explicit streamline diffusion finite element methods for the compressible euler equations in conservation variables the paper concerns the streamline diffusion finite element method applied to one and two dimensional gas flow described by the inviscid euler equations in conservation variables we point out that the streamline diffusion method is a natural finite element analogue to upstream type finite difference volume schemes and in fact constitutes a general framework for a large class of them we study explicit implementations of the method and derive different choices of stabilizing streamline diffusion matrices in particular we propose a consistent fully multidimensional version a brief review of the theoretical background to the method is presented and some numerical results in two dimensions are given

asymptotics for the minimum covariance determinant estimator consistency is shown for the minimum covariance determinant mcd estimators of multivariate location and scale and asymptotic normality is shown for the former the proofs are made possible by showing a separating ellipsoid property for the mcd subset of observations an analogous property is shown for the mcd subset computed from the population distribution

effect of variability in level on forward masking and on increment detection in the first of four experiments all with the same four subjects varying the level of a forward masker from interval to interval in a two interval forced choice 2ifc adaptive procedure had little effect on threshold in the second experiment the signal level was fixed and performance was measured in units of d varying the level of the forward masker again had little effect analyses of trial by trial data indicated that subjects did not vote for the interval with the higher level masker as would an energy detector performance was better on trials where the masker level in the interval with the signal was lower and was relatively independent of masker level in the nonsignal interval in the third experiment these results were replicated for a wider range of masker variability and with maskers lower in frequency than the signal in the fourth experiment the same range of variability from interval to interval was imposed on the level of the pedestal in an increment detection task results were sim

hyper markov laws in the statistical analysis of decomposable graphical models this paper introduces and investigates the notion of a hyper markov law which is a probability distribution over the set of probability measures on a multivariate space that i is concentrated on the set of markov probabilities over some decomposable graph and ii satisfies certain conditional independence restrictions related to that graph a stronger version of this hyper markov property is also studied our analysis starts by reconsidering the properties of markov probabilities using an abstract approach which thereafter proves equally applicable to the hyper markov case next it is shown constructively that hyper markov laws exist that they appear as sampling distributions of maximum likelihood estimators in decomposable graphical models and also that they form natural conjugate prior distributions for a bayesian analysis of these models as examples we construct a range of specific hyper markov laws including the hyper multinomial hyper dirichlet and the hyper wishart and inverse wishart laws these laws occur naturally in connection with the analysis of decomposable log linear and covariance selection models

detectability of increments and decrements in spectral profiles in auditory profile analysis the subject typically has to discriminate a standard spectrum consisting of widely spaced equal amplitude sinusoids from a comparison in which one or several components have been elevated relative to the others according to the widely accepted multichannel model however it should not matter whether the spectral shape alteration consists of incrementing or decrementing a component by a small number of decibels thus in order to investigate the generality of the hypothesized mechanism and to explore the role of pitch salience cues which might be thought to favor increments to single components two experiments comparing the detectability of intensity increments and decrements in spectral profiles were conducted in experiment 1 in which the number of components was varied from 3 to 15 within a fixed frequency range decrements to the central 800 hz component produced significantly larger thresholds than did increments experiment 2 which employed three tone complexes spanning different frequency ranges revealed that this effect is entirely due to the spectral density of the frequency components as the distance between the variable signal component and the flanking reference sinusoids decreased the increment decrement disparity became larger these effects may at least qualitatively be accounted for when peripheral excitation patterns are considered suggesting that local decrements are constrained more than increments by the excitation intruding from flanking stimulus components

decomposability and selection of graphical models for multivariate time series summary we derive conditions for decomposition and collapsibility of graphical interaction models for multivariate time series these properties enable us to perform stepwise model selection under certain restrictions for illustration we apply the results to a multivariate time series describing the haemodynamic system as monitored in intensive care

transport and diffusion of material quantities on propagating interfaces via level set methods we develop theory and numerical algorithms to apply level set methods to problems involving the transport and diffusion of material quantities in a level set framework level set methods are computational techniques for tracking moving interfaces they work by embedding the propagating interface as the zero level set of a higher dimensional function and then approximate the solution of the resulting initial value partial differential equation using upwind finite difference schemes the traditional level set method works in the trace space of the evolving interface and hence disregards any parameterization in the interface description consequently material quantities on the interface which themselves are transported under the interface motion are not easily handled in this framework we develop model equations and algorithmic techniques to extend the level set method to include these problems we demonstrate the accuracy of our approach through a series of test examples and convergence studies

robustness and efficiency properties of scatter matrices the robustness and efficiency properties of likelihood ratio tests for functions of the population covariance matrix are studied an alternative class of tests based upon affineinvariant m estimates of scatter is proposed whenever the function of the covariance matrix is invariant under a common scale change for such inferences it is shown that a single scalar valued index of efficiency is sufficient

a nurbs based generalized finite element scheme for 3d simulation of heterogeneous materials a 3d nurbs based interface enriched generalized finite element method nigfem is introduced to solve problems with complex discontinuous gradient fields observed in the analysis of heterogeneous materials the method utilizes simple structured meshes of hexahedral elements that do not necessarily conform to the material interfaces in heterogeneous materials by avoiding the creation of conforming meshes used in conventional fem the nigfem leads to significant simplification of the mesh generation process to achieve an accurate solution in elements that are crossed by material interfaces the nigfem utilizes non uniform rational b splines nurbs to enrich the solution field locally the accuracy and convergence of the nigfem are tested by solving a benchmark problem we observe that the nigfem preserves an optimal rate of convergence and provides additional advantages including the accurate capture of the solution fields in the vicinity of material interfaces and the built in capability for hierarchical mesh refinement finally the use of the nigfem in the computational analysis of heterogeneous materials is discussed development of generalized finite element method for 3d mesoscale modeling of materials with complex microstructures novel nurbs based enrichment functions built in capability to perform hierarchical local mesh refinement method is applicable to engineering problems characterized by discontinuous gradient and complex internal geometry

a fast procedure for model search in multidimensional contingency tables summary a procedure to select the simplest acceptable models for a multidimensional contingency table is proposed it is based on two rules first that if a model is accepted then all models that include it are considered to be accepted and secondly that if a model is rejected then all its submodels are considered to be rejected two versions are described one for the class of graphical models and the other for the class of hierarchical log linear models application of both versions to a six dimensional table is illustrated the procedure can be regarded as an alternative to fitting all possible models made computationally feasible by application of the two rules it is a generalization of the procedure proposed by havr anek 1984 but is in many cases considerably faster

masked detection thresholds and temporal integration for noise band signals masked detection thresholds were measured at a center frequency of 2500 hz for a range of noise signal bandwidths w 62 to 6000 hz and durations t 10 to 480 ms approximating that found acoustically in speech the signals were presented in an uncorrelated 480 ms 6000 hz wide masker the masker was presented 1 at a constant spectrum level 53 db spl hz or 2 with the overall level varied randomly over a 50 db range from interval to interval of a trial performance was disrupted in the random level masker only for the condition where the signal and uncorrelated masker were gated on and off simultaneously and were matched spectrally time constants estimated from temporal integration functions fit to the masked detection threshold data were related inversely to w for w broader than the critical bandwidth sensitivity to the noise signals was evaluated in the context of an optimum detection model green 1960 the results did not follow the prediction of a constant bandwidth duration wt product but may be understood in terms of cues available to the listener from the relative combination of signal and masker parameters at least three cues for detection were identified in these experiments 1 a relative timing cue 2 a spectral shape cue and 3 a traditional energy cue compared across observation intervals the relative timing cue and spectral shape cue together contributed as much as a 10 to 12 db advantage relative to detection based on the traditional energy cue alone a new multi cue detection model for predicting the masked detection thresholds was derived predictions from the new model were highly correlated r 0 95 with the empirically measured masked detection thresholds

some improvements of the fast marching method the fast marching method published by sethian proc natl acad sci usa 93 1996 pp 1591 1595 is an optimally efficient algorithm for solving problems of front evolution where the front speed is monotonic it has been used in a wide variety of applications such as robotic path planning r kimmel and j sethian fast marching methods for computing distance maps and shortest paths tech report 669 cpam university of california berkeley 1996 crack propagation m stolarska et al modelling crack growth by level sets in the extended finite element method comput methods appl mech engrg to appear internat j numer methods engrg 51 2001 pp 943 960 n sukumar d l chopp and b moran extended finite element method and fast marching method for three dimensional fatigue crack propagation j comput phys submitted seismology j sethian and a popovici geophysics 64 1999 pp 516 523 photolithography j sethian fast marching level set methods for three dimensional photolithography development in proceedings of the spie 1996 international symposium on microlithography santa clara ca 1996 and medical imaging r malladi and j sethian proc natl acad sci usa 93 1996 pp 9389 9392 it has also been a valuable tool for the implementation of modern level set methods where it is used to efficiently compute the distance to the front and or an extended velocity function in this paper we improve upon the second order fast marching method of sethian siam rev 41 1999 pp 199 235 by constructing a second order approximation of the interface generated from local data on the mesh the data is interpolated on a single box of the mesh using a bicubic approximation the distance to the front is then calculated by using a variant of newton s method to solve both the level curve equation and the orthogonality condition for the nearest point to a given node the result is a second order approximation of the distance to the interface which can then be used to produce second order accurate initial conditions for the fast marching method and a third order fast marching method

asymptotic behaviour of s estimates of multivariate location parameters and dispersion matrices it is shown under appropriate conditions that rousseeuw s minimum volume estimator and other s estimators of multivariate location and dispersion parameters are consistent under certain differentiability conditions the estimates are asymptotically normally distributed with a norming factor of n 1 2

breakdown and groups the concept of breakdown point was introduced by hampel ph d dissertation 1968 univ california berkeley ann math statist 42 1971 1887 1896 and developed further by among others huber robust statistics 1981 wiley new york and donoho and huber in a festschrift for erich l lehmann 1983 157 184 wadsworth belmont ca it has proved most successful in the context of location scale and regression problems attempts to extend the concept to other situations have not met with general acceptance in this paper we argue that this is connected to the fact that in the location scale and regression problems the translation and affine groups give rise to a definition of equivariance for statistical functionals comparisons in terms of breakdown points seem only useful when restricted to equivariant functionals and even here the connection between breakdown and equivariance is a tenuous one institute of mathematical statistics 2005

a distribution free m estimator of multivariate scatter the existence and uniqueness of a limiting form of a huber type m estimator of multivariate scatter is established under certain conditions on the observed sample these conditions hold with probability one when sampling randomly from a continuous multivariate distribution the existence of the estimator is proven by showing that it is the limiting point of a specific algorithm hence the proof is constructive for continuous populations the estimator of multivariate scatter is shown to be strongly consistent and asymptotically normal an important property of the estimator is that its asymptotic distribution is distribution free with respect to the class of continuous elliptically distributed populations this distribution free property also holds for the finite sample size distribution when the location parameter is known in addition the estimator is the most robust estimator of the scatter matrix of an elliptical distribution in the sense of minimizing the maximum asymptotic variance

efficient across frequency integration in short signal detection a series of experiments was performed on the influence of bandwidth on the masked threshold of brief deterministic signals in continuous broadband noise the signal bandwidth is quantified by the number n of constituent 1 3 oct bands for n increasing from 1 to typically 9 the masked threshold level in the constituent 1 3 oct bands is found to decrease by 8 log n this integration rule is obtained when each of the 1 3 oct bands covered by the signal equally contributes to detection i e that for each of these 1 3 oct bands the difference between signal level and the individual masked threshold level is the same it was found that this integration rule also applies to noncontiguous signal spectra and that it remains intact over a broad range of masker levels commonly the masked threshold of compound signals for instance n frequency components with a spacing of typically 1 3 oct relative to the masked threshold of single component signals has been described by a 5 log n integration rule however this rule was obtained for signal durations of typically 100 ms or more for the present brief signals typically 10 ms or less the across frequency integration is found to be more effective

regularized gaussian discriminant analysis through eigenvalue decomposition abstract friedman proposed a regularization technique rda of discriminant analysis in the gaussian framework rda uses two regularization parameters to design an intermediate classifier between the linear the quadratic the nearest means classifiers in this article we propose an alternative approach called edda that is based on the reparameterization of the covariance matrix k of a group gk in terms of its eigenvalue decomposition k k d k a k d k where k specifies the volume of density contours of gk the diagonal matrix of eigenvalues specifies its shape the eigenvectors specify its orientation variations on constraints concerning volumes shapes orientations k a k and d k lead to 14 discrimination models of interest for each model we derived the normal theory maximum likelihood parameter estimates our approach consists of selecting a model by minimizing the sample based estimate of future misclassification risk by cross validation numerical experiments on simulated and rea

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

high order x fem and levelsets for complex microstructures uncoupling geometry and approximation in this contribution a strategy is proposed for uncoupling geometrical description and approximation with the x fem the strategy is based on an uniform coarse mesh that defines a high order approximation of the mechanical fields and an adapted mesh that defines the geometrical features by means of levelsets the connection between the geometry and the approximation is obtained by sharing the quadtree trees of the two meshes numerical examples involving level set based parts convergence studies mechanical computations and numerical homogenization show good promise for this approach

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

a fast algorithm for the minimum covariance determinant estimator the minimum covariance determinant mcd method of rousseeuw is a highly robust estimator of multivariate location and scatter its objective is to find h observations out of n whose covariance matrix has the lowest determinant until now applications of the mcd were hampered by the computation time of existing algorithms which were limited to a few hundred objects in a few dimensions we discuss two important applications of larger size one about a production process at philips with n 677 objects and p 9 variables and a dataset from astronomy with n 137 256 objects and p 27 variables to deal with such problems we have developed a new algorithm for the mcd called fast mcd the basic ideas are an inequality involving order statistics and determinants and techniques which we call selective iteration and nested extensions for small datasets fast mcd typically finds the exact mcd whereas for larger datasets it gives more accurate results than existing algorithms and is faster by orders

detection of partially filled gaps in noise and the temporal modulation transfer function results of experiments on the detection of silent intervals or gaps in broadband noise are reported for normal hearing listeners in some preliminary experiments a gap threshold of about 2 ms was measured this value was independent of the duration of the noise burst variation of the noise level on each presentation or the temporal position of the gap within the noise burst in the main experiments the thresholds for partial decrements in the noise waveform as well as brief increments were determined as predicted by a model that assumes a single fixed peak to valley detection ratio thresholds for increments are slightly higher than thresholds for decrements when the signal is measured as the change in rms noise level a first order model describes the temporal properties of the auditory system as a low pass filter with a 7 to 8 ms time constant temporal modulation transfer functions were determined for the same subjects and the estimated temporal parameters agreed well with those estimated from the gap detection data more detailed modeling was carried out by simulating viemeister s three stage temporal model simulations using an initial stage bandwidth of 4000 hz and a 3 ms time constant for the low pass filter generate data that are very similar to those obtained from human subjects in both modulation and gap detection

on the relation between s estimators and m estimators of multivariate location and covariance we discuss the relation between s estimators and m estimators of multivariate location and covariance as in the case of the estimation of a multiple regression parameter s estimators are shown to satisfy first order conditions of m estimators we show that the influence function if x s f of s functionals exists and is the same as that of corresponding m functionals also we show that s estimators have a limiting normal distribution which is similar to the limiting normal distribution which is similar to the limiting normal distribution of m estimators finally we compare asymptotic variances and breakdown point of both types of estimators

a cautionary note on robust covariance plug in methods many multivariate statistical methods rely heavily on the sample covariance matrix it is well known though that the sample covariance matrix is highly non robust one popular alternative approach for robustifying the multivariate method is to simply replace the role of the covariance matrix with some robust scatter matrix the aim of this paper is to point out that in some situations certain properties of the covariance matri x are needed for the corresponding robust plug in method to be a valid approach and that not all scatter matrices necessarily possess these important properties in particular the fol lowing three multivariate methods are discussed in this paper independent components analysis observational regression and graphical modeling for each case it is shown that using a symmetrized robust scatter matrix in place of the covariance matrix results in a proper robust multivariate method

a computational approach to handle complex microstructure geometries in multiscale analysis of components there is usually a need to solve microstructures with complex geometries in this paper we use the extended finite element method x fem to solve scales involving complex geometries the x fem allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach for material interfaces this is achieved by introducing a new enrichment strategy although the mesh does not need to conform to the physical surfaces it needs to be fine enough to capture the geometry of these surfaces a simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement numerical experiments on the periodic homogenization of two phase complex cells demonstrate the accuracy and simplicity of the x fem c 2003 elsevier b v all rights reserved

a new concept for separability problems in blind source separation the goal of blind source separation bss lies in recovering the original independent sources of a mixed random vector without knowing the mixing structure a key ingredient for performing bss successfully is to know the indeterminacies of the problem that is to know how the separating model relates to the original mixing model separability for linear bss comon 1994 showed using the darmois skitovitch theorem that the linear mixing matrix can be found except for permutation and scaling in this work a much simpler direct proof for linear separability is given the idea is based on the fact that a random vector is independent if and only if the hessian of its logarithmic density resp characteristic function is diagonal everywhere this property is then exploited to propose a new algorithm for performing bss furthermore first ideas of how to generalize separability results based on hessian diagonalization to more complicated nonlinear models are studied in the setting of postnonlinear bss

the behavior of the stahel donoho robust multivariate estimator abstract the stahel donoho estimators t v of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w r where w is a weight function and r is a measure of outlyingness obtained by considering all univariate projections of the data it has a high breakdown point for all dimensions and order n consistency the asymptotic bias of v for point mass contamination for suitable weight functions is compared with that of rousseeuw s minimum volume ellipsoid mve estimator a simulation shows that for a suitable w t and v exhibit high efficiency for both normal and cauchy distributions and are better than their competitors for normal data with point mass contamination the performances of the estimators for detecting outliers are compared for both a real and a synthetic data set

asymptotics of reweighted estimators of multivariate location and scatter we investigate the asymptotic behavior ofa weighted sample mean and covariance where the weights are determined by the mahalanobis distances with respect to initial robust estimators we derive an explicit expansion for the weighted estimators from this expansion it can be seen that reweighting does not improve the rate ofconvergence ofthe initial estimators we also show that ifone uses smooth s estimators to determine the weights the weighted estimators are asymptotically normal finally we will compare the efficiency and local robustness of the reweighted s estimators with two other improvements of s estimators estimators and constrained m estimators

roving level tone in noise detection the detectability of tones or of intensity increments to tones in bands of random noise was measured for conditions in which the overall level was fixed or was randomly roved from interval to interval of every experimental trial the purpose of the within trial rove was to limit the usefulness of a detection strategy based on overall level or level within a single critical band at supracritical bandwidths the functions relating masked threshold to noise bandwidth for the roved conditions were similar to those obtained when no rove was employed at subcritical bandwidths thresholds were higher in some roved conditions but for the largest rove were still lower than would be predicted from arguments based purely on level detection with one exception a comparison of observer performance relative to the statistical limits imposed by the roving level procedure indicated that the traditional critical band energy detector model could not account for the results which are attributed to discrimination based on spectral shape or on waveshape

relative effects of increment and pedestal duration on the detection of intensity increments the detection of a brief increment in the intensity of a longer duration pedestal is commonly used as a measure of intensity resolution increment detection is known to improve with increasing duration of the increment and also with increasing duration of the pedestal but the relative effects of these two parameters have not been explored in the same study in several past studies of the effects of increment duration pedestal duration was increased as increment duration increased in the present study increment and pedestal duration were independently manipulated increment detection thresholds were determined for four subjects with normal hearing using a 500 or 4000 hz pedestal presented at 60 db sound pressure level spl increment durations were 10 20 40 80 160 and 320 ms pedestal durations were 20 40 80 160 and 320 ms each increment duration was combined with all pedestals of equal or greater duration multiple regression analyses indicate that increment detection under these conditions is determined primarily by pedestal duration follow up experiments ruled out effects of off frequency listening or overshoot the results suggest that effects of increment duration have been confounded by effects of pedestal duration in studies that co varied increment and pedestal duration implications for models of temporal integration are discussed

a robust procedure for gaussian graphical model search from microarray data with p larger than n learning of large scale networks of interactions from microarray data is an important and challenging problem in bioinformatics a widely used approach is to assume that the available data constitute a random sample from a multivariate distribution belonging to a gaussian graphical model as a consequence the prime objects of inference are full order partial correlations which are partial correlations between two variables given the remaining ones in the context of microarray data the number of variables exceed the sample size and this precludes the application of traditional structure learning procedures because a sampling version of full order partial correlations does not exist in this paper we consider limited order partial correlations these are partial correlations computed on marginal distributions of manageable size and provide a set of rules that allow one to assess the usefulness of these quantities to derive the independence structure of the underlying gaussian graphical model furthermore we introduce a novel structure learning procedure based on a quantity obtained from limited order partial correlations that we call the non rejection rate the applicability and usefulness of the procedure are demonstrated by both simulated and real data

robust estimators for nondecomposable elliptical graphical models robust estimators of the restricted covariance matrices associated with elliptical graphical models are studied general asymptotic results which apply to both decomposable and nondecomposable graphical models are presented for robust plug in type estimators these extend results previously established only for the decomposable case furthermore a class of graphical m estimators for the restricted covariance matrices is introduced and compared with the corresponding plug in m estimators the two approaches are shown to be asymptotically equivalent under random sampling from an elliptical distribution a simulation study demonstrates the superiority of the graphical m estimators for small samples

robust estimates of location and dispersion for high dimensional datasets the computing times of high breakdown point estimates of multivariate location and scatter increase rapidly with the number of variables which makes them impractical for high dimensional datasets such as those used in data mining we propose an estimator of location and scatter based on a modified version of the gnanadesikan kettenring robust covariance estimate we compare its behavior with that of the stahel donoho sd and rousseeuw and van driessen s fast mcd fmcd estimates in simulations with contaminated multivariate normal data our estimate is almost as good as sd and clearly better than fmcd it is much faster than both especially for large dimension we give examples with real data with dimensions between 5 and 93 in which the proposed estimate is as good as or better than sd and fmcd at detecting outliers and other structures with much shorter computing times

asymptotic data analysis on manifolds given an m dimensional compact submanifold m of euclidean space r s the concept of mean location of a distribution related to mean or expected vector is generalized to more general r s valued functionals including median location which is derived from the spatial median the asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated convergence properties are studied in relation to the behavior of the underlying distributions with respect to the cutlocus an application is given in the context of independent but not identically distributed samples in particular to a multisample setup

depth weighted scatter estimators general depth weighted scatter estimators are introduced and investigated for general depth functions we find out that these affine equivariant scatter estimators are fisher consistent and unbiased for a wide range of multivariate distributions and show that the sample scatter estimators are strong and n consistent and asymptotically normal and the influence functions of the estimators exist and are bounded in general we then concentrate on a specific case of the general depth weighted scatter estimators the projection depth weighted scatter estimators which include as a special case the well known stahel donoho scatter estimator whose limiting distribution has long been open until this paper large sample behavior including consistency and asymptotic normality and efficiency and finite sample behavior including breakdown point and relative efficiency of the sample projection depth weighted scatter estimators are thoroughly investigated the influence function and the maximum bias of the projection depth weighted scatter estimators are derived and examined unlike typical high breakdown competitors the projection depth weighted scatter estimators can integrate high breakdown point and high efficiency while enjoying a bounded influence function and a moderate maximum bias curve comparisons with leading estimators on asymptotic relative efficiency and gross error sensitivity reveal that the projection depth weighted scatter estimators behave very well overall and consequently represent very favorable choices of affine equivariant multivariate scatter estimators

semiparametrically efficient rank based inference for shape ii optimal r estimation of shape a class of r estimators based on the concepts of multivariate signed ranks and the optimal rank based tests developed in hallin and paindaveine 2006a is proposed for the estimation of the shape matrix of an elliptical distribution these r estimators are root n consistent under any radial density g without any moment assumptions and semiparametrically efficient at some prespecified density f when based on normal scores they are uniformly more efficient thanthe traditional normal theory estimator based on empirical covariance matrices the asymptotic normality of which moreover requires finite moments of order four irrespective of the actual underlying elliptical density they rely on an original rank based version of le cam s one step methodology which avoids the unpleasant nonparametric estimation of cross information quantities that is generally required in the context of r estimation although they are not strictly equivariant they are shown to be equivariant in a weak asymptotic sense simulations confirm their feasability and excellent finite sample performances

statistical analysis for the angular central gaussian distribution on the sphere summary the angular central gaussian distribution is an alternative to the bingham distribution for modeling antipodal symmetric directional data in this paper the statistical theory for the angular central gaussian model is presented some topics treated are maximum likelihood estimation of the parameters testing for uniformity and circularity and principal components analysis comparisons to methods based upon the sample second moments are made via an example

decrement detection in normal and impaired ears the smallest detectable duration of a brief decrement in the intensity of wideband noise was measured as a function of the depth of the decrement in the first experiment conditions were tested in which the noise before the decrement was more intense than the noise after the decrement and vice versa these data were used to estimate the shape of an intensity weighting function or temporal window describing the temporal resolution of the ear the equivalent rectangular durations erds of the temporal windows measured in this way had values of about 5 5 4 6 and 6 6 ms for noise spectrum levels of 10 30 and 50 db respectively in a second experiment decrement detection was measured in subjects with unilateral sensorineural hearing loss one set of thresholds was measured in the impaired ear and two sets of thresholds were measured in the normal ear one with the noise level at equal spl to the level in the impaired ear and one with the noise at equal sl temporal window shapes were also estimated from these data only one of the subjects showed reduced temporal resolution in the impaired ear the other two subjects having similar erd values for all three conditions

a topology preserving level set method for geometric deformable models active contour and surface models also known as deformable models are powerful image segmentation techniques geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior parameterization independence and ease of implementation however a long claimed advantage of geometric deformable models the ability to automatically handle topology changes turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved we present a new class of geometric deformable models designed using a novel topology preserving level set method which achieves topology preservation by applying the simple point concept from digital topology these new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces moreover since the topology preserving constraint is enforced efficiently through local computations the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

auditory filters and the benefit measured from spectral enhancement algorithms designed to improve speech intelligibility for those with sensorineural hearing loss snhl by enhancing peaks in a spectrum have had limited success since testing of such algorithms cannot separate the theory of the design from the implementation itself the contribution of each of these potentially limiting factors is not clear therefore psychophysical paradigms were used to test subjects with either normal hearing or snhl in detection tasks using well controlled stimuli to predict and assess the limits in performance gain from a spectrally enhancing algorithm a group of normal hearing nh and hearing impaired hi subjects listened in two experiments auditory filter measurements and detection of incremented harmonics in a harmonic spectrum the results show that nh and hi subjects have an improved ability to detect incremented harmonics when there are spectral decrements surrounding the increment various decrement widths and depths were compared against subjects equivalent rectangula

robustness properties of s estimators of multivariate location and shape in high dimension author s rocke david abstract for the problem of robust estimation of multivariate location and shape defilllng s estimators using scale transformations of a fixed p function regardless of the dimension as is usually done leads to a perverse outcome estimators in high dimension can have a breakdown point approaching 50 but still fail to reject as outliers points that are large distances from the main mass of points this leads to a form of nonrobustness that has important practical consequences in this paper estimators are defined that improve on known s estimators in having alll of the following properties 1 maximal breakdown for the given sample size and dimension 2 ability completely to reject as outliers points that are far from the main mass of points 3 convergence to good solutions with a modest amount of computation from a nonrobust starting point for large though not near 50 contamination however to attain maximal breakdown these estimates like other known maximal breakdown estimators require large amounts of computational effort this greater ability of the new estimators to reject outliers comes at a modest cost in efficiency and gross error sensitivity and at a greater but finite cost in local shift sensitivity

elliptical graphical modelling we propose elliptical graphical models based on conditional uncorrelatedness as a gen eralization of gaussian graphical models by letting the population distribution be elliptical instead of normal allowing the tting of data with arbitrarily heavy tails we study the class of propor tionally ane equivariant scatter estimators and show how they can be used to perform elliptical graphical modelling leading to a new class of partial correlation estimators and analogues of the classical deviance test general expressions for the asymptotic variance of partial correlation esti mators unconstrained and under decomposable models are given and the asymptotic chi square approximation of the pseudo deviance test statistic is proved the feasibility of our approach is demonstrated by a simulation study using among others tyler s scatter estimator which is distribution free within the elliptical model our approach provides a robustication of gauss ian graphical modelling the latter is likelihood based and known to be very sensitive to model misspecication and outlying observations 1 introduction and notation the statistical theory of undirected graphical models for continuous variables is usually based on the assumption of multivariate normality in practice data may deviate from the normal model in various ways outliers and heavy tails pose a problem of particular gravity they frequently occur and the normal likelihood methods such as the sample covariance matrix are very susceptible to them our objective is to deal with heavy tailed data and to safeguard graphical modelling against the impact of faulty outliers we restrict our attention to the case where we have only continuous variables and only undirected edges joint multivariate normality is often assumed in this situation and the statistical methodology is called gaussian graphical modelling we propose the class of elliptical distributions as a more general model and call our approach elliptical graphical modelling the lack of robustness of gaussian graphical modelling has been noted by several authors four proposals of robust approaches to gaussian graphical modelling are known to us becker 2005 and gottard and pacillo 2010 suggest replacing the sample covariance matrix by the reweighted minimum covariance determinant estimator miyamura and kano 2006 propose an alternative m type estimation and finegold drton arxiv 1009 3669 consider robustied versions of the graphical lasso by friedman et al 2008 this article delivers a systematic treatment of the plug in approach used in the rst two ref erences we show that the sample covariance matrix may be replaced by any ane equivariant

model selection and estimation in the gaussian graphical model summary we propose penalized likelihood methods for estimating the concentration matrix in the gaussian graphical model the methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite and thus conduct model selection and estimation simultaneously the implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix but we show that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization we propose a bic type criterion for the selection of the tuning parameter in the penalized likelihood methods the connection between our methods and existing methods is illustrated simulations and real examples demonstrate the competitive performance of the new methods

detection of time and bandlimited increments and decrements in a random level noise the purpose of this study was to compare detection of increments and decrements occurring over limited regions of time and frequency within a 500 ms broadband 0 6000 hz noise three listeners tracked detection thresholds adaptively in a two interval two alternative forced choice task thresholds were measured for both increments and decrements in level l 10 log10 1 n0 n0 db where n0 is the spectral power density of the noise as a function of signal duration t 30 500 ms for a range of signal bandwidths w 62 6000 hz that were logarithmically centered around 2500 hz listeners were forced to rely on temporal and spectral profile cues for detection due to randomization of overall presentation level from interval to interval which rendered overall energy an inconsistent cue increments were detectable for all combinations of w and t whereas decrements were not consistently detectable for w 500 hz narrow band decrements were not detectable due to spread of excitation from the spectral edges of

robust functional estimation using the median and spherical principal components summary we present robust estimators for the mean and the principal components of a stochastic process in l2 r robustness and asymptotic properties of the estimators are studied theoretically by simulation and by example it is shown that the proposed estimators are generally more robust to outliers than the commonly used sample mean and principal components although their properties depend on the spacings of the eigenvalues of the covariance function

efficient methods for implicit geometrical representation of complex material microstructures summary we present two methods for initializing distance functions on adaptively refined finite element meshes to represent complex material microstructures from segmented x ray tomographic data implicit microstructure representation combined with the extended fem allows modelers to represent complex material microstructures with consistent mesh quality and accuracy in the first method a level set evolution equation is formulated and solved by the galerkin method on an adaptively refined mesh we show that the convergence and stability of this method is optimal for the order of elements used in the second approach we initialize the distance field by the fast marching method on a uniform grid and then project the solution onto the finite element mesh by least squares we show that this latter approach is superior in speed and accuracy as an example problem both methods are demonstrated in the initialization of distance fields for two inclusion phases within a al 7075 alloy copyright 2014 john wiley sons ltd

uniqueness of the spatial median on montre que si une mesure de probabilite sur un espace euclidien n est pas concentree sur une droite alors sa mediane spatiale est unique

a practical affine equivariant multivariate median summary a robust affine equivariant estimator of location for multivariate data is proposed which becomes the univariate median for data of dimension one the estimator is robust in the sense that it has a bounded influence function a positive breakdown value and has high efficiency compared to the sample mean for heavy tailed distributions perhaps its greatest strength is that unlike other affine equivariant multivariate medians it is easily computed for data in any practical dimension

constrained m estimation for multivariate location and scatter consider the problem of estimating the location vector and scatter matrix from a set of multivariate data two standard classes of robust estimates are m estimates and s estimates the m estimates can be tuned to give good local robustness properties such as good efficiency and a good bound on the influence function at an underlying distribution such as the multivariate normal however m estimates suffer from poor breakdown properties in high dimensions on the other hand s estimates can be tuned to have good breakdown properties but when tuned in this way they tend to suffer from poor local robustness properties in this paper a hybrid estimate called a constrained m estimate is proposed which combines both good local and good global robustness properties

stochastic inequalities relating a class of log likelihood ratio statistics to their asymptotic chi 2 distribution for decomposable covariance selection models stochastic inequalities which relate the null distribution of the log likelihood ratio statistic to its asymptotic 2 distribution are obtained the implications are twofold first the null distribution of the log likelihood ratio statistic is seen to be stochastically larger than its asymptotic 2 distribution second a simple adjustment to the log likelihood ratio statistic similar in spirit to the bartlett adjustment yields a conservative test

the asymptotics of rousseeuw s minimum volume ellipsoid estimator rousseeuw s minimum volume estimator for multivariate location and dispersion parameters has the highest possible breakdown point for an affine equivariant estimator in this paper we establish that it satisfies a local holder condition of order 1 2 and converges weakly at the rate of n 1 3 to a non gaussian distribution

a combined extended finite element and level set method for biofilm growth this paper presents a computational technique based on the extended finite element method xfem and the level set method for the growth of biofilms the discontinuous derivative enrichment of the standard finite element approximation eliminates the need for the finite element mesh to coincide with the biofilm fluid interface and also permits the introduction of the discontinuity in the normal derivative of the substrate concentration field at the biofilm fluid interface the xfem is coupled with a comprehensive level set update scheme with velocity extensions which makes updating the biofilm interface fast and accurate without need for remeshing the kinetics of biofilms are briefly given and the non linear strong and weak forms are presented the non linear system of equations is solved using a newton raphson scheme example problems including 1d and 2d biofilm growth are presented to illustrate the accuracy and utility of the method the 1d results we obtain are in excellent agreement with previous 1d results obtained using finite difference methods our 2d results that simulate finger formation and finger tip splitting in biofilms illustrate the robustness of the present computational technique copyright 2007 john wiley sons ltd

subspace based direction of arrival estimation using nonparametric statistics the problem of subspace estimation using multivariate nonparametric statistics is addressed we introduce new high resolution direction of arrival doa estimation methods that have almost optimal performance in nominal conditions and are robust in the face of heavy tailed noise the extensions of the techniques for the case of coherent sources are considered as well the proposed techniques are based on spatial sign and rank concepts we show that spatial sign and rank covariance matrices can be used to obtain convergent estimates of the signal and noise subspaces in the proofs the noise is assumed to be spherically symmetric moreover we illustrate how the number of signals may be determined using the proposed covariance matrix estimates and a robust estimator of variance the performance of the algorithms is studied using simulations in a variety of noise conditions including noise that is not spherically symmetric the results show that the algorithms perform near optimally in the case of gaussian noise and highly reliably if the noise is non gaussian

successive versus simultaneous comparison in auditory intensity discrimination the ability to discriminate between two brief sounds having identical frequency components but differing in the intensity of one or more of the components is studied the stimulus manipulations include randomizing the overall intensity of the sounds varying the number and spacing of the components and varying the interval of time between the sounds the results from the experiment in which interstimulus interval is manipulated clearly support a profile analysis mechanism that computes two rough spectral analyses stores a classification of these spectra in memory and compares the two stores this profile mechanism involves a simultaneous comparison of different components of the complex some remote from the signal frequency rather than a successive comparison of the difference in intensity at the signal frequency the simultaneous comparison process is more sensitive when the profile is composed of many components spaced over a wide frequency range

auditory filter shapes of normal hearing and hearing impaired listeners in continuous broadband noise listeners with sensorineural hearing impairment typically exhibit auditory processing deficits such as reduced frequency and or temporal resolution such deficits may represent separate sequela of auditory pathology or may result directly from the sensitivity loss and the requirement to listen at high levels to assess the impact of increased thresholds on frequency resolution auditory filter characteristics were determined for hearing impaired and normal hearing listeners at 500 and 2000 hz in the presence of continuous broadband noise meant as a rough simulation of hearing loss in the fitting procedure the low frequency skirt of the derived auditory filter was allowed to vary as a function of signal level permitting different filter shapes to be estimated at high versus low signal levels listeners with moderate hearing losses at 2000 hz demonstrated near normal auditory filter shapes for lower signal levels but increasingly broad and asymmetric filters as signal level was raised at 500 hz where hearing losses were mild filter bandwidths increased little at the higher signal levels the presence of broadband noise had essentially no effect on filter shapes of either listener group the filter shape abnormalities demonstrated by listeners with moderate hearing loss which were not observed in normal hearing listeners at the same signal levels indicate that poor frequency resolution in these patients for high intensity stimuli does not follow directly from decreased sensitivity but instead reflects an independent pathology

penalty based aggregation of multidimensional data abstract research in aggregation theory is nowadays still mostly focused on algorithms to summarize tuples consisting of observations in some real interval or of diverse general ordered structures of course in practice of information processing many other data types between these two extreme cases are worth inspecting this contribution deals with the aggregation of lists of data points in r d for arbitrary d 1 even though particular functions aiming to summarize multidimensional data have been discussed by researchers in data analysis computational statistics and geometry there is clearly a need to provide a comprehensive and unified model in which their properties like equivariances to geometric transformations internality and monotonicity may be studied at an appropriate level of generality the proposed penalty based approach serves as a common framework for all idempotent information aggregation methods including componentwise functions pairwise distance minimizers and data depth based medians it also allows for deriving many new practically useful tools

on m estimators and normal quantiles this paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles our estimators are linear combinations of m estimators their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators compared with empirical quantiles the new estimators offer considerable reduction of variance at near normal probability distributions

cholesky decomposition of a hyper inverse wishart matrix the canonical parameter of a covariance selection model is the inverse covariance matrix 1 whose zero pattern gives the conditional independence structure characterising the model in this paper we consider the upper triangular matrix obtained by the cholesky decomposition 1 t this provides an interesting alternative parameterisation of decomposable models since its upper triangle has the same zero structure as 1 and its elements have an interpretation as parameters of certain conditional distributions for a distribution for the strong hyper markov property is shown to be characterised by the mutual independence of the rows of this is further used to generalise to the hyper inverse wishart distribution some well known properties of the inverse wishart distribution in particular we show that a hyper inverse wishart matrix can be decomposed into independent normal and chi squared random variables and we describe a family of transformations under which the family of hyper inverse wishart distributions is closed

level discrimination of tones as a function of duration difference limens for level ls db 20 log p p p where p is the pressure were measured as a function of duration for tones at 250 500 and 8000 hz stimulus durations ranged from 2 ms to 2 s and the stimulus power was held constant rise and fall times were 1 ms the interstimulus interval was 250 ms at each frequency three levels were tested 85 65 and approximately 40 db spl an adaptive two alternative forced choice procedure with feedback was used for three normal listeners ls decreased as duration increased up to at least 2 s except at 250 hz at 250 hz l stopped decreasing at durations between 0 5 and 1 s in a double logarithmic plot of l versus duration the rate of decrease is generally well fitted by a sloping line the average slope is 0 28 it is steeper at high levels than at low levels because the average slope is shallower than the 0 5 slope predicted for an optimum detector it may be that fast adaptation of auditory nerve activity and or memory effects interfere w

convergence of markovian stochastic approximation with discontinuous dynamics this paper is devoted to the convergence analysis of stochastic approximation algorithms of the form theta n 1 theta n gamma n 1 h theta n x n 1 where left theta n n in mathbb n right is an mathbb r d valued sequence left gamma n n in mathbb n right is a deterministic stepsize sequence and left x n n in mathbb n right is a controlled markov chain we study the convergence under weak assumptions on smoothness in theta of the function theta mapsto h theta x it is usually assumed that this function is continuous for any x in this work we relax this condition our results are illustrated by considering stochastic approximation algorithms for adaptive quantile estimation and a penalized version of the vector quantization

psychometric functions for level discrimination to determine the form of psychometric functions for 2i 2afc level discrimination ten increment levels were presented in random order within blocks of 100 trials stimuli were chosen to encompass a wide range of conditions and difference limens eight 10 ms tones had frequencies of 0 25 1 8 or 14 khz and levels of 30 60 or 90 db spl two 500 ms stimuli also were tested a 1 khz tone at 90 db spl and a white noise at 63 db spl for each condition at least 20 blocks were presented in mixed order results for three normal listeners show that the sensitivity d is nearly proportional to l 20 log p p p where p is pressure over the entire range of difference limens when d is plotted against weber fractions for pressure p p or intensity i i exponents of the best fitting power functions decrease with increasing difference limens and are less than one for large difference limens these results indicate that the transformation from stimulus intensity to decision variable may be approximately lo

multi scale constitutive modelling of heterogeneous materials with a gradient enhanced computational homogenization scheme a gradient enhanced computational homogenization procedure that allows for the modelling of microstructural size effects is proposed within a general non linear framework in this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element rve this enables us to incorporate the microstructural size and to account for non uniform macroscopic deformation fields within the microstructural cell every microstructural constituent is modelled as a classical continuum and the rve problem is formulated in terms of standard equilibrium and boundary conditions from the solution of the microstructural boundary value problem the macroscopic stress tensor and the higher order stress tensor are derived based on an extension of the hill mandel condition this automatically delivers the microstructurally based constitutive response of the higher order macro continuum and deals with the microstructural size in a natural way several examples illustrate the approach particularly the microstructural size effects

gaussian markov distributions over finite graphs on s interesse aux modeles de selection de covariance introduites par dempster 1972 et etudies par wermuth 1976

the extended finite element method xfem for solidification problems an enriched finite element method for the multi dimensional stefan problems is presented in this method the standard finite element basis is enriched with a discontinuity in the derivative of the temperature normal to the interface the approximation can then represent the phase interface and the associated discontinuity in the temperature gradient within an element the phase interface can be evolved without re meshing or the use of artificial heat capacity techniques the interface is described by a level set function that is updated by a stabilized finite element scheme several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method copyright 2001 john wiley sons ltd

measures of intensity discrimination several different measures have been employed in the literature to describe performance by human observers in intensity discrimination tasks these measures include the difference limen dl or i in db the weber fraction i i and signal to masker ratio ps pm this article describes the mathematical relationship among these measures for conditions in which masker and signal are 1 sinusoids of the same frequency 2 sinusoids of different frequencies and 3 noise waveforms we provide a table which contains values of each of these measures describing equivalent performance over the typical range obtained in most intensity discrimination experiments we express some cautions that should be observed in choosing and reporting particular measures of intensity discrimination

the identification of multiple outliers abstract one approach to identifying outliers is to assume that the outliers have a different distribution from the remaining observations in this article we define outliers in terms of their position relative to the model for the good observations the outlier identification problem is then the problem of identifying those observations that lie in a so called outlier region methods based on robust statistics and outward testing are shown to have the highest possible breakdown points in a sense derived from donoho and huber but a more detailed analysis shows that methods based on robust statistics perform better with respect to worst case behavior a concrete outlier identifier based on a suggestion of hampel is given

model selection for gaussian concentration graphs gga multivariate gaussian graphical markov model for an undirected graph g also called a covariance selection model or concentration graph model is defined in terms of the markov properties i e conditional independences associated with g which in turn are equivalent to specified zeros among the set of pairwise partial correlation coefficients by means of fisher s z transformation and sidak s correlation inequality conservative simultaneous confidence intervals for the entire set of partial correlations can be obtained leading to a simple method for model selection that controls the overall error rate for incorrect edge inclusion the simultaneous p values corresponding to the partial correlations are partitioned into three disjoint sets a significant set s an indeterminate set i and a nonsignificant set n our model selection method selects two graphs a graph g si whose edges correspond to the set s i and a more conservative graph g s whose edges correspond to s only similar considerations apply to covariance graph models which are defined in terms of marginal independence rather than conditional independence the method is applied to some well known examples and to simulated data