discrete laguerre gaussian transforms and their applications laguerre gaussian functions serve as a complete and orthonormal basis for a variety of physical problems such as 2d isotropic quantum harmonic oscillators and circularly symmetric laser modes in this paper we propose discrete laguerre gaussian functions which are defined such that some elegant physical properties are preserved and a fast computation algorithm of complexity o n log n is available discrete laguerre gaussian transforms as introduced in this paper inherit nice properties from discrete laguerre gaussian functions and admit signal analysis over circularly symmetric patterns it is demonstrated through examples that discrete laguerre gaussian transforms find applications in circular pattern keypoints selection object detection image compression rotational invariance feature for pattern recognition and rotational angle estimation

resolution bias errors in spectral density frequency response and coherence function measurements vi non white noise at the input the general theory of spectral estimation presented in a previous part of this series of papers is applied exemplarily to the case of a non white 1 f 2 noise excited rc low pass filter it is shown that the differences compared to the case of white noise excitation observed in the frequency response and coherence estimates are small if the hanning or another continuous window is used but that they can become drastic for the rectangular window experimental results are in accord with the theoretical prediction further experiments with an electrical lrc resonance circuit second order system show that the same applies in this case

simultaneous inference for high dimensional linear models abstractthis article proposes a bootstrap assisted procedure to conduct simultaneous inference for high dimensional sparse linear models based on the recent desparsifying lasso estimator our procedure allows the dimension of the parameter vector of interest to be exponentially larger than sample size and it automatically accounts for the dependence within the desparsifying lasso estimator moreover our simultaneous testing method can be naturally coupled with the margin screening to enhance its power in sparse testing with a reduced computational cost or with the step down method to provide a strong control for the family wise error rate in theory we prove that our simultaneous testing procedure asymptotically achieves the prespecified significance level and enjoys certain optimality in terms of its power even when the model errors are non gaussian our general theory is also useful in studying the support recovery problem to broaden the applicability we further extend our main results to general

hierarchical testing in the high dimensional setting with correlated variables we propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high dimensional linear model in presence of highly correlated variables as is very common in high dimensional data it seems indispensable to go beyond an approach of inferring individual regression coefficients and we show that detecting smallest groups of variables mtds minimal true detections is realistic thanks to the hierarchy among the groups of variables powerful multiple testing adjustment is possible which leads to a data driven choice of the resolution level for the groups our procedure based on repeated sample splitting is shown to asymptotically control the familywise error rate and we provide empirical results for simulated and real data which complement the theoretical analysis supplementary materials for this article are available online

resolution bias errors in spectral density frequency response and coherence function measurements iii application to second order systems white noise excitation a general theory of spectral estimation given in a previous paper is applied to second order systems such as a simple spring mass system where either the displacement velocity or acceleration of the vibrating mass may be considered as the output signals by means of approximate formulas an extensive bias error discussion of frequency response output power spectral density and coherence estimates is given which clarifies characteristic differences between spectral estimators obtained with the rectangular window on the one hand and the hanning window or another continuous window on the other hand in particular characteristic coherence notches in the measurement of resonance systems as reported in the literature are explained from first principles all of the theoretical predictions are verified experimentally to great accuracy by using electrical lrc resonance circuits which are equivalent to the respective mechanical systems

adapting to unknown sparsity by controlling the false discovery rate we attempt to recover an n dimensional vector observed in white noise where n is large and the vector is known to be sparse but the degree of sparsity is unknown we consider three different ways of defining sparsity of a vector using the fraction of nonzero terms imposing power law decay bounds on the ordered entries and controlling the lp norm for p small we obtain a procedure which is asymptotically minimax for l r loss simultaneously throughout a range of such sparsity classes the optimal procedure is a data adaptive thresholding scheme driven by control of the false discovery rate fdr fdr control is a relatively recent innovation in simultaneous testing ensuring that at most a certain fraction of the rejected null hypotheses will correspond to false rejections in our treatment the fdr control parameter qn also plays a determining role in asymptotic minimaxity if q lim qn 0 1 2 and also qn log n we get sharp asymptotic minimaxity simultaneously over a wide range of sparse parameter spaces and loss functions on the other hand q lim qn 1 2 1 forces the risk to exceed the minimax risk by a factor growing with q to our knowledge this relation between ideas in simultaneous inference and asymptotic decision theory is new our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors these new rules impose complexity penalization of the form 2 log potential model size actual model size we exhibit a close connection with fdr controlling procedures under stringent control of the false discovery rate

resolution bias errors in spectral density frequency response and coherence function measurements i general theory a general theory of resolution bias errors inherent in the usual ensemble segment averaging estimation procedure for spectral density frequency response and coherence functions has been developed it is shown that the estimation procedure is mathematically equivalent to a situation where the true correlation functions would be modified in a specified manner that is they would be multiplied with the normalized autocorrelation function of the window function and transformed into the frequency domain to yield the spectral density estimates the theory is worked out for an arbitrary ideal linear and time invariant system which is driven by a stationary stochastic input and for an arbitrary window function specifically the rectangular and hanning windows are compared with each other and the theoretical results are verified experimentally to great accuracy by using electrical rc and lrc circuits and a true random noise generator see later parts of this series of papers furthermore as an application of the theory approximate formulas for the bias errors of spectral estimators are derived and discussed thus extending some older results given in the literature

estimation of fmri response delays we present an efficient algorithm using the hilbert transform for estimating the delay of the bold response to neuronal stimulation with minimal additional computations the algorithm estimates parameters generated in the widely used cross correlation method and simplifies the interpolation required to estimate the response delay from the cross correlation function we examined errors in the hilbert based delay estimate associated with the use of dft on short duration discrete signals and proposed a method for minimizing these errors furthermore we compared the delay estimates obtained with the hilbert method to those obtained using the onset of the bold response the hilbert method resulted in less variance in the delay estimate despite the potential for higher variability in the latter part of the bold response this improved delay estimate was attributed to the reduced sensitivity of the hilbert method to noise contamination compared to the onset method

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

characterization of dose response relationships inferred by statistically significant trend tests summary a method is proposed for classifying various experimental outcomes associated with statistically significant trend tests according to a set of results of sequential testing within a family of closed under intersections one sided tests the intent of the procedure is to characterize the general shape of implied dose response relationships taking care neither to inflate the false positive type i error rate by overtesting nor to sacrifice power by overadjusting for mulitple comparisons

an improved bonferroni inequality and applications summary we present an improved bonferroni inequality which gives an upper bound for the probability of the union of an arbitrary sequence of events the bound is constructed in terms of the joint probability of pairs of events which are represented by edges on a graph examples of applications to periodicity location shift detection kolmogorovsmirnov tests and outlier detection are given

on asymmetrical performance of discrete cosine transform the discrete cosine transform dct is considered as a suboptimum transform for many practical source coding applications autoregressive order 1 ar 1 source models are good first approximations to several natural signals it is known that the performance of the dct depends on the sign of the autocorrelation coefficient of the ar 1 source the authors explain theoretically this asymmetrical performance of the dct as well as the behavior of the modified hermite transform mht and the discrete hadamard transform dht which perform symmetrically regardless of the sign of the autocorrelation coefficient

constructing multiple test procedures for partially ordered hypothesis sets a popular method to control multiplicity in confirmatory clinical trials is to use a so called hierarchical or fixed sequence test procedure this requires that the null hypotheses are ordered a priori for example in order of clinical importance the procedure tests the hypotheses in this order using level tests until one is not rejected it then stops so that no subsequent hypotheses are eligible for rejection this procedure strongly controls the familywise error rate fwe that is to say the probability that any true hypotheses are rejected this paper describes a simple generalization of this approach in which the null hypotheses are partially ordered it is convenient to display the partial ordering in a directed acyclic graph dag we consider sequentially rejective procedures based on the partial ordering in which a hypothesis is tested only when all preceding hypotheses have been tested and rejected in general such procedures do not control the fwe but it is shown that when certain intersection hypotheses are added strong control of the fwe is obtained the purpose of the method is to construct inference strategies for confirmatory clinical trials that better reflect the trial objectives copyright 2007 john wiley sons ltd

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

a new orthogonal transform for signal coding the authors propose an orthogonal unitary transformation called the modified hermite transformation mht and its extension which is called the modular modified hermite transformation mmht the mht algorithm which is an efficient algorithm is explained and explored the mht is compared to the discrete cosine transform dct for various ar 1 input signal source models using the performance criterion of gain over pcm denoted by sup n g sub tc the mht algorithm requires only 2n real multiplications or divisions for a transformation of a signal block of n samples it is also used for the inverse transformation imht and makes this new transform attractive it is efficient computationally and comparable to the dct for ar 1 source models with positive correlation coefficients it is somewhat better than the dct for negative correlation coefficients

application of multivariate uncertainty analysis to frequency response function estimates uncertainty estimation is an important part of any measurement but is often neglected for complex valued or multivariate data e g vectors this paper presents a methodology for estimating the uncertainty in multivariate experimental data and applies it to the measurement of the frequency response function obtained when using a periodic random input signal this multivariate uncertainty method is an extension of classical uncertainty methods used for scalar variables and tracks the correlation between all variates along with the sample variance instead of just tracking the standard uncertainty the method is used in this paper to propagate the sample covariance matrix from spectral density estimates to the uncertainty in the frequency response function estimate for two different system models in the first model the case when only the output signal is corrupted by noise is considered while in the second model both the input and output signals are corrupted by uncorrelated noise sources the results for the single noise model are verified by comparing them to published expressions in the literature while the results for the two noise model are verified by using a direct computation of the statistics finally the method is applied to experimental data from two microphone measurements within an acoustic waveguide the random uncertainty estimates in the frequency response function from the multivariate method agree well with the results from a direct computation of the statistics

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter

modified sequentially rejective multiple test procedures abstract suppose that n hypotheses h 1 h 2 h n with associated test statistics t 1 t 2 t n are to be tested by a procedure with experimentwise significance level the probability of rejecting one or more true hypotheses smaller than or equal to some specified value a commonly used procedure satisfying this condition is the bonferroni b procedure which consists of rejecting h i for any i iff the associated test statistic t i is significant at the level n holm 1979 introduced a modified bonferroni procedure with greater power than the b procedure under holm s sequentially rejective bonferroni srb procedure if any hypothesis is rejected at the level n the denominator of for the next test is n 1 and the criterion continues to be modified in a stagewise manner with the denominator of reduced by 1 each time a hypothesis is rejected so that tests can be conducted at successively higher significance levels holm proved that the experimentwise significance level

a bottom up approach to testing hypotheses that have a branching tree dependence structure with error rate control modern statistical analyses often involve testing large numbers of hypotheses in many situations these hypotheses may have an underlying tree structure that both helps determine the order that te

hierarchical testing designs for pattern recognition we explore the theoretical foundations of a twenty questions approach to pattern recognition the object of the analysis is the computational process itself rather than probability distributions bayesian inference or decision boundaries statistical learning our formulation is motivated by applications to scene interpretation in which there are a great many possible explanations for the data one background is statistically dominant and it is imperative to restrict intensive computation to genuinely ambiguous regions the focus here is then on pattern filtering given a large set mathcal y of possible patterns or explanations narrow down the true one y to a small random subset widehat y subset mathcal y of detected patterns to be subjected to further more intense processing to this end we consider a family of hypothesis tests for y a versus the nonspecific alternatives y ac each test has null type i error and the candidate sets a subset mathcal y are arranged in a hierarchy of nested partitions these tests are then characterized by scope a power or type ii error and algorithmic cost we consider sequential testing strategies in which decisions are made iteratively based on past outcomes about which test to perform next and when to stop testing the set y is then taken to be the set of patterns that have not been ruled out by the tests performed the total cost of a strategy is the sum of the testing cost and the postprocessing cost proportional to y and the corresponding optimization problem is analyzed as might be expected under mild assumptions good designs for sequential testing strategies exhibit a steady progression from broad scope coupled with low power to high power coupled with dedication to specific explanations in the assumptions ensuring this property a key role is played by the ratio cost power these ideas are illustrated in the context of detecting rectangles amidst clutter

a hidden markov model approach to testing multiple hypotheses on a tree transformed gene ontology graph gene category testing problems involve testing hundreds of null hypotheses that correspond to nodes in a directed acyclic graph the logical relationships among the nodes in the graph imply that only some configurations of true and false null hypotheses are possible and that a test for a given node should depend on data from neighboring nodes we developed a method based on a hidden markov model that takes the whole graph into account and provides coherent decisions in this structured multiple hypothesis testing problem the method is illustrated by testing gene ontology terms for evidence of differential expression

the binomial qmf wavelet transform for multiresolution signal decomposition perfect reconstruction quadrature mirror filters pr qmf s have been proposed as structures suitable for hierarchical subband coding ll 4 and also for multiresolution signal decomposition as might be used in image pyramid coding 5 more recently multiresolution signal decomposition methods are being examined from the standpoint of the discrete wavelet transform for continuous time signals 6 8 in this paper we describe a class of orthogonal binomial filters that provide basis functions for a perfect reconstruction bank of finite impulse response qmf s the orthonormal wavelet filters derived by daubechies 171 from a discrete wavelet transform approach are shown to be the same as the solutions inherent in the binomial based filters the energy compaction performance of the binomial qmf decomposition is computed and shown to be better than the dct for the markov source models as well as real world images considered the proposed binomial structure is efficient simple to implement on vlsi and suitable for multiresolution signal decomposition and coding applications

factorization of the coefficient variance matrix in orthogonal transforms the authors derive a matrix factorization of the coefficient variances for any fixed transformation this factorization formulation provides a better framework for understanding the role of transform on the one hand and the signal source model on the other it also greatly simplifies the number of computational operations required for each variance calculation a transform specific matrix which links the transform to the signal correlation model is derived this factorization provides a conceptual framework for understanding the behaviour of the transform for different source models it also significantly simplifies the calculation of the variance of each transform coefficient from a quadruple sum over four indices to a double sum over two indices this simplification can be used in adaptive transform coding which requires an estimate of the variances test results demonstrate that this mode based variance calculation provides an accurate basis for adaptive transform coding particularly at low bit rates

some metaheuristics should be simplified abstract users have a large and constantly increasing number of optimization metaheuristics at their disposal in pursuit of ever better approaches popular and successful methods are often improved a number of times in a row or various methods are hybridized one should however pay attention to whether such deliberately improved or hybridized methods do not become unnecessarily complicated or if some of their elements do not introduce a structural bias in the first case the algorithm should be simplified by eliminating the unneeded elements this will make it more clear to the users and as shown in this study may even improve the results in the second case operators that are responsible for over frequent sampling of some part of the search space have to be removed in this study we address the problem of over complexity of metaheuristics focusing on two joint winners of the cec2016 competition on single objective numerical optimization l shade epsin and umoea ii algorithms it is shown that each of them includes a procedure which introduces a structural bias by attracting population towards the origin o as discussed in the text in the case of seven out of 30 benchmark problems considered in the cec2016 competition the objective function values in the origin o are better than those found by the vast majority of algorithms hence structural bias affects the results obtained by l shade epsin and umoea ii in this work we simplify both algorithms by removing operators that are the main cause of structural bias further we show that in the l shade epsin algorithm the ensemble sinusoidal adaptation mechanism of control parameter f that is used during the first half of the search is not needed slightly better results on both artificial benchmarks used in the cec2016 competition and on a wide set of real world problems may be obtained if during that period of the search the value of f is simply set to 0 5 such a simplified algorithm is competitive against a large number of metaheuristics and may be much easier for the users to understand

sensitivity analysis for multiple comparisons in matched observational studies through quadratically constrained linear programming abstracta sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding while sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest this stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant which in turn results in an overly pessimistic assessment of a study s sensitivity to unobserved biases by solving a quadratically constrained linear program we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatm

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

the effect of bandwidth on the accuracy of transfer function measurements of single degree of freedom system response to random excitation abstract whenever random excitation is used in the determination of frequency response functions for a single degree of freedom system the measurement accuracy depends on the frequency resolution of the measurement technique if the ratio of measurement bandwidth to the 3 db bandwidth of the resonance is too great negative bias errors occur at resonance in estimates of power spectral levels and the transfer function parameters of amplitude and coherence numerical integration has been used to calculate teh expected errors that result whenever hanning or kaiser bessel weighting is applied in a fast fourier transform fft analysis and the errors that would be expected if an idealized rectangular frequency domain filter could be employed have also been similarly derived the numerical data are presented and compared with appropriate experimental data

engineering applications of correlation and spectral analysis 1994 engineering applications of correlation and spectral analysis technometrics vol 36 no 2 pp 220 221

hierarchical recognition of sparse patterns in large scale simultaneous inference summary we study how to accurately separate signals from noisy data and determine the patterns of the selected signals controlling the inflation of false positive errors is an important issue in largescale simultaneous inference but has not been addressed in the pattern recognition literature we develop a decision theoretic framework and formulate the sparse pattern recognition problem as a simultaneous inference problem with multiple decision trees oracle and adaptive classifiers are proposed for maximizing the expected number of true positives subject to a constraint on the overall false positive rate existing results on multiple testing are extended by allowing more than two states of nature hierarchical decision making and new error rate concepts

a note on multiple testing procedures in dose finding it is shown that in some recently proposed multiple test procedures for dose finding tamhane hochberg and dunnett 1996 biometrics 52 21 37 strong control of the familywise error is only guaranteed if order relations are assumed to hold among the means procedures that can be applied safely without assuming any restrictions on the means can be based on the classical many one comparisons of doses with the zero dose

optimal screening and discovery of sparse signals with applications to multistage high throughput studies summary a common feature in large scale scientific studies is that signals are sparse and it is desirable to narrow down significantly the focus to a much smaller subset in a sequential manner we consider two related data screening problems one is to find the smallest subset such that it virtually contains all signals and another is to find the largest subset such that it essentially contains only signals these screening problems are closely connected to but distinct from the more conventional signal detection or multiple testing problems we develop phase transition diagrams to characterize the fundamental limits in simultaneous inference and derive data driven screening procedures which control the error rates with near optimality properties applications in the context of multistage high throughput studies are discussed

statistical significance for hierarchical clustering cluster analysis has proved to be an invaluable tool for the exploratory and unsupervised analysis of high dimensional datasets among methods for clustering hierarchical approaches have enjoyed substantial popularity in genomics and other fields for their ability to simultaneously uncover multiple layers of clustering structure a critical and challenging question in cluster analysis is whether the identified clusters represent important underlying structure or are artifacts of natural sampling variation few approaches have been proposed for addressing this problem in the context of hierarchical clustering for which the problem is further complicated by the natural tree structure of the partition and the multiplicity of tests required to parse the layers of nested clusters in this article we propose a monte carlo based approach for testing statistical significance in hierarchical clustering which addresses these issues the approach is implemented as a sequential testing procedure guaranteeing control of the family wise error rate theoretical justification is provided for our approach and its power to detect true clustering structure is illustrated through several simulation studies and applications to two cancer gene expression datasets

resolution bias errors in spectral density frequency response and coherence function measurements iv time delay bias errors the problem of time delay bias errors is treated in this part of the present series of papers as a special case of a general theory of resolution bias errors in spectral estimation presented in a previous part it is shown that the main effect of an additional time delay between the output and the input of a physical system is to multiply the frequency response and coherence estimators which would be obtained without delay with the normalized autocorrelation function of the window function and its square respectively experimental results for the rectangular and hanning windows are in accord with the theoretical predictions the theoretical results given in the literature previously are valid for the rectangular window only but not for an arbitrary window function

correlation and spectral methods for determining uncertainty in propagating discontinuities the accurate determination of the speed of a propagating disturbance is important for a number of applications a nonstationary cross spectral density phase ncsdp technique was developed to provide a statistical estimate of the propagation time of sharp discontinuities such as steps or spikes that model shock or detonation waves the uncertainty of the phase estimate is dependent on the coherence between the signals for discrete implementation of the ncsdp technique a weighted resetting unwrap of the phase angle was proposed to discard values of the coherence below a threshold value that is only the unwrapped phase angle above the threshold was accepted in addition an envelop function was used which improved the technique the technique was found to be unsuitable for step disturbances but was more effective in estimating the time delay with a small standard deviation if the sharp disturbance also showed a rapid decay the method was applied to shock and detonation waves

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

hierarchical testing of variable importance a frequently encountered challenge in high dimensional regression is the detection of relevant variables variable selection suffers from instability and the power to detect relevant variables is typically low if predictor variables are highly correlated when taking the multiplicity of the testing problem into account the power diminishes even further to gain power and insight it can be advantageous to look for influence not at the level of individual variables but rather at the level of clusters of highly correlated variables we propose a hierarchical approach variable importance is first tested at the coarsest level corresponding to the global null hypothesis the method then tries to attribute any effect to smaller subclusters or even individual variables the smallest possible clusters which still exhibit a significant influence on the response variable are retained it is shown that the proposed testing procedure controls the familywise error rate at a prespecified level simultaneously over all resolution levels the method has power comparable to the bonferroni holm procedure on the level of individual variables and dramatically larger power for coarser resolution levels the best resolution level is selected adaptively

a powerful approach to the study of moderate effect modification in observational studies effect modification means the magnitude or stability of a treatment effect varies as a function of an observed covariate generally larger and more stable treatment effects are insensitive to larger biases from unmeasured covariates so a causal conclusion may be considerably firmer if this pattern is noted if it occurs we propose a new strategy called the submax method that combines exploratory and confirmatory efforts to determine whether there is stronger evidence of causality that is greater insensitivity to unmeasured confounding in some subgroups of individuals it uses the joint distribution of test statistics that split the data in various ways based on certain observed covariates for l binary covariates the method splits the population l times into two subpopulations perhaps first men and women perhaps then smokers and nonsmokers computing a test statistic from each subpopulation and appends the test statistic for the whole population making 2 l 1 test statistics in total although l binary covariates define 2 l interaction groups only 2 l 1 tests are performed and at least l 1 of these tests use at least half of the data the submax method achieves the highest design sensitivity and the highest bahadur efficiency of its component tests moreover the form of the test is sufficiently tractable that its large sample power may be studied analytically the simulation suggests that the submax method exhibits superior performance in comparison with an approach using cart when there is effect modification of moderate size using data from the nhanes i epidemiologic follow up survey an observational study of the effects of physical activity on survival is used to illustrate the method the method is implemented in the r package submax which contains the nhanes example an online appendix provides simulation results and further analysis of the example

a general interactive framework for false discovery rate control under structural constraints we propose a general framework based on selectively traversed accumulation rules star for interactive multiple testing with generic structural constraints on the rejection set it combines accumulation tests from ordered multiple testing with data carving ideas from post selection inference allowing for highly flexible adaptation to generic structural information our procedure defines an interactive protocol for gradually pruning a candidate rejection set beginning with the set of all hypotheses and shrinking with each step by restricting the information at each step via a technique we call masking our protocol enables interaction while controlling the false discovery rate fdr in finite samples for any data adaptive update rule that the analyst may choose we suggest update rules for a variety of applications with complex structural constraints show that star performs well for problems ranging from convex region detection to fdr control on directed acyclic graphs and show how to extend it to regression problems where knockoff statistics are available in lieu of p values

on lapped orthogonal transforms signal coding applications the energy compaction performance of several lapped orthogonal transforms lots are presented it is shown that the lot outperforms the conventional block transforms for all the cases considered the performance of the poorly performing block transforms for high correlation sources increased dramatically in their lot versions it is found that the energy compaction performance of the lot versions of the different block transforms considered is about the same therefore the choice of lot is based on the efficiency of the transform algorithm the lot is an alternative to the block transforms for signal coding applications also the blocking effect is reduced with the increase in the computational complexity of the transform algorithm

resolution bias errors in spectral density frequency response and coherence function measurements v comparison of different frequency response estimators three different types of frequency response estimators are considered and compared with each other with respect to the inherent resolution bias errors the behavior of these estimators is shown to differ considerably especially with respect to peak estimation in resonance systems such as a simple spring mass system one of these estimators is shown to exhibit almost no peak bias error at resonance under noise free measurement conditions whereas the peak bias error of the estimator most commonly used is maximum however aside from resonance the peak bias free estimator proves to be the worst of the three estimators the theoretical predictions are accurately verified by experiments with an electrical lrc resonance circuit

the spatial extent of the bold response functional magnetic resonance imaging is routinely used to localize brain function with multiple brain scans averaged together to reveal activation volumes in this study we examine the seldom studied effect of multiple scan averaging on the extent of activation volume using restricted visual field stimulation we obtained a large number of scan repetitions and analyzed changes in activation volume with progressively increased averaging and across single scans activation volume increased monotonically with averaging and failed to asymptote when as many as 22 scans were averaged together expansions in the spatial extent of activation were not random rather they were centered about activation loci that appear with little or no averaging using empirical and simulated data changes with averaging in activation volumes and cross correlation coefficient distributions revealed the presence of considerably more activated voxels than commonly surmised many voxels have low snr and remain undetected without extensive averaging the primary source of such voxels was not downstream venous drainage since there was no significant and consistent delay difference between voxels activated at different averaging levels voxels with low snr may reflect a diffuse subthreshold activity centered about spiking neurons dephasing gradients from distal veins or simply a blood flow response extending beyond the locus of neuronal firing across single scans as much as twofold changes in activation volume were observed these changes were not correlated with the order of scan acquisition subject task performance or signal and noise properties of activated voxels instead they may reflect subtle changes between overlapping noise and signal frequency components

the sequential rejection principle of familywise error control closed testing and partitioning are recognized as fundamental principles of familywise error control in this paper we argue that sequential rejection can be considered equally fundamental as a general principle of multiple testing we present a general sequentially rejective multiple testing procedure and show that many well known familywise error controlling methods can be constructed as special cases of this procedure among which are the procedures of holm shaffer and hochberg parallel and serial gatekeeping procedures modern procedures for multiple testing in graphs resampling based multiple testing procedures and even the closed testing and partitioning procedures themselves we also give a general proof that sequentially rejective multiple testing procedures strongly control the familywise error if they fulfill simple criteria of monotonicity of the critical values and a limited form of weak familywise error control in each single step the sequential rejection principle gives a novel theoretical perspective on many well known multiple testing procedures emphasizing the sequential aspect its main practical usefulness is for the development of multiple testing procedures for null hypotheses possibly logically related that are structured in a graph we illustrate this by presenting a uniform improvement of a recently published procedure

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

a cochran armitage type and a score free global test for multivariate ordinal data we propose a cochran armitage type and a score free global test that can be used to assess the presence of an association between a set of ordinally scaled covariates and an outcome variable within the range of generalized linear models both tests are developed within the framework of the well established global test methodology and as such are feasible in high dimensional data situations under any correlation and enable adjustment for covariates the cochran armitage type test for which an intimate connection with the traditional score based cochran armitage test is shown rests upon explicit assumptions on the distances between the covariates ordered categories the score free test in contrast parametrizes these distances and thus keeps them flexible rendering it ideally suited for covariates measured on an ordinal scale as confirmed by means of simulations the cochran armitage type test focuses its power on set outcome relationships where the distances between the covariates categories are equal or close to those assumed whereas the score free test spreads its power over a wide range of possible set outcome relationships putting more emphasis on monotonic than on non monotonic ones based on the tests power properties it is discussed when to favour one or the other and the practical merits of both of them are illustrated by an application in the field of rehabilitation medicine our proposed tests are implemented in the r package globaltest copyright 2016 john wiley sons ltd

time delay estimation using phase data the estimation of time delays between two received signals using phase measurements is discussed and the accuracy of such estimates is detailed for the ideal case of statistically independent noise and no scattering at the receiver locations it is shown that phase data regression lines yield time delay estimates with the same accuracy as other optimal time delay estimation procedures for less ideal situations the potential advantages of time delay estimation using phase data are discussed and illustrated it is shown that regression analysis of phase estimates at properly selected frequencies can sometimes be employed to reduce bias errors in time delay estimates due to correlated receiver noise it is also shown that the estimation errors due to scattering at the receiver location can often be assessed in nonparametric terms to provide time delay estimates with a realistic error bound

the p filter multilayer false discovery rate control for grouped hypotheses summary in many practical applications of multiple testing there are natural ways to partition the hypotheses into groups by using the structural spatial or temporal relatedness of the hypotheses and this prior knowledge is not used in the classical benjamini hochberg procedure for controlling the false discovery rate fdr when one can define possibly several such partitions it may be desirable to control the group fdr simultaneously for all partitions as special cases the finest partition divides the n hypotheses into n groups of one hypothesis each and this corresponds to controlling the usual notion of fdr whereas the coarsest partition puts all n hypotheses into a single group and this corresponds to testing the global null hypothesis we introduce the p filter which takes as input a list of n p values and m 1 partitions of hypotheses and produces as output a list of n or fewer discoveries such that the group fdr is provably simultaneously controlled for all partitions importantly since the partitions are arbitrary our procedure can also handle multiple partitions which are non hierarchical the p filter generalizes two classical procedures when m 1 choosing the finest partition into n singletons we exactly recover the benjamini hochberg procedure whereas choosing instead the coarsest partition with a single group of size n we exactly recover the simes test for the global null hypothesis we verify our findings with simulations that show how this technique can not only lead to the aforementioned multilayer fdr control but also lead to improved precision of rejected hypotheses we present some illustrative results from an application to a neuroscience problem with functional magnetic resonance imaging data where hypotheses are explicitly grouped according to predefined regions of interest in the brain thus allowing the scientist to employ field specific prior knowledge explicitly and flexibly

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

large multiple neighborhood search for the clustered vehicle routing problem abstract the clustered vehicle routing problem is a variant of the classical capacitated vehicle routing problem in which customers are partitioned into clusters and it is assumed that each cluster must have been served completely before the next cluster is served this decomposes the problem into three subproblems i e the assignment of clusters to routes the routing inside each cluster and the sequencing of the clusters in the routes the second task requires the solution of several hamiltonian path problems one for each possibility to route through the cluster we pre compute the hamiltonian paths for every pair of customers of each cluster we present a large multiple neighborhood search which makes use of multiple cluster destroy and repair operators and a variable neighborhood descent vnd for post optimization the vnd is based on classical neighborhoods such as relocate 2 opt and swap all working on the cluster level and a generalization of the balas simonetti neighborhood modifying simultaneously the intra cluster routings and the sequence of clusters in a route computational results with our new approach compare favorably to existing approaches from the literature

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

delayed block transfer function in the frequency domain when the impulse response of a transfer system is long it is difficult for the standard cross spectrum method to obtain an accurate estimate of the transfer function by applying the fast fourier transform fft with a finite length window the bias error in the estimate is large especially around the resonant frequency of the transfer system in the paper therefore the authors propose an alternative new method to obtain an accurate estimate of the transfer function the delayed block transfer function is introduced to detect the components that are correlated to the signal in the input window but leak from the output window based on these transfer functions the total characteristics of the transfer system are estimated accurately in the latter half of the paper the authors derive the theoretical expressions for the bias errors in the transfer functions estimated by the proposed and the standard methods by thoroughly comparing the resultant expressions the superiority and the usefulness of the proposed method are theoretically confirmed finally the simulation experiments show the advantages of the proposed method

direct effects testing a two stage procedure to test for effect size and variable importance for correlated binary predictors and a binary response in applications such as medical statistics and genetics we encounter situations where a large number of highly correlated predictors explain a response for example the response may be a disease indicator and the predictors may be treatment indicators or single nucleotide polymorphisms snps constructing a good predictive model in such cases is well studied less well understood is how to recover the true sparsity pattern that is finding which predictors have direct effects on the response and indicating the statistical significance of the results restricting attention to binary predictors and response we study the recovery of the true sparsity pattern using a two stage method that separates establishing the presence of effects from inferring their exact relationship with the predictors simulations and a real data application demonstrate that the method discriminates well between associations and direct effects comparisons with lasso based methods demonstrate favourable performance of the proposed method

an objective performance measure in multiresolution signal decomposition presents an analysis of band energies and evaluates the effects of aliasing in perfect reconstruction pr multirate systems an objective performance measure called nonaliasing energy ratio ner is defined the merit of the new measure is emphasized with performance comparisons of popular block transforms and 2 band pr qmf based hierarchical filter banks it is shown that the new measure complements the widely used energy compaction measure

higher criticism for detecting sparse heterogeneous mixtures higher criticism or second level significance testing is a multiplecomparisons concept mentioned in passing by tukey it concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis tukey suggested comparing the fraction of observed significances at a given level to the expected fraction under the joint null in fact he suggested standardizing the difference of the two quantities and forming a z score the resulting z score tests the significance of the body of significance tests we consider a generalization where we maximize this z score over a range of significance levels 0 0 we are able to show that the resulting higher criticism statistic is effective at resolving a very subtle testing problem testing whether n normal means are all zero versus the alternative that a small fraction is nonzero the subtlety of this sparse normal means testing problem can be seen from work of ingster and jin who studied such problems in great detail in their studies they identified an interesting range of cases where the small fraction of nonzero means is so small that the alternative hypothesis exhibits little noticeable effect on the distribution of the p values either for the bulk of the tests or for the few most highly significant tests in this range when the amplitude of nonzero means is calibrated with the fraction of nonzero means the likelihood ratio test for a precisely specified alternative would still succeed in separating the two hypotheses we show that the higher criticism is successful throughout the same region of amplitude sparsity where the likelihood ratio test

bias in the cross spectrum and time delay estimates due to misalignment the effect of misalignment in the weighted overlapped segment averaging method used for estimating time delay is investigated with nonwhite input it is shown that the phase of the cross spectrum and the location of the peak in the cross correlator are biased

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates

testing against a high dimensional alternative summary as the dimensionality of the alternative hypothesis increases the power of classical tests tends to diminish quite rapidly this is especially true for high dimensional data in which there are more parameters than observations we discuss a score test on a hyperparameter in an empirical bayesian model as an alternative to classical tests it gives a general test statistic which can be used to test a point null hypothesis against a high dimensional alternative even when the number of parameters exceeds the number of samples this test will be shown to have optimal power on average in a neighbourhood of the null hypothesis which makes it a proper generalization of the locally most powerful test to multiple dimensions to illustrate this new locally most powerful test we investigate the case of testing the global null hypothesis in a linear regression model in more detail the score test is shown to have significantly more power than the f test whenever under the alternative the large variance principal components of the design matrix explain substantially more of the variance of the outcome than do the small variance principal components the score test is also useful for detecting sparse alternatives in truly high dimensional data where its power is comparable with the test based on the maximum absolute t statistic

characterizing the hemodynamic response effects of presentation rate sampling procedure and the possibility of ordering brain activity based on relative timing rapid presentation event related functional mri er fmri allows neuroimaging methods based on hemodynamics to employ behavioral task paradigms typical of cognitive settings however the sluggishness of the hemodynamic response and its variance provide constraints on how er fmri can be applied in a series of two studies estimates of the hemodynamic response in or near the primary visual and motor cortices were compared across various paradigms and sampling procedures to determine the limits of er fmri procedures and more generally to describe the behavior of the hemodynamic response the temporal profile of the hemodynamic response was estimated across overlapping events by solving a set of linear equations within the general linear model no assumptions about the shape were made in solving the equations following estimation of the temporal profile the amplitude and timing were modeled using a gamma function results indicated that 1 within a region for a given subject estimation of the hemodynamic response is extremely stable for both amplitude r 2 0 98 and time to peak r 2 0 95 from one series of measurements to the next and slightly less stable for estimation of time to onset r 2 0 60 2 as the trial presentation rate changed from those spaced 20 s apart to temporally overlapping trials the hemodynamic response amplitude showed a small but significant decrease trial onsets spaced on average 5 s apart showed a 17 25 reduction in amplitude compared to those spaced 20 s apart power analysis indicated that the increased number of trials at fast rates outweighs this decrease in amplitude if statistically reliable response detection is the goal 3 knowledge of the amplitude and timing of the hemodynamic response in one region failed to predict those properties in another region even for within subject comparisons 4 across subjects the amplitude of the response showed no significant correlation with timing of the response for either time to onset or time to peak estimates 5 the within region stability of the response was sufficient to allow offsets in the timing of the response to be detected that were under a second placing event related fmri methods in a position to answer questions about the change in relative timing between regions

a sequential algorithm for false discovery rate control on directed acyclic graphs summary we propose a linear time single pass top down algorithm for multiple testing on directed acyclic graphs where nodes represent hypotheses and edges specify a partial ordering in which the hypotheses must be tested the procedure is guaranteed to reject a sub directed acyclic graph with bounded false discovery rate while satisfying the logical constraint that a rejected node s parents must also be rejected it is designed for sequential testing settings where the directed acyclic graph structure is known a priori but the p values are obtained selectively such as in a sequence of experiments however the algorithm is also applicable in nonsequential settings where all p values can be calculated in advance such as in model selection our algorithm provably controls the false discovery rate under independence positive dependence or arbitrary dependence of the p values and specializes to known algorithms in the special cases of trees and line graphs it simplifies to the classical benjamini hochberg procedure when the directed acyclic graph has no edges we explore the empirical performance of our algorithm through simulations and analysis of a real dataset corresponding to a gene ontology and we demonstrate its favourable performance in terms of computational time and power

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

high dimensional variable selection this paper explores the following question what kind of statistical guarantees can be given when doing variable selection in high dimensional models in particular we look at the error rates and power of some multi stage regression methods in the first stage we fit a set of candidate models in the second stage we select one model by cross validation in the third stage we use hypothesis testing to eliminate some variables we refer to the first two stages as screening and the last stage as cleaning we consider three screening methods the lasso marginal regression and forward stepwise regression our method gives consistent variable selection under certain conditions

uncertainty analysis of the two microphone method accurate duct acoustic propagation models are required to characterize and subsequently reduce aircraft engine noise the boundary conditions for these models ultimately rely on accurate measurements of the acoustic impedance for candidate nacelle liners the standard two microphone method is widely used to estimate acoustic impedance but does not provide uncertainty estimates that are essential for data quality assessment and model validation a systematic framework is presented in this paper to propagate the experimental 95 confidence interval uncertainty estimates in the measured quantities to the calculated acoustic impedance data using the two microphone method for small and large input uncertainties one method is an analytical small perturbation technique using multivariate statistics this method provides useful analytical scaling information a second monte carlo method is utilized to validate the analytical multivariate method both methods are applied to the two microphone method for simulated data representative of sound hard and sound soft acoustic materials the results indicate that for realistic experimental parameters the uncertainty in the input measurements results in nonlinear perturbations therefore the small perturbation technique fails and the monte carlo method should be used to obtain uncertainty estimates furthermore the nonlinear perturbations also distort the output statistical distributions of the calculated acoustic impedance and reflection coefficient which results in significant deviation from gaussian behavior the distortion is a function of the acoustic impedance of the specimen itself finally the monte carlo method is applied to experimental data for a ceramic tubular specimen and compared to the multivariate results to demonstrate the implementation and usefulness of the technique

artificial shifting of fmri activation localized by volume and surface based analyses spatial smoothing is an important post processing procedure that is used to increase the signal to noise ratio snr of blood oxygenation level dependent signals bold in common functional magnetic resonance imaging fmri applications however recent studies have shown that smoothing artificially shifts probabilistic local maxima of fmri activations in this study we show shifting of the localization of functional centers in hand motor areas of the cerebral cortex by three dimensional isotropic gaussian kernel smoothing or two dimensional heat kernel smoothing in volume and surface based fmri analyses activation maps derived from smoothed echo planar imaging epi data by volume and surface based analyses were assigned to the nodes of individual cortical surface models and local maxima in the primary motor area m1 and the primary somatosensory cortex s1 were compared with those derived from non smoothed risk map analysis which is commonly used in presurgical applications for each analysis the euclidean and geodesic distances between the correlation coefficients of local maxima derived from smoothed and non smoothed epi data were measured the results show that the correlation coefficients derived from the volume and surface based analyses were about 29 4 and 42 9 higher for smoothed than for non smoothed risk map analyses and show minimum shifting of localizations by 12 1 mm and 6 9 mm on average in euclidean distance respectively and about 9 5 mm and 5 7 mm on average in geodesic distance respectively