on the convergence of a finite element method for a nonlinear hyperbolic conservation law we consider a space time finite element discretization of a time dependent nonlinear hyperbolic conservation law in one space dimension burgers equation the finite element method is higher order accurate and is a petrov galerkin method based on the so called streamline diffusion modification of the test functions giving added stability we first prove that if a sequence of finite element solutions converges boundedly almost everywhere as the mesh size tends to zero to a function u then u is an entropy solution of the conservation law this result may be extended to systems of conservation laws with convex entropy in several dimensions we then prove using a compensated compactness result of murat tartar that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of burgers equation we also consider a further modification of the test functions giving a method with improved shock capturing finally we present the results of some numerical experiments

intelligent meshing technique for 2d resistivity inverse problems abstractin geophysical inverse problems an a priori structured mesh is often used for inversion and mesh refinement is applied if needed by the user after observation of inversion results we have developed a new intelligent self adaptive unstructured finite element meshing technique for electrical resistivity tomography inverse problems this new approach uses harris corner and edge detectors that are based on the local autocorrelation function of 2d distribution of pixels this meshing technique optimizes the size of the inverse problem by refining areas where variations in the physical property structure are sensed to be important the meshing technique also generates a more appropriate and optimum mesh for the inverse problem that is dependent on the problem itself tests on modeled data have demonstrated that the proposed intelligent meshing technique can reduce data misfit produce a better reconstruction of the true physical properties and minimize the size of the inverse problem the synthetic m

dcca cross correlation coefficient quantifying level of cross correlation abstract in this paper a new coefficient is proposed with the objective of quantifying the level of cross correlation between nonstationary time series this cross correlation coefficient is defined in terms of the dfa method and the dcca method the implementation of this cross correlation coefficient will be illustrated with selected time series

error estimates for the combinedh andp versions of the finite element method in theh version of the finite element method convergence is achieved by refining the mesh while keeping the degree of the elements fixed on the other hand thep version keeps the mesh fixed and increases the degree of the elements in this paper we prove estimates showing the simultaneous dependence of the order of approximation on both the element degrees and the mesh in addition it is shown that a proper design of the mesh and distribution of element degrees lead to a better than polynomial rate of convergence with respect to the number of degrees of freedom even in the presence of corner singularities numerical results comparing theh version p version and combinedh p version for a one dimensional problem are presented

testing dependence among serially correlated multicategory variables the contingency table literature on tests for dependence among discrete multicategory variables is extensive standard tests assume however that draws are independent and only limited results exist on the effect of serial dependency a problem that is important in areas such as economics finance medical trials and meteorology this article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions the tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite order markov processes for three way or higher order tables we propose new tests of joint and marginal independence monte carlo experiments show that the proposed tests have good finite sample properties an empirical application to microeconomic survey data on firms forecasts of changes to their production and prices demonstrates the importance of correcting fo

convergence estimates for semidiscrete parabolic equation approximations semidiscrete methods for approximating the solutions of initial boundary value problems for parabolic equations are studied the construction of these semidiscrete methods is based upon the availability of several different galerkin type approximation methods for the associated elliptic steadystate problem the properties required of the spacial discretization methods are listed and estimates of the error made by the resulting semidiscrete approximations and of their time derivatives are given in particular estimates are given that require only weak smoothness assumptions on the initial data verifications of the required properties for various galerkin type methods are provided

sample size determination within the scope of conditional maximum likelihood estimation with special focus on testing the rasch model this paper refers to the exponential family of probability distributions and the conditional maximum likelihood cml theory it is concerned with the determination of the sample size for three groups of tests of linear hypotheses known as the fundamental trinity of wald score and likelihood ratio tests the main practical purpose refers to the special case of tests of the class of rasch models the theoretical background is discussed and the formal framework for sample size calculations is provided given a predetermined deviation from the model to be tested and the probabilities of the errors of the first and second kinds

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions convergence of a shock capturing streamline diffusion nite element method for a conservation law in two space dimensions

a stability result for sectorial operators in branch spaces in this paper the author considers approximations of holomorphic semigroups on general banach spaces based on a acceptable rational functions a general stability theorem is proved it covers rational functions r z with r infty 1 and can be applied even to variable step cases in particular the question of the text l p stability p ne 2 of crank nicolson schemes for parabolic initial value problems is settled

measuring correlations between non stationary series with dcca coefficient abstract in this short report we investigate the ability of the dcca coefficient to measure correlation level between non stationary series based on a wide monte carlo simulation study we show that the dcca coefficient can estimate the correlation coefficient accurately regardless the strength of non stationarity measured by the fractional differencing parameter d for a comparison we also report the results for the standard pearson correlation coefficient the dcca coefficient dominates the pearson coefficient for non stationary series

discontinuous galerkin methods for ordinary differential equations a class of galerkin methods derived from discontinuous piecewise polynomial spaces is analyzed for polynomials of degree k these methods lead to a family of one step schemes generating approximations up to order 2k 2 for the solution of an ordinary differential equation

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

models for the analysis of association in multivariate contingency tables abstract the present work describes a family of models that can be used for the analysis of association in multiway cross classifications the models are complementary to the usual i e the so called hierarchical log linear models an advantage of this family of models is that it is frequently possible to give a more parsimonious description of the association than is possible with the usual log linear models approach the models will be especially useful when some or all of the variables are ordinal the models are derived from a reparameterization of the saturated model based on singular value decompositions of interaction terms in the log linear parameterization multivariate association models given in goodman 1979 1986 clogg 1982a b agresti and kezouh 1983 gilula and haberman 1988 and becker and clogg 1989 are obtained as special cases the utility of the models developed in this article is demonstrated with the analysis of two examples the first example a cross classification of

non commutative discretize then optimize algorithms for elliptic pde constrained optimal control problems abstract in this paper we analyze the convergence of several optimize then discretize and discretize then optimize algorithms based on either a second order or a fourth order finite difference discretization for solving elliptic pde constrained optimal control problems to ensure the convergence of a discretize then optimize algorithm one well accepted criterion is to design the discretization scheme such that the resulting discretize then optimize algorithm commutes with the corresponding optimize then discretize algorithm in other words both algorithms should give rise to exactly the same discrete optimality system however such a restrictive criterion is not trivial to fulfill by investigating a distributed control problem governed by an elliptic equation we first show that enforcing such a stringent condition of commutative property is only sufficient but not necessary for achieving the desired convergence we then introduce some suitable h 1 semi norm penalty regularization terms to recover the lost convergence due to the inconsistency caused by the loss of commutativity numerical experiments are carried out to verify our theoretical analysis and also validate the effectiveness of our proposed regularization techniques

quasisymmetric models for the analysis of square contingency tables summary a parametric model is presented for the analysis of square contingency tables where there is a one to one correspondence between the categories of the row variable and the categories of the column variable the model is applicable to cross classifications where the categories are unordered partially ordered or completely ordered but the interpretation of the model and associated parameters is most straightforward when the categories are at least partially ordered connections with the mover stayer model and the usual model of quasisymmetry are described two data sets are used to illustrate the utility of the model

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

autocorrelation and cross correlation in time series of homicide and attempted homicide abstract we propose in this paper to establish the relationship between homicides and attempted homicides by a non stationary time series analysis this analysis will be carried out by detrended fluctuation analysis dfa detrended cross correlation analysis dcca and dcca cross correlation coefficient d c c a n through this analysis we can identify a positive cross correlation between homicides and attempted homicides at the same time looked at from the point of view of autocorrelation dfa this analysis can be more informative depending on time scale for short scale days we cannot identify auto correlations on the scale of weeks dfa presents anti persistent behavior and for long time scales n 90 days dfa presents a persistent behavior finally the application of this new type of statistical analysis proved to be efficient and in this sense this paper can contribute to a more accurate descriptive statistics of crime

a stable finite element method for initial boundary value problems for first order hyperbolic systems a nonstandard finite element method for initial boundary value problems for first order hyperbolic systems in one space dimension with general boundary conditions is analyzed the method can be considered as a generalization of the box scheme we first establish a stability result for the method and then derive several error estimates u x t a x ux x t b x u x t f x t 1 1 o 0 t g kxu l t u x 0 u0 x for x t e i x j 0 1 x 0 where t 0 here aix and 5 x are n x n matrices we assume that aix has n real eigenvalues xx x a2 x a x and that there exist a constant t0 0 and an integer m 0 t0 for all xg furthermore we assume that for each x e there is a nonsingular matrix qix such that

mixed correlated arfima processes for power law cross correlations abstract we introduce a general framework of the mixed correlated arfima mc arfima processes which allows for various specifications of univariate and bivariate long term memory apart from a standard case when h x y 1 2 h x h y mc arfima also allows for processes with h x y 1 2 h x h y but also for long range correlated processes which are either short range cross correlated or simply correlated the major contribution of mc arfima lies in the fact that the processes have well defined asymptotic properties for h x h y and h x y which are derived in the paper so that the processes can be used in simulation studies comparing various estimators of the bivariate hurst exponent h x y moreover the framework allows for modeling of processes which are found to have h x y 1 2 h x h y

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

the convergence of even degree spline collocation solution for potential problems in smooth domains of the plane in this article we derive new error estimates for collocation solution of potential type problems by using even degree smooth splines as trial functions it turns out that for smooth potentials the assured convergence is of the same order as by using splines of the odd degreed 1 some numerical examples which conform the theoretical results are presented

assessing rater agreement using marginal association models new models that are useful in the assessment of rater agreement particularly when the rating scale is ordered or partially ordered are presented the models are parameterized to address two important aspects of rater agreement i agreement in terms of the overall frequency in which raters assign categories and ii the extent to which raters agree on the category assigned to individual subjects or items we present methodology for the simultaneous modelling of univariate marginal responses and bivariate marginal associations in the k way contingency table representing the joint distribution of k rater responses the univariate marginal responses provide information for evaluating agreement in terms of the overall frequency of responses and the bivariate marginal associations provide information on category wise agreement among pairs of raters in addition estimated scores within a generalized log non linear model for bivariate associations facilitate the assessment of category distinguishability

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

on some similarities between canonical correlation models and latent class models for two way contingency tables summary relationships between parameters of canonical correlations models and latent class models for two way contingency tables are explored it is found that under certain conditions canonical models and latent models are equivalent as a result a new interpretation of canonical variables in contingency tables is proposed let p be an i x j probability matrix describing the joint distribution of two categorical random variables x and y having i and j categories respectively in canonical analysis e g fisher 1940 williams 1952 and lancaster 1958 p is decomposed into a sum of r 2 which is discussed in 3

regression and ordered categorical variables read before the royal statistical society by professor r l plackett on behalf of the late professor anderson at a meeting organized by the research section on wednesday october 5th 1983 professor j b copas in the chair summary a general approach to regression modelling for ordered categorical response variables y is given which is equally applicable to ordered and unordered y the regressor variables xt xi x may be continuous or categorical the method is based on the logistic family which contains a hierarchy of regression models ranging from ordered to unordered models ordered properties of the former the stereotype model are established the choice between models is made empirically on the basis of model fit this is particularly important for assessed ordered categorical response variables where it is not obvious a priori whether or not the ordering is relevant to the regression relationship model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x the models are fitted iteratively using the method of maximum likelihood examples are given

quantifying cross correlation between ibovespa and brazilian blue chips the dcca approach abstract the objective of this paper is to demonstrate the influence of the blue chips companies in the stock market in this we apply the detrended cross correlation coefficient dcca at the sao paulo stock market ibovespa brazil initially we found that there is a positive cross correlation between these companies and the index afterwards we show that the cross correlation coefficient value depends on the time scale and the specific company blue chips thus this type of analysis lets to infer what is the most adherent company with ibovespa also in this paper we analyze in the point of view of dcca the 2008 financial crisis before after altogether the results show that there is more cross correlation between ibovespa index the blue chips after the 2008 crisis

on the boundary element method for some nonlinear boundary value problems here we analyse the boundary element galerkin method for two dimensional nonlinear boundary value problems governed by the laplacian in an interior or exterior domain and by highly nonlinear boundary conditions the underlying boundary integral operator here can be decomposed into the sum of a monotoneous hammerstein operator and a compact mapping we show stability and convergence by using leray schauder fixed point arguments due to petryshyn and necas

stability analyticity and almost best approximation in maximum norm for parabolic finite element equations we consider semidiscrete solutions in quasi uniform finite element spaces of order o hr of the initial boundary value problem with neumann boundary conditions for a second order parabolic differential equation with time independent coefficients in a bounded domain in r n we show that the semigroup on l defined by the semidiscrete solution of the homogeneous equation is bounded and analytic uniformly in h we also show that the semidiscrete solution of the inhomogeneous equation is bounded in the space time l norm modulo a logarithmic factor for r 2 and we give a corresponding almost best approximation property

monotonicity of some perturbations of irreducibly diagonally dominant m matrices this paper presents a new result concerning the perturbation theory of m matrices we give the proof of a theorem showing that some perturbations of irreducibly diagonally dominant m matrices are monotone together with an explicit bound of the norm of the perturbation one of the assumptions concerning the perturbation matrix is that the sum of the entries of each of its row is nonnegative the resulting matrix is shown to be monotone although it may not be diagonally dominant and its off diagonal part may have some positive entries we give as an application the proof of the second order convergence of an non centered finite difference scheme applied to an elliptic boundary value problem

modeling long range cross correlations in two component arfima and fiarch processes we investigate how simultaneously recorded long range power law correlated multivariate signals cross correlate to this end we introduce a two component arfima stochastic process and a two component fiarch process to generate coupled fractal signals with long range power law correlations which are at the same time long range cross correlated we study how the degree of cross correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals our findings have relevance when studying parallel outputs of multiple component of physical physiological and social systems

loglinear models and categorical data analysis with psychometric and econometric applications revision abstract the past decade has seen the publication of a large number of books and papers on the analysis of multi way contingency tables using loglinear and logic models the present article presents a summary of the statistical theory that underlies much of this work and provides some linkage to models and methods of special interest to psychometricians and econometricians the discussion includes a review of recent and current research on the computation of maximum likelihood estimates for loglinear and logit models especially for large multi way contingency tables

ordinal association in contingency tables some interpretive aspects abstract two families of models for ordered contingency tables goodman s association models and canonical correlation models are investigated and compared with respect to the interpretation of their parameters we show that the two families of models actually refer to different kinds of ordinal association stochastic order extremity for correlation models and stochastic order entropy for association models this difference is related to the way the two models scale interaction the scale difference is proven to be of substantial consequence especially under strong association

detrended fluctuation analysis as a regression framework estimating dependence at different scales we propose a framework combining detrended fluctuation analysis with standard regression methodology the method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and under potential nonstationarity and power law correlations the former feature allows for distinguishing between effects for a pair of variables from different temporal perspectives the latter ones make the method a significant improvement over the standard least squares estimation theoretical claims are supported by monte carlo simulations the method is then applied on selected examples from physics finance environmental science and epidemiology for most of the studied cases the relationship between variables of interest varies strongly across scales

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

bayesian inference for the stereotype regression model application to a case control study of prostate cancer the stereotype regression model for categorical outcomes proposed by anderson j roy statist soc b 1984 46 1 30 is nested between the baseline category logits and adjacent category logits model with proportional odds structure the stereotype model is more parsimonious than the ordinary baseline category or multinomial logistic model due to a product representation of the log odds ratios in terms of a common parameter corresponding to each predictor and category specific scores the model could be used for both ordered and unordered outcomes for ordered outcomes the stereotype model allows more flexibility than the popular proportional odds model in capturing highly subjective ordinal scaling which does not result from categorization of a single latent variable but are inherently multi dimensional in nature as pointed out by greenland statist med 1994 13 1665 1677 an additional advantage of the stereotype model is that it provides unbiased and valid inference under outcome stratified sampling as in case control studies in addition for matched case control studies the stereotype model is amenable to classical conditional likelihood principle whereas there is no reduction due to sufficiency under the proportional odds model in spite of these attractive features the model has been applied less as there are issues with maximum likelihood estimation and likelihood based testing approaches due to non linearity and lack of identifiability of the parameters we present comprehensive bayesian inference and model comparison procedure for this class of models as an alternative to the classical frequentist approach we illustrate our methodology by analyzing data from the flint men s health study a case control study of prostate cancer in african american men aged 40 79 years we use clinical staging of prostate cancer in terms of tumors nodes and metastasis as the categorical response of interest

on the asymptotic convergence of collocation methods we prove quasioptimal and optimal order estimates in various sobolev norms for the approximation of linear strongly elliptic pseudodifferential equations in one independent variable by the method of nodal collocation by odd degree polynomial splines the analysis pertains in particular to many of the boundary element methods used for numerical computation in engineering applications equations to which the analysis is applied include fredholm integral equations of the second kind certain first kind fredholm equations singular integral equations involving cauchy kernels a variety of integro differential equations and two point boundary value problems for ordinary differential equations the error analysis is based on an equivalence which we establish between the collocation methods and certain nonstandard galerkin methods we compare the collocation method with a standard galerkin method using splines of the same degree showing that the galerkin method is quasioptimal in a sobolev space of lower index and furnishes optimal order approximation for a range of sobolev indices containing and extending below that for the collocation method and so the standard galerkin method achieves higher rates of convergence

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

simple accurate and efficient revisions to maccormack and saulyev schemes high peclet numbers abstract stream water quality modeling often involves numerical methods to solve the dynamic one dimensional advection dispersion reaction equations adre there are numerous explicit and implicit finite difference schemes for solving these problems and two commonly used schemes are the maccormack and saulyev schemes this paper presents simple revisions to these schemes that make them more accurate without significant loss of computation efficiency using advection dominated high peclet number problems as test cases performances of the revised schemes are compared to performances of five classic schemes forward time centered space ftcs backward time centered space btcs crank nicolson and the traditional maccormack and saulyev schemes all seven of the above numerical schemes were tested against analytical solutions for pulse and step inputs of mass to a steady flow in a channel and performances were considered with respect to stability accuracy and computational efficiency results indicated that both the modified saulyev and the maccormack schemes which are named the saulyevc and maccormackc schemes respectively greatly improved the prediction accuracy over the original ones the computation efficiency in terms of cpu time was not impacted for the saulyevc scheme the maccormackc scheme demonstrated increased time consumption but was still much faster than implicit schemes

a new methodology for local cross correlation between two nonstationary time series abstract to measure the degree of local cross correlation between two nonstationary time series a new approach with a locally weighted pearson correlation coefficient based on a simple locally weighted linear regression model was proposed in this approach a gaussian decay based function is selected as a weighting function an appropriate bandwidth is selected using an alternative criterion some factors influencing the local cross correlation degree including long range exponent estimated by means of a detrended fluctuation analysis dfa and seasonal change in the series are discussed artificial and real world datasets are analyzed the results show that the proposed method can measure the degree of a locally intrinsic cross correlation between two series the contribution of this locally intrinsic cross correlation is attributed to original input excitation sources and dfa scaling exponents the effects of seasonal change with a high frequency in the series on a locally intrinsic cross correlation are significant the effects of a low frequency seasonal change are insignificant a positive local cross correlation between a synchronous wind speed and air pollution index series in nanjing china is observed which is related to externally imported air pollution sources consistent results are obtained by comparing the new method with the detrended cross correlation coefficient d c c a therefore the proposed approach is reliable reasonable and applicable and can examine the degree of the local intrinsic cross correlation between two nonstationary time series

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

stability and analyticity in maximum norm for simplicial lagrange finite element semidiscretizations of parabolic equations with dirichlet boundary conditions stability and analyticity estimates in maximum norm are shown for spatially discrete finite element approximations based on simplicial lagrange elements for the model heat equation with dirichlet boundary conditions the bounds are logarithm free and valid in arbitrary dimension and for arbitrary polynomial degree the work continues an earlier study by schatz et al 5 in which neumann boundary conditions were considered

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

grouping and association in contingency tables an exploratory canonical correlation approach abstract the criteria of homogeneity and structure were proposed by goodman 1981a for determining whether certain rows or columns of a contingency table should be grouped a data based procedure using the canonical form of bivariate distributions is presented in this article to guide exploratory analysis to determine which rows or columns of a table may be grouped this procedure facilitates the application of the homogeneity criterion relationships between the proposed method of grouping and the structural criterion are discussed as well as simultaneous inference for grouped tables the grouping method is extended to multiway tables the use of canonical forms as a model exploratory tool is addressed examples are discussed in detail

approximate analytic solution of the dirichlet problems for laplace s equation in planar domains by a perturbation method in this paper we propose a regular perturbation method to obtain approximate analytic solutions of exterior and interior dirichlet problems for laplace s equation in planar domains this method starting from a geometrical perturbation of these planar domains reduces our problems to a family of classical dirichlet problems for laplace s equation in a circle numerical examples are given and comparisons are made with the solutions obtained by other approximation methods

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

fully discrete approximation methods for parabolic poblems with nonsmooth initial data fully discrete approximation methods are studied for parabolic boundary value problems evolving from nonsmooth and noncompatible initial data galerkin methods are used for the spatial discretization and single step or backwards differentiation multistep methods are used in time the parabolic equation is assumed to be linear but the coefficients are allowed to depend on space and time an error estimate is given for the combined space time discretization scheme which contains the expected optional order space and time error contributions however another term appears which limits the accuracy of the method to second order or fractionally better in time if the time stepping method is of third or higher order this latter term arises from the time dependence of the equation s highest order coefficients and hence does not appear in analyses of problems with only spatially dependent coefficients for which optimal order estimates are known to hold it is shown through more detailed analysis of a speci

eine aussage zurl stabilitat und zur genauen konvergenzordnung derh 0 0 projektionen in this paper we settle a question concerning the necessity of the logh factor appearing in error estimates of linear finite element solutions let 2 be a bounded convex polygon and t h a regular family of subdivisions of into triangles be furthers 0 h h 0 1 the corresponding linear finite element spaces andp h h 0 1 s 0 h theh 0 1 projections with respect to the uniform norm asymptotically estimates of the form parallel u p h u parallel infty leqq c logh dist u s 0 h u in c bar omega cap h 0 1 omega hold as pointed out by schatz 1980 for functionsu with bounded second derivatives this implies parallel u p h u parallel infty leqq ch 2 log h u 2 infty a result which was proved by nitsche 1975 and scott 1976 with different methods it was an open question if the factor logh is necessary or only due to the methods of proof in this paper it is shown by an example that the cited estimates are sharp in the very strong sense that in general they are no longer valid if logh is replaced by a termo logh

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

1 f behavior in cross correlations between absolute returns in a us market abstract employing detrended fluctuation analysis dfa and detrended cross correlations analysis dcca we analyze auto correlations in the absolute returns for each of 30 dow jones industrial average djia constituents s i and cross correlations in the absolute returns between the djia and each s i we find that each djia member follows the djia in absolute returns since the dcca curve for each pair s i djia i exhibits strong cross correlations with average dcca exponent 1 03 0 04 this value for implies that the power law cross correlations are of the 1 f functional form for the financial firms comprising the djia we also find that the dfa and dcca exponents controlling the duration of firm risk are somewhat larger than the corresponding values for the rest of the us financial industry

numerical solution of the free boundary bernoulli problem using a level set formulation we present a numerical method based on a level set formulation to solve the bernoulli problem the formulation uses time as a parameter of boundary evolution the level set formulation enables to consider nonconnected domains numerical experiments show the efficiency of the method if boundary conditions are handled accurately in particular the case of multiple solutions is treated

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

analysis of mixed categorical data in 2 k contingency tables 2 k contingency tables having both ordinal and nominal categories are often encountered in various types of studies such data are referred to as mixed categorical data in this article to apply a method for ordered categorical data one has to discard the nominal categories and to apply a method for nominal categories one has to discard the ordering information inherent in the ordered categories therefore investigators often either discard observations in nominal categories or discard the ordering of the categories before analysing such data some information will be lost in both approaches a method for analysing data in 2 k mixed tables is proposed in this paper which can be considered as an extension of well known methods for nominal and ordered categories the proposed method utilizes observations in the nominal categories as well as the ordering information if all the categories were ordered then the proposed method reduces to the trend test and if all the categories were nominal then the proposed method reduced to pearson s chi square test copyright 2002 john wiley sons ltd

superconvergence of the gradient in piecewise linear finite element approximation to a parabolic problem some recent results concerning maximum norm superconvergence of the gradient in piecewise linear finite element approximations of an elliptic problem are carried over to a parabolic problem both the standard semidiscrete in space galerkin method and the lumped mass modification are analyzed for both smooth and nonsmooth data situations and the crank nicolson discretizations in time of these procedures are considered as examples of completely discrete schemes

ax one degree of freedom nominal association model for testing independence in two way contingency tables in testing the independence of the row and column variables in a two way contingency table the standard pearson and likelihood ratio chi square statistics often have low power especially as the dimensions of the table increase in this paper one degree of freedom tests of independence based on likelihood ratio and score statistics from an association model for tables with nominal row and column classifications are described the score statistic is especially easy to use since it can be expressed in closed form is simple to compute and has size and power properties which are only slightly inferior to those of the more complicated likelihood ratio statistic

a survey of strategies for modeling cross classifications having ordinal variables abstract a survey is given of the main strategies for modeling cross classifications that contain ordinal variables models are described for two way tables in which one or both classifications are ordered and for multidimensional tables in which at least one classification is ordered primary emphasis is given to construction interpretation and implications of loglinear and logit models

finite element solution of diffusion problems with irregular data diffusion problems occuring in practice often involve irregularities in the initial or boundary data resulting in a local break down of the solution s regularity this may drastically reduce the accuracy of discretization schemes over the whole interval of integration unless certain precautions are taken the diagonal pade schemes of order 2 combined with a standard finite element discretization usually require an unnatural step size restriction in order to achieve even locally optimal accuracy it is shown here that this restriction can be avoided by means of a sample damping procedure which preserves the order of the discretization and in the case 1 does not increase the costs

computation of maximum likelihood estimates in association models abstract in association models for cross classified data computation of maximum likelihood estimates mle s is relatively difficult due to the nonlinear constraints on the parameters currently available procedures based on the scoring algorithm for constrained maximum likelihood are relatively unreliable and other cyclic procedures are relatively slow and do not provide estimated asymptotic standard deviations as by products of calculations to facilitate computations it is noted that in standard association models removal of constraints results in underidentification of parameters but does not affect the model itself so that the mle s of cell probabilities and conditional probabilities are unaffected given this observation maximum likelihood estimation may be accomplished by unconstrained maximization of an objective function with two components a log likelihood ratio and a sum of squares representing deviations of parameters from their constraints the objective function is then maximized by u

using association models to analyse agreement data two examples two examples demonstrate how one can use association models to analyse agreement data the first example concerns intra rater variability in the classification of sputum cytology slides and the second deals with variability associated with the reporting of passive smoking histories the paper emphasizes models in which one estimates category scores from the data that is models that are not in the log linear family of models such models have use in assessment of category distinguishability and provide insights not easily obtained with log linear models

collapsed two way contingency tables and the chi square reduction principle summary the value of the chi square statistic for homogeneity of rows and columns in a contingency table remains unchanged if the table is collapsed grouped over homogeneous rows and columns the difference between the chi square values pertaining to the original table and to the collapsed table the chi square reduction is shown to have a meaningful canonical decomposition which can guide the researcher in detecting homogeneous rows and columns the methodology proposed generalizes an earlier methodology suggested by gilula for the same problem

extended rc association models allowing for order restrictions and marginal modeling in the context of two way contingency tables the rc model may be seen as a way of modeling the set of log odds ratios for adjacent 2 2 subtables through row and column scores this article presents an extended class of rc models that allows simultaneous modeling of the marginal distributions and the association between two categorical variables these components are parameterized with logits and log odds ratios that may be of different types e g global or continuation to suit the nature of the data and the type of dependence of interest an algorithm for maximum likelihood estimation under equality and inequality constraints is presented the asymptotic distribution of the likelihood ratio statistic to test some interesting hypotheses is derived and extensions to multiway tables are outlined three examples are presented to highlight the features of the new approach

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

continuous finite elements in space and time for the heat equation on analyse une nouvelle methode variationnelle pour l approximation de l equation de la chaleur a l aide des elements finis continus dans l espace et le temps on presente les estimations d erreurs et les resultats d experiences numeriques

the analysis of multivariate contingency tables by restricted canonical and restricted association models abstract restricted canonical models and restricted association models are proposed and applied to multiway contingency tables these models have been previously applied to two way contingency tables however multivariate generalization has been impeded in the past since canonical and association models both depend on singular value decompositions that apply only to two way arrays in this article this restriction to two way arrays is overcome by division of the cross classified variables into explanatory and response variables the explanatory variables are treated as a single polytomous variable and the response variables are treated as a second single polytomous variable in this fashion the multiway table is reduced to a two way array to which traditional canonical and association models may be applied use of linear restrictions on parameters in canonical and association models is especially important in multiway tables if useful models are to be constructed the class of models considered in th

a warning on the use of chi squared statistics with frequency tables with small expected cell counts abstract when applied to frequency tables with small expected cell counts pearson chi squared test statistics may be asymptotically inconsistent even in cases in which a satisfactory chi squared approximation exists for the distribution under the null hypothesis this problem is particularly important in cases in which the number of cells is large and the expected cell counts are quite variable to illustrate this bias of the chi squared test this article considers the pearson chi squared test of the hypothesis that the cell probabilities for a multinomial frequency table have specified values in this case the expected value and variance of the pearson chi square may be evaluated under both the null and alternative hypotheses when the number of cells is large normal approximations and discrete edgeworth expansions may also be used to assess the size and power of the pearson chi squared test these analyses show that unless all cell probabilities are equal it is possible to select a significance lev

canonical analysis of contingency tables by maximum likelihood abstract canonical analysis has often been employed instead of log linear models to analyze the relationship of two polytomous random variables however until the last few years analysis has been informal in this article models are examined that place nontrivial restrictions on the values of the canonical parameters so that a parsimonious description of association is obtained maximum likelihood is used to obtain parameter estimates for these restricted models approximate confidence intervals are derived for parameters and chi squared tests are used to check adequacy of models the resulting models may be used to determine the appropriateness of latent class analysis or to determine whether a set of canonical scores has specified patterns results are illustrated through analysis of two tables previously analyzed in the statistical literature comparisons are made with alternate methods of analysis based on a log linear parameterization of cell probabilities it is shown that canonical analysis wh

a quadrature based approach to improving the collocation method the collocation method is a popular method for the approximate solution of boundary integral equations but typically does not achieve the high order of convergence reached by the galerkin method in appropriate negative norms in this paper a quadrature based method for improving upon the collocation method is proposed and developed in detail for a particular case that case involves operators with even symbol such as the logarithmic potential operating on 1 periodic functions a smooth spline trial space of odd degree with constant mesh spacingh 1 n and a quadrature rule with 2n points where ann point quadrature rule would be equivalent to the collocation method in this setting it is shown that a special quadrature rule which depends on the degree of the splines and the order of the operator can yield a maximum order of convergence two powers ofh higher than the collocation method

from finite differences to finite elements a short history of numerical analysis of partial differential equations abstract this is an account of the history of numerical analysis of partial differential equations starting with the 1928 paper of courant friedrichs and lewy and proceeding with the development of first finite difference and then finite element methods the emphasis is on mathematical aspects such as stability and convergence analysis