approximate likelihood for large irregularly spaced spatial data likelihood approaches for large irregularly spaced spatial datasets are often very difficult if not infeasible to implement due to computational limitations even when we can assume normality exact calculations of the likelihood for a gaussian spatial process observed at n locations requires o n3 operations we present a version of whittle s approximation to the gaussian log likelihood for spatial regular lattices with missing values and for irregularly spaced datasets this method requires o nlog2n operations and does not involve calculating determinants we present simulations and theoretical results to show the benefits and the performance of the spatial likelihood approximation method presented here for spatial irregularly spaced datasets and lattices with missing values we apply these methods to estimate the spatial structure of sea surface temperatures using satellite data with missing values

edge effects and efficient parameter estimation for stationary random fields summary we consider the estimation of the parameters of a stationary random field on d dimensional lattice by minimizing the classical whittle approximation to the gaussian log likelihood if the usual biased sample covariances are used the estimate is efficient only in one dimension to remove this edge effect we introduce data tapers and show that the resulting modified estimate is efficient also in two and three dimensions this avoids the use of the unbiased sample covariances which are in general not positive definite

decorrelation property of discrete wavelet transform under fixed domain asymptotics theoretical aspects of the decorrelation property of the discrete wavelet transform when applied to stochastic processes have been studied exclusively from the increasing domain perspective in which the distance between neighboring observations stays roughly constant as the number of observations increases to understand the underlying data generating process and to obtain good interpolations fixed domain asymptotics in which the number of observations increases in a fixed region is often more appropriate than increasing domain asymptotics in the fixed domain setting we prove that for a general class of inhomogeneous covariance functions with suitable choice of wavelet filters the wavelet transform of a nonstationary process has mostly asymptotically uncorrelated components

nonparametric multivariate density estimation a comparative study the paper algorithmically and empirically studies two major types of nonparametric multivariate density estimation techniques where no assumption is made about the data being drawn from any of known parametric families of distribution the first type is the popular kernel method and several of its variants which uses locally tuned radial basis e g gaussian functions to interpolate the multidimensional density the second type is based on an exploratory projection pursuit technique which interprets the multidimensional density through the construction of several 1d densities along highly interesting projections of multidimensional data performance evaluations using training data from mixture gaussian and mixture cauchy densities are presented the results show that the curse of dimensionality and the sensitivity of control parameters have a much more adverse impact on the kernel density estimators than on the projection pursuit density estimators

nonparametric regression analysis achieved with topographic maps developed in combination with projection pursuit learning an application to density estimation and adaptive filtering of grey scale images a novel approach to nonparametric regression analysis using topographic maps is proposed the maps are trained with the extended maximum entropy learning rule emer in combination with projection pursuit regression ppr learning rather than a single map several maps are developed along optimally chosen projection directions in the input space in this way the regression performance improves in the case of sparsely sampled input spaces we explore two applications of the emer ppr combination 1 probability density estimation from pilot estimates and 2 adaptive filtering of grey scale images the first case is used as a testbed for comparing different both classic and neural network based regression techniques the results show that our emer ppr combination yields a superior regression performance for small data sets in the second case the regression model is trained on a noisy subimage the model obtained after training reduces the noise content of the full image by more than 20 db

a hybrid perturbation galerkin technique with applications to slender body theory a two step hybrid perturbation galerkin technique for solving a variety of applied mathematics problems involving a small parameter is presented the first step consists of using a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter then the approximate solution is assumed to have the form of a sum of perturbation coefficient functions multiplied by unknown amplitudes gauge functions in the second step the classical bubnov galerkin method is used to determine these amplitudes the resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and bubnov galerkin methods applied separately while combining some of the good features of both the proposed method is applied to some singular perturbation problems in slender body theory the results obtained from the hybrid method are compared with approximate solutions obtained by other methods and the applicability of the hybrid method to broade

on the use of discrete laplace operator for preconditioning kernel matrices this paper presents a preconditioning strategy applied to certain types of kernel matrices that are increasingly ill conditioned the ill conditioning of these matrices is tied to the unbounded variation of the fourier transform of the kernel function hence the basic idea is to differentiate the kernel in order to suppress the variation the idea resembles some existing preconditioning methods for toeplitz matrices where the theory heavily relies on the underlying fixed generating function the theory does not apply to the case of a fixed domain with increasingly fine discretizations because the generating function depends on the grid size for this case we prove equal distribution results on the spectrum of the resulting matrices furthermore the proposed preconditioning technique also applies to non toeplitz matrices thus eliminating the reliance on a regular grid structure of the points the preconditioning strategy can be used to accelerate an iterative solver for solving linear systems with res

regression modeling in back propagation and projection pursuit learning we study and compare two types of connectionist learning methods for model free regression problems 1 the backpropagation learning bpl and 2 the projection pursuit learning ppl emerged in recent years in the statistical estimation literature both the bpl and the ppl are based on projections of the data in directions determined from interconnection weights however unlike the use of fixed nonlinear activations usually sigmoidal for the hidden neurons in bpl the ppl systematically approximates the unknown nonlinear activations moreover the bpl estimates all the weights simultaneously at each iteration while the ppl estimates the weights cyclically neuron by neuron and layer by layer at each iteration although the bpl and the ppl have comparable training speed when based on a gauss newton optimization algorithm the ppl proves more parsimonious in that the ppl requires a fewer hidden neurons to approximate the true function to further improve the statistical performance of the ppl an orthogonal polynomial approximation is used in place of the supersmoother method originally proposed for nonlinear activation approximation in the ppl

spectral methods for nonstationary spatial processes summary we propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process we also study the asymptotic properties of the proposed estimators via shrinking asymptotics assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound with this type of asymptotic model we can uniquely determine the spectral density avoiding the aliasing problem we also present a new class of nonstationary processes based on a convolution of local stationary processes this model has the advantage that the model is simultaneously defined everywhere unlike moving window approaches but it retains the attractive property that locally in small regions it behaves like a stationary spatial process applications include the spatial analysis and modelling of air pollution data provided by the us environmental protection agency

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

parameter estimation for a stationary process on a d dimensional lattice summary we study asymptotic properties of various estimation procedures for a general stationary regular process on a d dimensional lattice differences between d 1 time series and d 2 spatial processes are pointed out we suppose that the process is observed on a set pn with cn points which tends to infinity with the same speed in all directions the relative edge effect is of order cn lid increasing with d this effect is without statistical importance if d 1 but is important if d 2 we give a lcn consistent asymptotically normal estimator of the underlying parameter the procedure being constructed by a modification of whittle s approximation to the log likelihood in the gaussian case this procedure is asymptotically efficient

covariance tapering for likelihood based estimation in large spatial data sets maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on gaussian processes but calculating the likelihood can be computationally infeasible for large data sets requiring o n3 calculations for a data set with n observations this article proposes the method of covariance tapering to approximate the likelihood in this setting in this approach covariance matrixes are tapered or multiplied element wise by a sparse correlation matrix the resulting matrixes can then be manipulated using efficient sparse matrix algorithms we propose two approximations to the gaussian likelihood using tapering one of these approximations simply replaces the model covariance with a tapered version whereas the other is motivated by the theory of unbiased estimating equations focusing on the particular case of the matern class of covariance functions we give conditions under which estimators maximizing the tapering approximations are like the maximum likelihood estimat

kernel based equiprobabilistic topographic map formation we introduce a new unsupervised competitive learning rule the kernel based maximum entropy learning rule kmer which performs equiprobabilistic topographic map formation in regular fixed topology lattices for use with nonparametric density estimation as well as nonparametric regression analysis the receptive fields of the formal neurons are overlapping radially symmetric kernels compatible with radial basis functions rbfs but unlike other learning schemes the radii of these kernels do not have to be chosen in an ad hoc manner the radii are adapted to the local input density together with the weight vectors that define the kernel centers so as to produce maps of which the neurons have an equal probability to be active equiprobabilistic maps both an online and a batch version of the learning rule are introduced which are applied to nonparametric density estimation and regression respectively the application envisaged is blind source separation bss from nonlinear noisy mixtures

a variable span smoother abstract a variable span smoother based on linear fits is described local cross validation is used to estimate the optimal span as a function of abscissa value computationally efficient algorithms making use of updating formulas are presented

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

bayesian wavelet networks for nonparametric regression radial wavelet networks have been proposed previously as a method for nonparametric regression we analyze their performance within a bayesian framework we derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model this process bypasses the need to test or select a finite number of networks during the modeling process predictions are formed by mixing over many models of varying dimension and parameterization we show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series

a hybrid perturbation galerkin technique that combines multiple expansions a two step hybrid perturbation galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed the method assumes that there is a parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this parameter an approximate solution is constructed in the form of a sum of perturbation coefficient functions multiplied by computed amplitudes in step one regular and or singular perturbation methods are used to determine the perturbation coefficient functions the results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions in step two the classical bubnov galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes that replace and improve upon the gauge functions the hybrid method has

minimum norm quadratic estimation of spatial variograms abstract the estimation of spatial variograms a measure of spatial correlation is a critical problem in the implementation of kriging a method for interpolating random fields we consider the use of minimum norm quadratic estimators of the variogram when it is specified up to a finite number of linear parameters we investigate the asymptotic behavior of such estimators for gaussian processes as the number of observations within some bounded region increases the basic conclusion is that we can estimate consistently those functions of the parameters and only those functions that have a nonnegligible impact asymptotically on the kriging procedure in general the behavior of the variogram over relatively short distances is the only aspect of the variogram that is asymptotically important as an example consider a gaussian process z on the real line with unknown constant mean and where is known as the semivariogram of the process and is a finite vector of unknown parameters suppose for 0

mixed models and reduced selective integration displacement models for nonlinear shell analysis simple mixed models are developed for the geometrically nonlinear analysis of shells a total lagrangian description of the shell deformation is used and the analytical formulation is based on a form of the nonlinear shallow shell theory with the effects of transverse shear deformation and bending extensional coupling included the fundamental unknowns consist of eight stress resultants and five generalized displacements of the shell and the element characteristic arrays are obtained by using the hellinger reissner mixed variational principle the polynomial interpolation or shape functions used in approximating the stress resultants are in general of different degree than those used for approximating the generalized displacements the stress resultants are discontinuous at the element boundaries and are eliminated on the element level the equivalence and near equivalence between the mixed models developed herein and displacement models based on reduced selective integration of both transverse shear and extensional energy terms is discussed the use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated analytic expressions are derived for the rigid body and spurious or zero energy models for the various mixed models and their equivalent displacement models also the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to compare their performance with other mixed models reported in the literature

fourier analysis of irregularly spaced data on rd summary the purpose of the paper is to propose a frequency domain approach for irregularly spaced data on rd we extend the original definition of a periodogram for time series to that for irregularly spaced data and define non parametric and parametric spectral density estimators in a way that is similar to the classical approach introduction of the mixed asymptotics which are one of the asymptotics for irregularly spaced data makes it possible to provide asymptotic theories to the spectral estimators the asymptotic result for the parametric estimator is regarded as a natural extension of the classical result for regularly spaced data to that for irregularly spaced data empirical studies are also included to illustrate the frequency domain approach in comparisons with the existing spatial and frequency domain approaches

new families of skewed higher order kernel estimators to solve the bss ica problem for multimodal sources mixtures this letter suggests two new types of asymmetrical higher order kernels hok that are generated using the orthogonal polynomials laguerre positive or right skew and bessel negative or left skew these skewed hok are implemented in the blind source separation independent component analysis bss ica algorithm the tests for these proposed hok are accomplished using three scenarios to simulate a real environment using actual sound sources an environment of mixtures of multimodal fast changing probability density function pdf sources that represent a challenge to the symmetrical hok and an environment of an adverse case near gaussian the separation is performed by minimizing the mutual information mi among the mixed sources the performance of the skewed kernels is compared to the performance of the standard kernels such as epanechnikov bisquare trisquare and gaussian and the performance of the symmetrical hok generated using the polynomials chebyshev1 chebyshev2 gegenbauer jacobi and legendre to the tenth order the gaussian hok are generated using the hermite polynomial and the wand and schucany procedure the comparison among the 96 kernels is based on the average intersymbol interference ratio aisir and the time needed to complete the separation in terms of aisir the skewed kernels performance is better than that of the standard kernels and rivals most of the symmetrical kernels performance the importance of these new skewed hok is manifested in the environment of the multimodal pdf mixtures in such an environment the skewed hok come in first place compared with the symmetrical hok these new families can substitute for symmetrical hoks in such applications

visualizing the function computed by a feedforward neural network a method for visualizing the function computed by a feedforward neural network is presented it is most suitable for models with continuous inputs and a small number of outputs where the output function is reasonably smooth as in regression and probabilistic classification tasks the visualization makes readily apparent the effects of each input and the way in which the functions deviate from a linear function the visualization can also assist in identifying interactions in the fitted model the method uses only the input output relationship and thus can be applied to any predictive statistical model including bagged and committee models which are otherwise difficult to interpret the visualization method is demonstrated on a neural network model of how the risk of lung cancer is affected by smoking and drinking

projection based approximation and a duality with kernel methods projection pursuit regression and kernel regression are methods for estimating a smooth function of several variables from noisy data obtained at scattered sites methods based on local averaging can perform poorly in high dimensions curse of dimensionality intuition and examples have suggested that projection based approaches can provide better fits for what sorts of regression functions is this true when and by how much do projection methods reduce the curse of dimensionality we make a start by focusing on the two dimensional problem and study the l 2 approximation error bias of the two procedures with respect to gaussian measure let ra stand for a certain ppr type approximation and ka for a particular kernel type approximation building on a simple but striking duality for polynomials we show that ra behaves significantly better than the minimax rate of approximation for radial functions while ka performs significantly better than the minimax rate for harmonic functions in fact the rate improvements carry over to large classes ra behaving very well for functions with enough angular smoothness oscillating slowly with angle while ka behaves very well for functions with enough laplacian smoothness oscillations averaging out locally the rate improvements matter they are equivalent to lowering the dimensionality of the problem for example for functions with nice tail behavior ra behaves as if the dimensionality of the problem were 1 5 rather than its nominal value 2 also ra and ka are complementary for a given function if one method offers a dimensionality reduction the other does not

review papers recent developments in nonparametric density estimation abstract advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where re

tracing post limit point paths with reduced basis technique abstract a reduced basis technique and a problem adaptive computational algorithm are presented for predicting the post limit point paths of structures in the proposed approach the structure is discretized by using displacement finite element models the nodal displacement vector is expressed as a linear combination of a small number of vectors and a rayleigh ritz technique is used to approximate the finite element equations by a small system of nonlinear algebraic equations to circumvent the difficulties associated with the singularity of the stiffness matrix at limit points a constraint equation defining a generalized arc length in the solution space is added to the system of nonlinear algebraic equations and the rayleigh ritz approximation functions or basis vectors are chosen to consist of a nonlinear solution of the discretized structure and its various order derivatives with respect to the generalized arc length the potential of the proposed approach and its advantages over the reduced basis load control technique are outlined the effectiveness of the proposed approach is demonstrated by means of numerical examples of structural problems with snap through and snap back phenomena

multimodality exploration by an unsupervised projection pursuit neural network graphical inspection of multimodality is demonstrated using unsupervised lateral inhibition neural networks three projection pursuit indexes are compared on low dimensional simulated and real world data principal components legendre polynomial and projection pursuit network

isotropic spectral additive models of the covariogram summary a class of additive covariance models of an isotropic random process is proposed motivated by the spectral representation of the covariance function model parameters are estimated by using a special case of the minimum norm quadratic estimation estimator whose asymptotic moments have convenient expressions in terms of spectral densities fitting a model in this class is equivalent to fitting an additive model of the spectral density the class of spectral additive models proposed is dense in the set of summable covariance functions having a spectral density allowing approximately unbiased estimation of an arbitrary covariance function and its spectral density theoretical results are supported by numerical comparison with commonly used models a procedure to assist model selection is proposed the techniques are illustrated with an application to contaminant data

bounds on the efficiency of linear predictions using an incorrect covariance function suppose z is a random process defined on a bounded set r r d with finite second moments consider the behavior of linear predictions based on z t 1 z t n where t 1 t 2 is a dense sequence of points in r a general method is described for obtaining rates of convergence when the covariance function is misspecified but compatible with the correct covariance function when z is gaussian these bounds are related to the entropy distance between the measures for the random field under the actual and presumed covariance functions explicit bounds are given when r 0 1 and z is stationary with spectral density of the form f a 2 2 p where is a known positive integer and a is the parameter that is misspecified

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments

static and dynamic stability of nonlinear elastic systems under nonconservative forces natural approach abstract the paper develops a nonlinear large displacement small strain finite element analysis of elastic structures subject to arbitrary nonconservative external forces both in the static and dynamic realms special attention is focused on the stability behaviour of such systems the methodology of the theory is general covering displacement dependent circulatory velocity dependent dissipative and acceleration dependent stationary as well as instationary explicitly on time dependent nonconservative forces the finite element formulation selected here is based on the natural mode technique permitting i a a simple but elegant as well as concise derivation of the contributory nonsymmetric matrices in conjunction with a clear physical interpretation some typical examples of coalescence and single mode flutter are presented most attention is focused on the evolution of highly nonlinear post flutter response due to various kinds of disturbances in both the stable and the unstable domains the discussion demonstrates the efficiency of the present finite element formulation

on polynomial based projection indices for exploratory projection pursuit we develop asymptotic theory for two polynomial based methods of estimating orientation in projection pursuit density approximation one of the techniques uses legendre polynomials and has been proposed and implemented by friedman 1 the other employs hermite functions issues of smoothing parameter choice and robustness are addressed it is shown that each method can be used to construct sqrt n consistent estimates of the projection which maximizes distance from normality although the former can only be employed in that manner when the underlying distribution has extremely light tails the former can be used very generally to measure low frequency departure from normality

robust projection indices loosely speaking a robust projection index is one that prefers projections involving true clusters over projections consisting of a cluster and an outlier we introduce a mathematical definition of one dimensional index robustness and describe a numerical experiment to measure it we design five new indices based on measuring divergence from student s t distribution which are intended to be especially robust the experiment shows that they are more robust than several established indices the experiment also reveals more generally that the robustness of moment indices depends on the number of approximation terms providing additional practical guidance for existing projection pursuit implementations we investigate the theoretical properties of one new student t index and hall s index and show that the new index automatically adapts its robustness to the degree of outlier contamination we conclude by outlining the possibilities for extending our experiments to both higher dimensions and other new indices

on the theory and error estimation of the reduced basis method for multi parameter problems abstract in an earlier paper zamm 63 1983 21 j p fink and w c rheinboldt developed a priori local error estimates for the scalar parameter case of the reduced basis method by considering the method in a differential geometric setting here it is shown that an analogous setting can be used for the analysis of the method applied to problems with a multidimensional parameter vector and that this leads to a corresponding local error theory also in this general case

mixed models and reduction techniques for large rotation nonlinear problems abstract mixed models and reduction techniques are presented for the large rotation nonlinear analysis of curved beams a total lagrangian description of the beam deformation is used and the analytical formulation is based on a form of reissner s large deformation theory with the effects of transverse shear deformation and extensibility of the centerline included only planar deformations are considered and the fundamental unknowns consist of the three internal forces and the three generalized displacements of the beam the element characteristic arrays are obtained by using the hellinger reissner mixed variational principle the polynomial interpolation or shape functions used in approximating the internal forces are in general of different degree than those used for approximating the generalized displacements and the forces are discontinuous at interelement boundaries the use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated numerical results are presented to demonstrate the high accuracy and effectiveness of both the mixed models and the reduction techniques

characterizing surface smoothness via estimation of effective fractal dimension the fractal dimension d of stationary gaussian surfaces may be expressed very simply in terms of behaviour of the covariance function near the origin indeed only the covariance of line transect samples is required and that fact makes practical estimation of d relatively straightforward the case of non gaussian surfaces is more poorly understood but we might define effective fractal dimension in terms of the covariance function as though the surface were gaussian in the present paper we suggest simple practical methods for estimating effective fractal dimension based on the variogram like techniques proposed recently by taylor and taylor ours are founded on log linear regression

solution of non linear thermal transient problems by a reduction method a new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described the basis of the subspace is formed by using the system response at the first time step or an approximation to it and a set of orthogonal vectors obtained by the algorithm of lanczos derivatives of these vectors are included when treating non linear cases the method allows one to handle the sharp gradients that appear in thermally loaded structures and the response is accurately predicted by using only a small number of degrees of freedom in the reduced system the algorithm is specially well suited for treating large scale problems examples dealing with one two and three dimensional cases of linear and non linear conduction problems are presented

projection pursuit in high dimensions projection pursuit is a classical exploratory data analysis method to detect interesting low dimensional structures in multivariate data originally projection pursuit was applied mostly to data of moderately low dimension motivated by contemporary applications we here study its properties in high dimensional settings specifically we analyze the asymptotic properties of projection pursuit on structureless multivariate gaussian data with an identity covariance as both dimension p and sample size n tend to infinity with p n 0 our main results are that i if then there exist projections whose corresponding empirical cumulative distribution function can approximate any arbitrary distribution and ii if 0 not all limiting distributions are possible however depending on the value of various non gaussian distributions may still be approximated in contrast if we restrict to sparse projections involving only a few of the p variables then asymptotically all empirical cumulative distribution functions are gaussian and iii if 0 then asymptotically all projections are gaussian some of these results extend to mean centered sub gaussian data and to projections into k dimensions hence in the small n large p setting unless sparsity is enforced and regardless of the chosen projection index projection pursuit may detect an apparent structure that has no statistical significance furthermore our work reveals fundamental limitations on the ability to detect non gaussian signals in high dimensional data in particular through independent component analysis and related non gaussian component analysis

fuzzy regression wiht radial basis function network radial basis function network is used in fuzzy regression analysis without predefined functional relationship between the input and the output the proposed approach is a fuzzification of the connection weights between the hidden and the output layers this fuzzy network is trained by a hybrid learning algorithm where self organized learning is used for training the parameters of the hidden units and supervised learning is used for updating the weights between the hidden and the output layers the c mean clustering method and the k nearest neighbor heuristics are used for the self organized learning the supervised learning is carried out by solving a linear possibilistic programming problem techniques for the generalization of the network are also proposed numerical examples are used to illustrate and to test the performances of the approach

mixed models and reduced selective integration displacement models for nonlinear analysis of curved beams simple mixed models are developed for the geometrically nonlinear analysis of deep arches a total lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included the fundamental unknowns consist of the six internal forces and generalized displacements of the arch and the element characteristic arrays are obtained by using hellinger reissner mixed variational principle the polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements and the forces are discontinuous at the interelement boundaries the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and compare their performance with other mixed models reported in the literature

applying fuzzy adaptive network to fuzzy regression analysis abstract a fuzzy inference system based on the sugeno inference model is first formulated for fuzzy regression analysis this system is then represented by a fuzzy adaptive network this approach combines the power of representation of fuzzy inference system with the ability of learning of the neural network numerical examples are trained and solved to illustrate the approach the results are compared with other approaches

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

fixed domain asymptotics for spatial periodograms abstract the periodogram for a spatial process observed on a lattice is often used to estimate the spectral density the bases for such estimators are two asymptotic properties that periodograms commonly possess 1 the periodogram at a particular frequency is approximately unbiased for the spectral density and 2 the correlation of the periodogram at distinct frequencies is approximately zero for spatial data it is often appropriate to use fixed domain asymptotics in which the observations get increasingly dense in some fixed region as their number increases using fixed domain asymptotics this article shows that standard asymptotic results for periodograms do not apply and that using the periodogram of the raw data can yield highly misleading results but by appropriately filtering the data before computing the periodogram it is possible to obtain results similar to the standard asymptotic results for spatial periodograms

spectral density estimation for random fields via periodic embeddings we introduce methods for estimating the spectral density of a random field on a formula see text dimensional lattice from incomplete gridded data data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function the imputations are convenient computationally in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in formula see text time and formula see text memory however these so called periodic imputations are motivated mainly by their ability to produce accurate spectral density estimates in addition we introduce a parametric filtering method that is designed to reduce periodogram smoothing bias the paper contains theoretical results on properties of the imputed data periodogram and numerical and simulation studies comparing the performance of the proposed methods to existing approaches in a number of scenarios we present an application to a gridded satellite surface temperature dataset with missing values

on a conjecture of huber concerning the convergence of projection pursuit regression we generalize the projection pursuit procedure of friedman and stuetzle abstract version and prove strong convergence this answers a question of huber

bayesian radial basis functions of variable dimension a bayesian framework for the analysis of radial basis functions rbf is proposed that accommodates uncertainty in the dimension of the model a distribution is defined over the space of all rbf models of a given basis function and posterior densities are computed using reversible jump markov chain monte carlo samplers green 1995 this alleviates the need to select the architecture during the modeling process the resulting networks are shown to adjust their size to the complexity of the data

on principal hessian directions for data visualization and dimension reduction another application of stein s lemma abstract modern graphical tools have enhanced our ability to learn many things from data directly with much user friendly graphical software available we are encouraged to plot a lot more often than before the benefits from direct interaction with graphics have been enormous but trailing behind these high tech advances is the issue of appropriate guidance on what to plot there are too many directions to project a high dimensional data set and unguided plotting can be time consuming and fruitless in a recent article li set up a statistical framework for study on this issue based on a notion of effective dimension reduction edr directions they are the directions to project a high dimensional input variable for the purpose of effectively viewing and studying its relationship with an output variable a methodology sliced inverse regression was introduced and shown to be useful in finding edr directions this article introduces another method for finding edr directions it begins with the observat

thin shells with finite rotations formulated in biot stresses theory and finite element formulation a bending theory for thin shells undergoing finite rotations is presented and its associated finite element model is described the kinematic assumption is based on a shear elastic reissner mindlin theory the starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures the associated work conjugate stress resultants and stress couples are integrals of the biot stress tensor this tensor is invariant with respect to rigid body motions and therefore appropriate for the formulation of constitutive equations finite rotations are introduced via eulerian angles the finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration the numerical model is applied to different non linear plate and shell problems and compared with existing formulations due to a consistent linearization the step size of a load increment is only limited by the local convergence behaviour of newton s method

maximum likelihood neural approximation in presence of additive colored noise in many practical situations the noise samples may be correlated in this case the estimation of noise parameters can be used to improve the approximation estimation of the noise structure can also be used to find a stopping criterion in constructive neural networks to avoid overfitting a network construction procedure must be stopped when residual can be considered as noise the knowledge on the noise may be used for whitening the residual so that a correlation hypothesis test determines if the network growing must be continued or not in this paper supposing a gaussian noise model we study the problem of multi output nonlinear regression using mlp when the noise in each output is a correlated autoregressive time series and is spatially correlated with other output noises we show that the noise parameters can be determined simultaneously with the network weights and used to construct an estimator with a smaller variance and so to improve the network generalization performance moreover if a constructive procedure is used to build the network the estimated parameters may be used to stop the procedure