high breakdown linear discriminant analysis abstract the classification rules of linear discriminant analysis are defined by the true mean vectors and the common covariance matrix of the populations from which the data come because these true parameters are generally unknown they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population however these sample statistics are notoriously susceptible to contamination by outliers a problem compounded by the fact that the outliers may be invisible to conventional diagnostics high breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers regardless of their severity in this article we motivate and develop a high breakdown criterion for linear discriminant analysis and give an algorithm for its implementation the procedure is intended to supplement rather than replace the usual sample moment methodology of discri

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

generalization of space filling bearings to arbitrary loop size a model for space filling packing of discs rolling sliplessly on each other is presented this model is an extension of the model presented by herrmann et al to a basic loop size of an arbitrary even number of discs this model might have application in geophysics dense granular flows and turbulence we show the existence and uniqueness of such constructions analytically for loop size up to eight and numerically for bigger basic loop sizes and make precise the algorithm to construct them a classification of the solution is also given and extensive studies of the fractal dimension are performed showing that it varies considerably with the base loop size

power law distributions for the areas of the basins of attraction on a potential energy landscape energy landscape approaches have become increasingly popular for analyzing a wide variety of chemical physics phenomena basic to many of these applications has been the inherent structure mapping which divides up the potential energy landscape into basins of attraction surrounding the minima here we probe the nature of this division by introducing a method to compute the basin area distribution and applying it to some archetypal supercooled liquids we find that this probability distribution is a power law over a large number of decades with the lower energy minima having larger basins of attraction interestingly the exponent for this power law is approximately the same as that for a high dimensional apollonian packing providing further support for the suggestion that there is a strong analogy between the way the energy landscape is divided into basins and the way that space is packed in self similar space filling hypersphere packings such as the apollonian packing these results suggest that the basins of attraction provide a fractal like tiling of the energy landscape and that a scale free pattern of connections between the minima is a general property of energy landscapes

on adaptive estimation in stationary arma processes on demontre la normalite asymptotique locale puis on construit des estimateurs localement asymptotiquement minimax

multifractality of space filling bearings and apollonian packings we study the structure of space filling bearings sfb and apollonian packings ap by determining the scaling behavior of the density distribution of points where the circles touch each other application of the sand box method to the average of theqth power of the number of touching points reveals the multifractal aspects of the structure of sfb and ap

breakdown points of affine equivariant estimators of multivariate location and covariance matrices finite sample replacement breakdown points are derived for different types of estimators of multivariate location and covariance matrices the role of various equivariance properties is illustrated the breakdown point is related to a measure of performance based on large deviations probabilities finally we show that one step reweighting preserves the breakdown point

plato apollonius and klein playing with spheres abstract we describe the group theoretical background and the numerical techniques which enable us to compute new families of apollonian circle packings we provide examples of these constructions and we motivate this research from the physical and the mathematical point of view

r estimation in semiparametric dynamic location scale models we propose rank based estimation r estimators as an alternative to gaussian quasi likelihood and standard semiparametric estimation in time series models where conditional location and or scale depend on a euclidean parameter of interest while the unspecified innovation density is a nuisance we show how to construct r estimators achieving semiparametric efficiency at some predetermined reference density while preserving root n consistency and asymptotic normality irrespective of the actual density contrary to the standard semiparametric estimators our r estimators neither require tangent space calculations nor innovation density estimation numerical examples illustrate their good performances on simulated and real data

random sequential adsorption of spheres of different sizes the random sequential adsorption of spheres selected from monodisperse binary and polydisperse distributions on a three dimensional substrate has been studied by computer simulations in the monodisperse case the adsorbed particle density algebraically approaches an asymptotic value of 0 384 0 001 according to feder s law feder j theor biol 87 1980 237 for the case of spheres of two different sizes the large sphere density approaches its asymptotic value exponentially while the small sphere density increases according to feder s law if the sphere radii ri are uniformly distributed over the range ra ri rb before testing for overlaps then the approach to the asymptotic density is algebraic but the effective exponent depends on the model parameter r rb ra

independent component analysis via distance covariance abstractthis article introduces a novel statistical framework for independent component analysis ica of multivariate data we propose methodology for estimating mutually independent components and a versatile resampling based procedure for inference including misspecification testing independent components are estimated by combining a nonparametric probability integral transformation with a generalized nonparametric whitening method based on distance covariance that simultaneously minimizes all forms of dependence among the components we prove the consistency of our estimator under minimal regularity conditions and detail conditions for consistency under model misspecification all while placing assumptions on the observations directly not on the latent components u statistics of certain euclidean distances between sample elements are combined to construct a test statistic for mutually independent components the proposed measures and tests are based on both necessary and sufficient conditions for

self similar disk packings as model spatial scale free networks the network of contacts in space filling disk packings such as the apollonian packing is examined these networks provide an interesting example of spatial scale free networks where the topology reflects the broad distribution of disk areas a wide variety of topological and spatial properties of these systems is characterized their potential as models for networks of connected minima on energy landscapes is discussed

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

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

complex networks in confined comminution the physical process of confined comminution is investigated within the framework of complex networks we first characterize the topology of the unweighted contact networks as generated by the confined comminution process we find this process gives rise to an ultimate contact network which exhibits a scale free degree distribution and small world properties in particular if viewed in the context of networks through which information travels along shortest paths we find that the global average of the node vulnerability decreases as the comminution process continues with individual node vulnerability correlating with grain size a possible application to the design of synthetic networks e g sensor networks is highlighted next we turn our attention to the physics of the granular comminution process and examine force transmission with respect to the weighted contact networks where each link is weighted by the inverse magnitude of the normal force acting at the associated contact we find that the strong forces i e force chains are transmitted along pathways in the network which are mainly following shortest path routing protocols as typically found for example in communication systems motivated by our earlier studies of the building blocks for self organization in dense granular systems we also explore the properties of the minimal contact cycles the distribution of the contact strain energy intensity of 4 cycle motifs in the ultimate state of the confined comminution process is shown to be consistent with a scale free distribution with infinite variance thereby suggesting that 4 cycle arrangements of grains are capable of storing vast amounts of energy in their contacts without breaking

space filling tiling by random packing of discs abstract we study here a space filling tiling generated by random non overlapping packing of discs to place the n th disc we randomly choose a point in the empty pore space of the n 1 discs and place a disc with the centre at this point and touching the nearest disc we measure the fractal dimension of the pore space left in the asymptotic limit for these space filling patterns

apollonian arrangements of spheres in d dimensional space the problem of arranging d dimensional spheres in such a way that each sphere touches exactly d 1 others is formulated by means of linear recursions involving d 1 different d 2 d 2 matrices the average curvatures are calculated exactly for any dimension special scaling limits for the powers of one matrix or of the products of two matrices show interesting behaviour the corresponding curvatures either diverge quadratically or form a six step cycle only for d 3 and one matrix or show ergodic behaviour sometimes with universal invariant measure the latter type of behaviour is also found if the results are formally extended to non integer values of d

the hausdorf dimension of the apollonian packing of circles we formulate the problem of determining the hausdorf dimension df of the apollonian packing of circles as an eigenvalue problem of a linear integral equation we show that solving a finite dimensional approximation to this infinite order matrix equation and extrapolating the results provides a fast algorithm for obtaining high precision numerical estimates for df we find that df 1 305 686 729 10 this is consistent with the rigorously known bounds on df and improves the precision of the existing estimate by three orders of magnitude

comment on random sequential packing in square cellular structures based on a paper by nakamura j phys a vol 19 p 2345 1986 the authors correlate two methods for packing squares on a square lattice and find agreement with published computer simulation results

pattern formation by growing droplets the touch and stop model of growth we investigate a novel model of pattern formation phenomena in this model spherical droplets are nucleated on a substrate and grow at constant velocity when two droplets touch each other they stop their growth we examine the heterogeneous process in which the droplet formation is initiated on randomly distributed centers of nucleation and the homogeneous process in which droplets are nucleated spontaneously at constant rate for the former process we find that in arbitrary dimensiond the system reaches a jamming state where further growth becomes impossible for the latter process we observe the appearance of fractal structures we develop mean field theories that predict that the fraction of uncovered material t approaches to the jamming limit as t exp ctd for the heterogeneous process and as a power law for the homogeneous process exact solutions in one dimension are obtained and numerical simulations ford 1 3 are performed and compared with mean field predictions

rank based estimates in the linear model with high breakdown point abstract an estimator in the linear model is defined by minimizing an objective function the derivative of which is a signed rank statistic the scores are generated from a function h 0 1 0 which is not necessarily nondecreasing as is usually assumed it is shown that this estimator can be chosen with a maximal breakdown point of 5 moreover strong consistency and asymptotic normality with convergence rate n 1 2 of the proposed estimator are proved under various regularity conditions because the objective function generally is not convex in the regression parameters the usual proofs of asymptotic normality do not carry over instead the proof is based on an asymptotic linearity result similar to that obtained by huber for m estimates and some moment estimates for signed rank statistics numerical examples illustrate the behavior of the estimator

computable robust estimation of multivariate location and shape in high dimension using compound estimators abstract estimation of multivariate shape and location in a fashion that is robust with respect to outliers and is affine equivariant represents a significant challenge the use of compound estimators that use a combinatorial estimator such as rousseeuw s minimum volume ellipsoid mve or minimum covariance determinant mcd to find good starting points for high efficiency robust estimators such as s estimators has been proposed in this article we indicate why this scheme will fail in high dimension due to combinatorial explosion in the space that must be searched for the mve or mcd we propose a meta algorithm based on partitioning the data that enables compound estimators to work in high dimension we show that even when the computational effort is restricted to a linear function of the number of data points the algorithm results in an estimator with good asymptotic properties extensive computational experiments are used to confirm that significant benefits accrue in finite samples as well we also g

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

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

the deflation based fastica estimator statistical analysis revisited this paper provides a rigorous statistical analysis of the deflation based fastica estimator where the independent components ics are extracted sequentially the focus is on two aspects of the estimator robustness against outliers as measured by the influence function if and on its asymptotic relative efficiency are as measured by the ratio of the asymptotic variance of the fastica w r t the optimal maximum likelihood estimator mle the derived compact closed form expression of the if reveals the vulnerability of the fastica estimator to outliers regardless of the used nonlinearity a cautionary finding is that even a moderate observation towards certain directions can render the estimator deficient in the sense that its separation performance degrades worse than a plain guess the if allows the derivation of a compact closed form expression for the asymptotic covariance matrix of the fastica estimator and subsequently its asymptotic relative efficiencies ares the are figures calculated for some selected source distributions illustrate the fact that the order which the ics are found is crucial as the accuracy of the previously extracted components can dominantly affect the accuracy of the successive deflation stages

r estimation for asymmetric independent component analysis independent component analysis ica recently has attracted much attention in the statistical literature as an appealing alternative to elliptical models whereas k dimensional elliptical densities depend on one single unspecified radial density however k dimensional independent component distributions involve k unspecified component densities in practice for given sample size n and dimension k this makes the statistical analysis much harder we focus here on the estimation from an independent sample of the mixing demixing matrix of the model traditional methods fobi kernel ica fastica mainly originate from the engineering literature their consistency requires moment conditions they are poorly robust and do not achieve any type of asymptotic efficiency when based on robust scatter matrices the two scatter methods developed by oja sirkia and eriksson in 2006 and nordhausen oja and ollila in 2008 enjoy better robustness features but their optimality properties remain unclear the clas

fractional boundary for the gott hiscock string a fractional boundary condition is used to join the gott hiscock string to a levi civita vacuum the use of a fractional derivative generates israel boundary layers whose density depends on the order of the fractional derivative variable boundary layers for the same two bounding space times can be studied the string angular deficit depends on the order of the fractional deficit

efficient independent component analysis independent component analysis ica has been widely used for blind source separation in many fields such as brain imaging analysis signal processing and telecommunication many statistical techniques based on m estimates have been proposed for estimating the mixing matrix recently several nonparametric methods have been developed but in depth analysis of asymptotic efficiency has not been available we analyze ica using semiparametric theories and propose a straightforward estimate based on the efficient score function by using b spline approximations the estimate is asymptotically efficient under moderate conditions and exhibits better performance than standard ica methods in a variety of simulations

kernel independent component analysis we present a class of algorithms for independent component analysis ica which use contrast functions based on canonical correlations in a reproducing kernel hilbert space on the one hand we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence on the other hand building on recent developments in kernel methods we show that these criteria and their derivatives can be computed efficiently minimizing these criteria leads to flexible and robust algorithms for ica we illustrate with simulations involving a wide variety of source distributions showing that our algorithms outperform many of the presently known algorithms

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

a simple r estimation method for semiparametric duration models modeling nonnegative financial variables e g durations between trades traded volumes or asset volatilities is central to a number of studies across financial econometrics and despite the efforts still poses several statistical challenges among them the efficiency aspects of semiparametric estimation in this paper we concentrate on estimation problems in autoregressive conditional duration acd models with unspecified innovation densities exponential quasi likelihood estimators qmle are the usual practice in that context the efficiency of those qmles the only fisher consistent qmles unfortunately rapidly deteriorates away from the reference exponential density a phenomenon that has been emphasized earlier by drost and werker 2003 who propose various semiparametrically efficient procedures to palliate that phenomenon those procedures rely on a general semiparametric approach which typically requires kernel estimation of the underlying innovation density we propose rank based estimators r estimators as a substitute just as the qmle r estimators remain root n consistent irrespective of the underlying density and rely on the choice of a reference density under which they achieve semiparametric efficiency that density however needs not be the exponential one contrary to the semiparametric estimators proposed by drost and werker 2003 r estimators neither require tangent space calculations nor kernel based density estimation numerical results moreover indicate that r estimators based on exponential reference densities uniformly outperform the exponential qmle under such families of innovations as the weibull or burr densities a real data example about modeling the price range of the swiss stock market index concludes the paper

projection estimates of multivariate location in this paper we study the maximum asymptotic bias of the projection estimate for multivariate location based on univariate estimates of location and dispersion in particular we study the projection estimate that uses the median and median absolute deviation about the median mad as univariate location and dispersion estimates respectively this estimator may be considered a natural affine equivariant multivariate median for spherical distributions the maximum bias of this estimate depends only on the marginal distributions and not on the dimension and is approximately twice the maximum bias of the univariate median we also show that for multivariate normal distributions its maximum bias compares favorably with those of the donoho stahel minimum volume ellipsoid and minimum covariance determinant estimates in all these cases the maximum bias increases with the dimension p

semiparametrically efficient inference based on signs and ranks for median restricted models since the pioneering work of koenker and bassett 1978 econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest contrary to the traditional models where the noise is assumed to have mean zero median restricted models enjoy a rich group invariance structure in this paper we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models these procedures are based on residual signs and ranks and therefore insensitive to possible misspecification of the underlying innovation density yet semiparametrically efficient at correctly specified densities this latter combination is a definite advantage of these procedures over classical quasi likelihood methods the techniques we propose can be applied without additional technical difficulties to both cross sectional and time series models they do not require any explicit tangent space calculation nor any projections on these

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

pattern formation in size polydisperse adsorption fractal properties and transition to order abstract random sequential adsorption of particles with size polydispersity prsa is investigated for the prsa with a power law small size distribution p r r 1 we reveal the fractal nature of the arising patterns the fractal dimension d is found to decrease from 2 to d a 1 305 the fractal dimension of the apollonian packing as increases from 0 to we examine prsa by a combination of exact scaling mean field and numerical approaches we find that the scaling theory works fairly well for the whole range of while the mean field theory mft is applicable only for small we attribute this failure of the mft to the increasing regularity of the prsa patterns with increasing we confirm this conclusion by the direct measurement of the entropy production rate of the pattern formation process which demonstrates the transition from an irregular regime of the pattern formation to the regular one

an efficient dense and stable particular elements generation method based on geometry summary in this paper a new discrete elements generation method based on geometry is proposed to fill geometric domains with particles disks or spheres by generating particles each one with a random radius or with a radius calculated from the iteration to ensure no overlaps exist between particles and identifying unstable particles and changing them to stable ones a dense and stable packing can be created a partitioning particle radius interval method and a particle stability inspection and improvement method are introduced to guarantee the algorithm s success and the stability of the particles some packings were created to evaluate the performances of the new method the results showed that the algorithm was very efficient and was able to create isotropic packings of low porosities and large coordinate numbers the partitioning particle radius interval method improved the generation efficiency significantly and increased the packing densities through the comparisons with several existing methods proposed recently the method proposed in this work is found to be more efficient and can fill geometric domains with the lowest porosities in addition the stability of the particles is guaranteed and no complex triangular or tetrahedral mesh is required in particle generation thereby making the new method simpler copyright 2016 john wiley sons ltd

on one step gm estimates and stability of inferences in linear regression abstract the folklore on one step estimation is that it inherits the breakdown point of the preliminary estimator and yet has the same large sample distribution as the fully iterated version as long as the preliminary estimate converges faster than n 1 4 where n is the sample size we investigate the extent to which this folklore is valid for one step gm estimators and their associated standard errors in linear regression we find that one step gm estimates based on newton raphson or scoring inherit the breakdown point of high breakdown point initial estimates such as least median of squares provided the usual weights that limit the influence of extreme points in the design space are based on location and scatter estimates with high breakdown points moreover these estimators have bounded influence functions and their standard errors can have high breakdown points the folklore concerning the large sample theory is correct assuming the regression errors are symmetrically distributed and homoscedastic

precise determination of the fractal dimensions of apollonian packing and space filling bearings the authors present high precision numerical values for the fractal dimensions of apollonian packing and various space filling bearings which might have application for mechanical gearworks for turbulence or for tectonic motion they find for the simplest apollonian packing df 1 305 684 or 0 000 010

stochastic processes slaves and supersymmetry we extend the work of t nase nicola and kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds we consider both the stochastic differential equations sdes for the process and the associated diffusion equation the influence of the disturbances can be understood by augmenting the original sde with an equation for slave variables the evolution of the slave variables describes the behaviour of line elements carried along in the stochastic flow these line elements together with the associated surface and volume elements constructed from them provide the basis of the supersymmetry properties of the theory for ease of visualization and in order to emphasize a helpful electromagnetic analogy we work in three dimensions the results are all generalizable to higher dimensions and can be specialized to one and two dimensions the electromagnetic analogy is a useful starting point for calculating asymptotic results at low temperature that can be compared with direct numerical evaluations we also examine the problems that arise in a direct numerical simulation of the stochastic equation together with the slave equations we pay special attention to the dependence of the slave variable statistics on temperature we identify in specific models the critical temperature below which the slave variable distribution ceases to have a variance and consider the effect on estimates of susceptibilities

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 bounded influence high breakdown efficient regression estimator abstract we consider the multiple linear regression model y i x i e i i 1 2 n with random carriers and focus on the estimation of this article s main contribution is to present an estimator that is affine regression and scale equivariant has both a high breakdown point and a bounded influence function and has an asymptotic efficiency greater than 95 versus least squares under gaussian errors we give conditions under which the estimator a one step general m estimator that uses schweppe weights and is based on a high breakdown initial estimator satisfies these properties the major conditions necessary for the estimator are a it must be based on a n consistent initial estimator with a 50 breakdown point and b it must be based on a psi function that is odd bounded and strictly increasing the advantage of this estimator over previous approaches is that it does not downweight high leverage points without first considering how they fit the bulk of the data methods of computi

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

outlier detection in functional observations with applications to profile monitoring the presence of outliers has serious adverse effects on the modeling and forecasting of functional data therefore outlier detection aiming at identifying abnormal functional curves from a dataset is quite important this article proposes a new testing procedure based on functional principal component analysis under mild conditions the null distribution of the test statistic is shown to be asymptotically pivotal with a well known asymptotic distribution simulation results demonstrate good finite sample performance of the asymptotic test and detection procedure finally by illustrating the connection between profile monitoring in statistical process control and outlier detection in functional data we apply the proposed approach to a real data example from a manufacturing process and show that it performs quite well in detecting outlying profiles supplementary material for this article is posted online on the journal web site

semiparametrically efficient inference based on signed ranks in symmetric independent component models we consider semiparametric location scatter models for which the p variate observation is obtained as x lambda z mu where mu is a p vector lambda is a full rank p p matrix and the unobserved random p vector z has marginals that are centered and mutually independent but are otherwise unspecified as in blind source separation and independent component analysis ica the parameter of interest throughout the paper is lambda on the basis of n i i d copies of x we develop under a symmetry assumption on z signed rank one sample testing and estimation procedures for lambda we exploit the uniform local and asymptotic normality ulan of the model to define signed rank procedures that are semiparametrically efficient under correctly specified densities yet as usual in rank based inference the proposed procedures remain valid correct asymptotic size under the null for hypothesis testing and root n consistency for point estimation under a very broad range of densities we derive the asymptotic properties of the proposed procedures and investigate their finite sample behavior through simulations

propagation of outliers in multivariate data we investigate the performance of robust estimates of multivariate location under nonstandard data contamination models such as componentwise outliers i e contamination in each variable is independent from the other variables this model brings up a possible new source of statistical error that we call propagation of outliers this source of error is unusual in the sense that it is generated by the data processing itself and takes place after the data has been collected we define and derive the influence function of robust multivariate location estimates under flexible contamination models and use it to investigate the effect of propagation of outliers furthermore we show that standard high breakdown affine equivariant estimators propagate outliers and therefore show poor breakdown behavior under componentwise contamination when the dimension d is high

identification and estimation of non gaussian structural vector autoregressions abstract conventional structural vector autoregressive svar models with gaussian errors are not identified and additional identifying restrictions are needed in applied work we show that the gaussian case is an exception in that a svar model whose error vector consists of independent non gaussian components is without any additional restrictions identified and leads to essentially unique impulse responses building upon this result we introduce an identification scheme under which the maximum likelihood estimator of the parameters of the non gaussian svar model is consistent and asymptotically normally distributed as a consequence additional economic identifying restrictions can be tested in an empirical application we find a negative impact of a contractionary monetary policy shock on financial markets and clearly reject the commonly employed recursive identifying restrictions

random space filling tiling fractal properties and kinetics a kinetic version of random apollonian packing model is introduced in this model droplets nucleate spontaneously grow at a uniform rate and stop growing upon collisions the fractal dimension df of the pore space is found to be equal to df d 1 exp 2 2d 2 2 d 2 a result which is confirmed exactly in 1d and numerically in 2d

semiparametrically efficient rank based inference for shape i optimal rank based tests for sphericity we propose a class of rank based procedures for testing that the shape matrix v of an elliptical distribution with unspecified center of symmetry scale and radial density has some fixed value v 0 this includes for v 0 i k the problem of testing for sphericity as an important particular case the proposed tests are invariant under translations monotone radial transformations rotations and reflections with respect to the estimated center of symmetry they are valid without any moment assumption for adequately chosen scores they are locally asymptotically maximin in the le cam sense at given radial densities they are strictly distribution free when the center of symmetry is specified and asymptotically so when it must be estimated the multivariate ranks used throughout are those of the distances in the metric associated with the null value v 0 of the shape matrix between the observations and the estimated center of the distribution local powers against elliptical alternatives and asymptotic relative efficiencies ares are derived with respect to the adjusted mauchly test a modified version of the gaussian likelihood ratio procedure proposed by muirhead and waternaux biometrika 67 1980 31 43 or equivalently with respect to an extension of the test for sphericity introduced by john biometrika 59 1972 169 173 for gaussian scores these ares are uniformly larger than one irrespective of the actual radial density necessary and or sufficient conditions for consistency under nonlocal possibly nonelliptical alternatives are given finite sample performance is investigated via a monte carlo study

multivariate outlier detection with high breakdown estimators in this paper we develop multivariate outlier tests based on the high breakdown minimum covariance determinant estimator the rules that we propose have good performance under the null hypothesis of no outliers in the data and also appreciable power properties for the purpose of individual outlier detection this achievement is made possible by two orders of improvement over the currently available methodology first we suggest an approximation to the exact distribution of robust distances from which cut off values can be obtained even in small samples our thresholds are accurate simple to implement and result in more powerful outlier identification rules than those obtained by calibrating the asymptotic distribution of distances the second power improvement comes from the addition of a new iteration step after one step reweighting of the estimator the proposed methodology is motivated by asymptotic distributional results its finite sample performance is evaluated through simulations and compared to

a two sample test for high dimensional data with applications to gene set testing we proposed a two sample test for means of high dimensional data when the data dimension is much larger than the sample size the classical hotelling s t 2 test does not work for this large p small n situation the proposed test does not require explicit conditions on the relationship between the data dimension and sample size this offers much flexibility in analyzing high dimensional data an application of the proposed test is in testing significance for sets of genes which we demonstrate in an empirical study on a leukemia data set

the pair correlation function in a randomly sequentially filled one dimensional lattice we study random sequential adsorption of particles on a one dimensional lattice with exclusion of nearest neighbor occupation the fraction of filled sites in the saturated state y 12 1 e 2 was obtained long ago by widom we show that in the saturated state the probability p k of having two sites a distance k apart both occupied is given by p k y 2 12 1 ke 2 p 0 2k 2p 1 k 2p 1 and hence decays faster than exponentially as k

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

kinetics of random sequential parking on a line we study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line for the simplest fixed length parking distribution the model reduces to the known car parking problem and we present an alternate solution to this problem we also consider the general homogeneous case when the parking distribution varies asx 1 atx 1 with the lengthx of the filling interval we develop a scaling theory describing such mixture deposition processes and show that the scaled hole size distribution with xtz a scaling variable decays with the scaled mass as exp const 1 as we determine scaling exponentsz and and find that at large times the coverage t has a power law form 1 t t v with nonuniversal exponent 2 1 depending on the homogeneity index

projection based outlier detection in functional data summarywe propose a procedure based on a high breakdown mean function estimator to detect outliers in functional data the robust estimator is obtained from a clean subset of observations excluding potential outliers by minimizing the least trimmed squares projection coefficients after functional principal component analysis a threshold rule based on the asymptotic distribution of the functional score based distance robustly controls the false positive rate and detects outliers effectively further improvement in power can be achieved by adding a one step reweighting procedure the finite sample performance of our method demonstrates satisfactory false positive and false negative rates compared with existing outlier detection methods for functional data

multiple influential point detection in high dimensional regression spaces influence diagnosis should be routinely conducted when one aims to construct a regression model despite its importance the problem of influence quantification is severely under investigated in a high dimensional setting mainly due to the difficulty of establishing a coherent theoretical framework and the lack of easily implementable procedures although some progress has been made in recent years existing approaches are ineffective in detecting multiple influential points especially due to the notorious masking and swamping effects to address this challenge we propose a new group deletion procedure referred to as mip by introducing two novel quantities named max and min statistics these two statistics have complimentary properties in that the max statistic is effective for overcoming the masking effect while the min statistic is useful for overcoming the swamping effect combining their strengths we further propose an efficient algorithm that can detect influential points with prespecified guarantees for wider applications we focus on developing the new proposal for the multiple response regression model encompassing the univariate response linear model as a special case the proposed influential point detection procedure is simple to implement efficient to run and enjoys attractive theoretical properties its effectiveness is verified empirically via extensive simulation study and data analysis

consistent independent component analysis and prewhitening we study the statistical merits of two techniques used in the literature of independent component analysis ica first we analyze the characteristic function based ica method chfica and study its statistical properties such as consistency spl radic n consistency and robustness against small additive noise second we study the validity of prewhitening a preprocessing technique used by many ica algorithms as applied to the chfica method in particular we establish the surprising effectiveness of this technique even when some components have heavy tails and others do not a fast new algorithm implementing the prewhitened chfica method is also provided

outlier detection for high dimensional data outlier detection is an integral component of statistical modelling and estimation for high dimensional data classical methods based on the mahalanobis distance are usually not applicable we propose an outlier detection procedure that replaces the classical minimum covariance determinant estimator with a high breakdown minimum diagonal product estimator the cut off value is obtained from the asymptotic distribution of the distance which enables us to control the type i error and deliver robust outlier detection simulation studies show that the proposed method behaves well for high dimensional data

outlier detection and robust normal curvature estimation in mobile laser scanning 3d point cloud data this paper proposes two robust statistical techniques for outlier detection and robust saliency features such as surface normal and curvature estimation in laser scanning 3d point cloud data one is based on a robust z score and the other uses a mahalanobis type robust distance the methods couple the ideas of point to plane orthogonal distance and local surface point consistency to get maximum consistency with minimum distance mcmd the methods estimate the best fit plane based on most probable outlier free and most consistent points set in a local neighbourhood then the normal and curvature from the best fit plane will be highly robust to noise and outliers experiments are performed to show the performance of the algorithms compared to several existing well known methods from computer vision data mining machine learning and statistics using synthetic and real laser scanning datasets of complex planar and non planar objects results for plane fitting denoising sharp feature preserving and segmentation are significantly improved the algorithms are demonstrated to be significantly faster more accurate and robust quantitatively for a sample size of 50 with 20 outliers the proposed mcmd z is approximately 5 15 and 98 times faster than the existing methods ulsif ransac and rpca respectively the proposed mcmd md method can tolerate 75 clustered outliers whereas rpca and ransac can only tolerate 47 and 64 outliers respectively in terms of outlier detection for the same dataset mcmd z has an accuracy of 99 72 0 4 false positive rate and 0 false negative rate for rpca ransac and ulsif the accuracies are 97 05 47 06 and 94 54 respectively and they have misclassification rates higher than the proposed methods the new methods have potential for local surface reconstruction fitting and other point cloud processing tasks highlightstwo statistical techniques are proposed for outlier detection in point cloud data the proposed methods can fit robust plane in laser scanning data the proposed methods produce robust normal and curvature in point cloud processing they are faster and robust than ransac robust pca and other existing efficient methods they have potential for point cloud denoising segmentation and reconstruction

a cluster based outlier detection scheme for multivariate data detection power of the squared mahalanobis distance statistic is significantly reduced when several outliers exist within a multivariate dataset of interest to overcome this masking effect we propose a computer intensive cluster based approach that incorporates a reweighted version of rousseeuw s minimum covariance determinant method with a multi step cluster based algorithm that initially filters out potential masking points compared to the most robust procedures simulation studies show that our new method is better for outlier detection additional real data comparisons are given supplementary materials for this article are available online