered and multiplied by the number selected if we further use the fdr controlling testing procedure of benjamini and hochberg for selecting the parameters the newly suggested procedure offers cis that are dual to the testing procedure and are shown to be optimal in the independent case under the positive re

testing multiple hypotheses with skewed alternatives in many practical cases of multiple hypothesis problems it can be expected that the alternatives are not symmetrically distributed if it is known a priori that the distributions of the alternatives are skewed we show that this information yields high power procedures as compared to the procedures based on symmetric alternatives when testing multiple hypotheses we propose a bayesian decision theoretic rule for multiple directional hypothesis testing when the alternatives are distributed as skewed under a constraint on a mixed directional false discovery rate we compare the proposed rule with a frequentist s rule of benjamini and yekutieli 2005 using simulations we apply our method to a well studied hiv dataset

development and analysis of a neural dynamical approach to nonlinear programming problems this technical note develops a neural dynamical approach to nonlinear programming np problems whose equilibrium points coincide with karush kuhn tucker points of the np problem a rigorous analysis on the global convergence and the convergence rate of the proposed neural dynamical approach is carried out under the condition that the associated lagrangian function is convex analysis results show that the proposed neural dynamical approach can solve general convex programming problems and a class of nonconvex programming problems two nonconvex programming examples are provided to demonstrate the performance of the developed neural dynamical approach

adaptive linear step up procedures that control the false discovery rate we provide a new two stage procedure in which the linear step up procedure is used in stage one to estimate mo providing a new level q which is used in the linear step up procedure in the second stage we prove that a general form of the two stage procedure controls the false discovery rate at the desired level q this framework enables us to study analytically the properties of other procedures that exist in the literature a simulation study is presented that shows that two stage adaptive procedures improve in power over the original procedure mainly because they provide tighter control of the false discovery rate we further study the performance of the current suggestions some variations of the procedures and previous suggestions in the case where the test statistics are positively dependent a case for which the original procedure controls the false discovery rate in the setting studied here the newly proposed two stage procedure is the only one that controls the false discovery rate the procedures are illustrated with two examples of biological importance

discovering the false discovery rate summary i describe the background for the paper controlling the false discovery rate a new and powerful approach to multiple comparisons by benjamini and hochberg that was published in the journal of the royal statistical society series b in 1995 i review the progress since made on the false discovery rate as well as the major conceptual developments that followed

stability and convergence analysis for a class of neural networks in this paper we analyze and establish the stability and convergence of the dynamical system proposed by xia and feng whose equilibria solve variational inequality and related problems under the pseudo monotonicity and other conditions this system is proved to be stable in the sense of lyapunov and converges to one of its equilibrium points for any starting point meanwhile the global exponential stability of this system is also shown under some mild conditions without the strong monotonicity of the mapping the obtained results improve and correct some existing ones the validity and performance of this system are demonstrated by some numerical examples

a bayesian perspective on the bonferroni adjustment summary bayes frequentist correspondences between the p value and the posterior probability of the null hypothesis have been studied in univariate hypothesis testing situations this paper extends these comparisons to multiple testing and in particular to the bonferroni multiple testing method in which p values are adjusted by multiplying by k the number of tests considered in the bayesian setting prior assessments may need to be adjusted to account for multiple hypotheses resulting in corresponding adjustments to the posterior probabilities conditions are given for which the adjusted posterior probabilities roughly correspond to bonferroni adjusted p values

an analysis of a class of neural networks for solving linear programming problems a class of neural networks that solve linear programming problems is analyzed the neural networks considered are modeled by dynamic gradient systems that are constructed using a parametric family of exact nondifferentiable penalty functions it is proved that for a given linear programming problem and sufficiently large penalty parameters any trajectory of the neural network converges in finite time to its solution set for the analysis lyapunov type theorems are developed for finite time convergence of nonsmooth sliding mode dynamic systems to invariant sets the results are illustrated via numerical simulation examples

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

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

irrational exuberance correcting bias in probability estimates we consider the common setting where one observes probability estimates for a large number of events such as default risks for numerous bonds unfortunately even with unbiased estimates selectin

minima of h valued gaussian processes we study low local extremes of gaussian random fields with values in a separable hilbert space and constant variance our results are sharp for certain stationary processes on the line and for these processes we also prove global limits

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

an empirical bayes method for chi squared data in a thought provoking paper efron investigated the merit and limitation of an empirical bayes method to correct selection bias based on tweedie s formula first reported in the study by robbins t

empirical bayes estimates for large scale prediction problems classical prediction methods such as fisher s linear discriminant function were designed for small scale problems in which the number of predictors n is much smaller than the number of observations n modern scientific devices often reverse this situation a microarray analysis for example might include n 100 subjects measured on n 10 000 genes each of which is a potential predictor this article proposes an empirical bayes approach to large scale prediction where the optimum bayes prediction rule is estimated employing the data from all of the predictors microarray examples are used to illustrate the method the results demonstrate a close connection with the shrunken centroids algorithm of tibshirani et al 2002 a frequentist regularization approach to large scale prediction and also with false discovery rate theory

exponential rm h _ infty synchronization of general discrete time chaotic neural networks with or without time delays this brief studies exponential h synchronization of a class of general discrete time chaotic neural networks with external disturbance on the basis of the drive response concept and h control theory and using lyapunov krasovskii or lyapunov functional state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays but also reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities most discrete time chaotic systems with or without time delays such as hopfield neural networks cellular neural networks bidirectional associative memory networks recurrent multilayer perceptrons cohen grossberg neural networks chua s circuits etc can be transformed into this general chaotic neural network to be h synchronization controller designed in a unified way finally some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods

should annual maximum temperatures follow a generalized extreme value distribution summary motivated by the study of annual temperature extremes two new results on the limiting distribution of block maxima of random variables with varying upper bounds are obtained one gives a generalized extreme value distribution as the limit but with a different shape parameter from that obtained when the bound on the random variables does not vary the other gives a limiting distribution that is only a generalized extreme value in certain cases both results consider triangular arrays of random variables in order to mimic the property of an upper bound that changes slowly with the day of the year as seems to occur for temperature data at many locations an analysis of 140 years of daily temperatures in new york city shows mixed results in terms of the ability of the theory presented here to provide new insights into the behaviour of extreme temperatures at this location

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

screening for partial conjunction hypotheses summary we consider the problem of testing for partial conjunction of hypothesis which argues that at least u out of n tested hypotheses are false it offers an in between approach to the testing of the conjunction of null hypotheses against the alternative that at least one is not and the testing of the disjunction of null hypotheses against the alternative that all hypotheses are not null we suggest powerful test statistics for testing such a partial conjunction hypothesis that are valid under dependence between the test statistics as well as under independence we then address the problem of testing many partial conjunction hypotheses simultaneously using the false discovery rate fdr approach we prove that if the fdr controlling procedure in benjamini and hochberg 1995 journal of the royal statistical society series b 57 289 300 is used for this purpose the fdr is controlled under various dependency structures moreover we can screen at all levels simultaneously in order to display the findings on a superimposed map and still control an appropriate fdr measure we apply the method to examples from microarray analysis and functional magnetic resonance imaging fmri two application areas where the need for partial conjunction analysis has been identified

constructing confidence intervals for selected parameters in large scale problems it is common practice to select important parameters by a procedure such as the benjamini and hochberg procedure and construct confidence intervals cis for further investigation while the false coverage statement rate fcr for the cis is controlled at a desired level although the well known by cis control the fcr they are uniformly inflated in this paper we propose two methods to construct shorter selective cis the first method produces shorter cis by allowing a reduced number of selective cis the second method produces shorter cis by allowing a prefixed proportion of cis containing the values of uninteresting parameters we theoretically prove that the proposed cis are uniformly shorter than by cis and control the fcr asymptotically for independent data numerical results confirm our theoretical results and show that the proposed cis still work for correlated data we illustrate the advantage of the proposed procedures by analyzing the microarray data from a hiv study

selective inference with unknown variance via the square root lasso summarythere has been much recent work on inference after model selection in situations where the noise level is known however the error variance is rarely known in practice and its estimation is difficult in high dimensional settings in this work we propose using the square root lasso also known as the scaled lasso to perform inference for selected coefficients and the noise level simultaneously the square root lasso has the property that the choice of a reasonable tuning parameter does not depend on the noise level in the data we provide valid p values and confidence intervals for coefficients after variable selection and estimates for the model specific variance our estimators perform better in simulations than other estimators of the noise variance these results make inference after model selection significantly more applicable

selection adjusted confidence intervals with more power to determine the sign in many current large scale problems confidence intervals cis are constructed only for the parameters that are large as indicated by their estimators ignoring the smaller parameters such selective inference poses a problem to the usual marginal cis that no longer offer the right level of coverage not even on the average over the selected parameters we address this problem by developing three methods to construct short and valid cis for the location parameter of a symmetric unimodal distribution while conditioning on its estimator being larger than some constant threshold in two of these methods the ci is further required to offer early sign determination that is to avoid including parameters of both signs for relatively small values of the estimator one of the two the conditional quasi conventional ci offers a good balance between length and sign determination while protecting from the effect of selection the ci is not symmetric extending more toward 0 than away from it nor is it of con

conjunction group analysis an alternative to mixed random effect analysis we address the problem of testing in every brain voxel v whether at least u out of n conditions or subjects considered shows a real effect the only statistic suggested so far the maximum p value method fails under dependency unless u n and in particular under positive dependency that arises if all stimuli are compared to the same control stimulus moreover it tends to have low power under independence for testing that at least u out of n conditions shows a real effect we suggest powerful test statistics that are valid under dependence between the individual condition p values as well as under independence and other test statistics that are valid under independence we use the above approach replacing conditions by subjects to produce informative group maps and thereby offer an alternative to mixed random effect analysis