improving stability by change of representation in time stepping analysis of non linear beams dynamics in this paper we propose a change in the representation of the discrete motion equations in structural non linear dynamics to obtain an improvement in the stability of time numerical integrations in particular natural local state variables are indicated for a finite element approach to beam problems the results relative to newmark approximations for the variations in the displacement and velocity vectors show a significant increase in the range of stability of the time integration process and a reduction in the number of newton iterations required in the time integration steps the proposed method further preserves energy as well as the linear and angular momentum of the dynamical system copyright 2006 john wiley sons ltd

co rotational beam elements with warping effects in instability problems the present paper investigates the formulation of 3d co rotational beam elements for the buckling and post buckling analysis of frame structures following pacoste and eriksson comput methods app

transformations in regression a robust analysis we consider two approaches to robust estimation for the box cox power transformation model one approach maximizes weighted modified likelihoods a second approach bounds a measure of gross error sensitivity among our primary concerns is the performance of these estimators on actual data in examples that we study there seem to be only minor differences between these two robust estimators but they behave rather differently than the maximum likelihood estimator or estimators that bound only the influence of the residuals these examples show that model selection determination of the transformation parameter and outlier identification are fundamentally interconnected

element formulation and numerical techniques for stability problems in shells in the context of instability problems in shells or shell like structures the objective of the present paper is twofold primarily the paper describes how quasi static conservative instability problems can be considered in a multi parametric context where generalized path following procedures for augmented equilibrium problems are used as computational tools these allow systematic treatment of the higher dimensional solution sets generated under the variations of certain parameters deemed relevant for the given problem the efficient implementation of the above mentioned procedures requires however as an essential ingredient a non linear finite element which is not only accurate but also inexpensive to this end a systematic view on a corotational total lagrangian formulation is described the tric element of argyris and coworkers is slightly modified and introduced as core element formulation special emphasis is given to the alternative methods for treatment of finite three dimensional rotations with reference to both the element definition and solution algorithms numerical examples verify the element capabilities and the possibility to completely describe instability phenomena of large discretized models

quadratically constrained least squares and quadratic problems we consider the following problem compute a vectorx such that ax b 2 min subject to the constraint x 2 a new approach to this problem based on gauss quadrature is given the method is especially well suited when the dimensions ofa are large and the matrix is sparse it is also possible to extend this technique to a constrained quadratic form for a symmetric matrixa we consider the minimization ofx t a x 2b t x subject to the constraint x 2 some numerical examples are given

corotational nonlinear dynamic analysis of thin shell structures with finite rotations a new formulation for corotational nonlinear dynamic analysis of thin shell structures involving large displacements and finite rotations has been presented in this paper by introducing the kinematic description of the geometrically exact quasi static shell model to describe the motion of an arbitrary material point in a triangular shell element the new expressions for the inertial force vector and tangent inertia matrix were derived systematically the elastic deformation was handled by using the consistent symmetrizable equilibrated corotational formulation which is independent with respect to the local finite element modeling an energy momentum conserving algorithm and an energy decaying momentum conserving algorithm were developed for nonlinear dynamic analysis by applying the generalized energy momentum method in the corotational formulation three classic numerical examples including the dynamic response free motion and dynamic buckling of thin shell structures were computed to verify the ac

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

energy conserving algorithms for a corotational formulation standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high speed rotations to tackle these problems we use a corotational framework and a corresponding specific linearization to design new energy conserving numerical schemes in the two dimensional case an algorithm preserving also angular momentum is presented the existence of a solution for the fully discrete setting of this algorithm is established numerical results illustrate the flexibility and efficiency of the proposed algorithms

a subspace minimization method for the trust region step we consider methods for large scale unconstrained minimization based on finding an approximate minimizer of a quadratic function subject to a two norm trust region constraint the steihaug toint method uses the conjugate gradient method to minimize the quadratic over a sequence of expanding subspaces until the iterates either converge to an interior point or cross the constraint boundary however if the conjugate gradient method is used with a preconditioner the steihaug toint method requires that the trust region norm be defined in terms of the preconditioning matrix if a different preconditioner is used for each subproblem the shape of the trust region can change substantially from one subproblem to the next which invalidates many of the assumptions on which standard methods for adjusting the trust region radius are based in this paper we propose a method that allows the trust region norm to be defined independently of the preconditioner the method solves the inequality constrained trust region subproblem over a sequence of evolving low dimensional subspaces each subspace includes an accelerator direction defined by a regularized newton method for satisfying the optimality conditions of a primal dual interior method a crucial property of this direction is that it can be computed by applying the preconditioned conjugate gradient method to a positive definite system in both the primal and dual variables of the trust region subproblem numerical experiments on problems from the cuter test collection indicate that the method can require significantly fewer function evaluations than other methods in addition experiments with general purpose preconditioners show that it is possible to significantly reduce the number of matrix vector products relative to those required without preconditioning

the masking breakdown point of multivariate outlier identification rules abstract in this article we consider simultaneous outlier identification rules for multivariate data generalizing the concept of so called outlier identifiers as presented by davies and gather for the case of univariate samples such multivariate outlier identifiers are based on estimators of location and covariance therefore it seems reasonable that characteristics of the estimators influence the behavior of outlier identifiers several authors mentioned that using estimators with low finite sample breakdown point is not recommended for identifying outliers to give a formal explanation we investigate how the finite sample breakdown points of estimators used in these identification rules influence the masking behavior of the rules

power transformations and reparameterizations in nonlinear regression models a two stage procedure is proposed to achieve normality and homoscedasticity of the classical error assumptions and to remove nonlinearity of the regression function this systematic approach involves power transformations and reparameterization test statistics are obtained to assess the necessity of power transformations and the validity of homoscedasticity of the errors in addition nonlinearity measures are provided to diagnose the accuracy of linearization based approximate confidence regions for parameters numerical illustrations of the two stage procedure arc presented

the standardized influence matrix and its applications abstract in this article we introduce the standardized influence matrix sim of parameter estimators as a conjugate of the sample covariance matrix of standardized influence functions sifs evaluated at the data points we propose principal component analysis for the sim and its complement sim analysis as a diagnostic tool for regression or other statistical inference and provide theoretical insight to the local influence defined by cook we show that sim analysis reveals the multivariate structure of outlying and or influential points specifically sim analysis uncovers hidden structures of influence such as clustering that cannot be identified by the lengths of the standardized influences finally examples in linear regression show that a diagnostic method using sim is more effective if robust parameter estimates are used in calculating the sample sim

a modified corotational framework for triangular shell elements the corotational framework for triangular shell elements has been presented by different authors see the introduction the purpose of this paper is to introduce three modifications in this approach the first one is a simplified definition of the local rotations the second one is a reduction of the number of local degrees of freedom from 18 to 15 the third and principal one concerns the parameterisation of the global finite rotations a new approach based on euler parameters quaternion is proposed in particular it is shown that only three parameters are required the purpose of these three modifications is to obtain a formulation which gives the same numerical results but which is computationally more efficient than the original one this aspect is illustrated in several numerical examples

more about transformations and influential cases in regression we extend the diagnostic method of cook and wang 1983 for assessing case influence to regression models in which both response and linear predictor are transformed we also suggest a possible improvement of cook and wang s method

plastic instability of beam structures using co rotational elements in a previous paper comput methods appl mech engrg 191 2002 1755 the authors have presented a 3d co rotational elastic beam element including warping effects this formulation is now further developed in order to incorporate elasto plastic deformations the element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross sections thus within the present approach the centroid and shear center of the cross section are not necessarily coincident the main purpose of this element is to model elasto plastic instability problems in this context two methods of branch switching are tested and discussed in the first one the bifurcation point is isolated by successive bisections and the branch switching is operated by using the eigenvector associated to the negative eigenvalue in the second one introduced by petryk an energy approach is used to select automatically the stable post bifurcation path six examples including large displacement and stability problems are used in order to assess the performances of the element

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

mallows type bounded influence regression trimmed means abstract the influence functions of the regression trimmed mean estimators proposed by koenker and bassett 1978 and welsh 1987 are bounded in the dependent variable space but not in the independent variable space this article follows the approach of mallows 1973 1975 and modifies these estimators so that the resulting estimators have bounded influence functions the large sample behavior of these estimators is studied and it is shown that they have the same asymptotic distribution the small sample behaviors of the ordinary regression and bounded influence regression trimmed means are then investigated by means of a monte carlo study and by applying the estimators to water salinity data see ruppert and carroll 1980 based on these results we conclude that one can potentially gain much by using bounded influence regression trimmed means over ordinary regression trimmed means however there does not seem to be a clear choice between the koenker bassett and welsh versions

beam elements in instability problems this paper deals with the formulation of beam elements for the numerical analysis of instability phenomena in frame type structures total versus co rotational approaches are discussed comparatively for both two dimensional and three dimensional problems and the similarities between the two types are outlined in the context of 3d beam elements special attention is given to the parameterisation of the orthogonal transformation used to define the rotational field of the beam the technique advocated in the paper is based on the so called rotational vector this leads to symmetric stiffness matrices and avoids the need for special updating procedures for the rotational variables a set of test problems for which the critical behaviour is governed by fold cusp and butterfly catastrophes is used to assess the performances of the considered element types it is shown that analytically verified identities in element formulation also hold in numerical application the examples also show how complex instability behaviour can be reproduced by all elements where sufficient accuracy is introduced into the kinematic expressions the analytical derivation of element expressions with symbolic manipulations from stated basic assumptions is consistently used in the paper

efficient bounded influence regression estimation abstract the least squares estimator for in the classical linear regression model is strongly efficient under certain conditions however in the presence of heavy tailed errors and or anomalous data the least squares efficiency can be markedly reduced in this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first order condition for strong efficiency subject to the constraint we then show that the estimator is asymptotically normal the article concludes with an outline of an algorithm for computing a bounded influence regression estimator and with an example comparing least squares robust regression as developed by huber and the estimator proposed in this article

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

computational aspects of vector like parametrization of three dimensional finite rotations theoretical and computational aspects of vector like parametrization of three dimensional finite rotations which uses only three rotation parameters are examined in detail in this work the relationship of the proposed parametrization with the intrinsic representation of finite rotations via an orthogonal matrix is clearly identified careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of reissner s non linear beam theory pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2 node three dimensional beam element a number of numerical simulations in three dimensional finite rotation analysis are presented in order to illustrate the proposed approach

minimax aspects of bounded influence regression abstract bounded influence regression in the sense of hampel mallows krasker welsch is examined critically from the point of view of finite sample minimax robust estimation theory the main conclusion is that the influence of position of very high leverage points that is of points where the diagonal element of the hat matrix h x xtx 1 xt exceeds a certain bound should be cut down selectively this bound should be chosen roughly between 2 and 5 for the upper of these values the resulting estimate can be approximated very simply by scaling the residuals by their own estimated standard deviation a conflict between decision theoretic estimation and data analytic diagnostic viewpoints is pointed out and briefly discussed

geometrically nonlinear dynamic formulation for three dimensional co rotational solid elements abstract this study presents a three dimensional nonlinear dynamic formulation based on a co rotational cr approach for solid elements the cr formulation is relatively efficient but it is based on the assumption of small strains during large displacement the novel idea of the present formulation involves the use of the cr formulation through a three dimensional solid element for inertial quantities in addition to an internal force vector and a stiffness matrix the present dynamic formulation is derived from lagrange s equation of motion in this procedure the cr formulation i e element independent cr is one of the most attractive features that is strongly manifested in an efficient manner consequently this obtains the governing equation of motion including motion driven inertial components physical quantities induced by the prescribed motion four examples are presented to demonstrate the accuracy of the present dynamic formulation finally the results are compared with those obtained by abaqus and the findings reveal that the proposed dynamic formulation is in good agreement with existing predictions

minimization of a large scale quadratic function subject to a spherical constraint an important problem in linear algebra and optimization is the trust region subproblem minimize a quadratic function subject to an ellipsoidal or spherical constraint this basic problem has several important large scale applications including seismic inversion and forcing convergence in optimization methods existing methods to solve the trust region subproblem require matrix factorizations which are not feasible in the large scale setting this paper presents an algorithm for solving the large scale trust region subproblem that requires a fixed size limited storage proportional to the order of the quadratic and that relies only on matrix vector products the algorithm recasts the trust region subproblem in terms of a parameterized eigenvalue problem and adjusts the parameter with a superlinearly convergent iteration to find the optimal solution from the eigenvector of the parameterized problem only the smallest eigenvalue and corresponding eigenvector of the parameterized problem needs to be computed the implicitly restarted lanczos method is well suited to this subproblem

higher order mitc general shell elements two mixed interpolated general shell finite elements for non linear analysis a 9 node element and a 16 node element are presented the elements are based on the mixed interpolation of tensorial components mitc approach in which the covariant strain component fields for the in plane and shear actions are interpolated and tied to the also interpolated displacement field both the 9 node element referred to as the mitc9 element and the 16 node element referred to as the mitc16 element are tested numerically and found to have high predictive capabilities

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

a mixed tetrahedral element with nodal rotations for large displacement analysis of inelastic structures summary a novel mixed four node tetrahedral finite element equipped with nodal rotational degrees of freedom is presented its formulation is based on a hu washizu type functional suitable to the treatment of material nonlinearities rotation and skew symmetric stress fields are assumed as independent variables the latter entering the functional to impose rotational compatibility and suppress spurious modes exploiting the choice of equal interpolation for strain and symmetric stress fields a robust element state determination procedure requiring no element level iteration is proposed the mixed element stability is assessed by means of an original and effective numerical test the extension of the present formulation to geometric nonlinear problems is achieved through a polar decomposition based corotational framework after validation in both material and geometric nonlinear context the element performances are investigated in demanding simulations involving complex shape memory alloy structures supported by the comparison with available linear and quadratic tetrahedrons and hexahedrons the numerical results prove accuracy robustness and effectiveness of the proposed formulation copyright 2016 john wiley sons ltd

equilibrium subsets for multi parametric structural analysis the paper discusses multi parametric formulations for structural equilibrium problems by seeking subsets of equilibrium states which also fulfil extra conditions more detailed information on structural behaviour can be obtained these conditions can be related to analyses of e g critical behaviour imperfections or optimisation the paper shows a general problem setting and some interesting augmentations a solution method for the special case of one dimensional equilibrium subsets is described the algorithm is a generalisation of a path following algorithm where new methods are developed for the evaluation of the path tangent and for the isolation of special solution points examples are used to show the properties and the possibilities of the ideas

a semidefinite framework for trust region subproblems with applications to large scale minimization primal dual pairs of semidefinite programs provide a general framework for the theory and algorithms for the trust region subproblem trs this latter problem consists in minimizing a general quadratic function subject to a convex quadratic constraint and therefore it is a generalization of the minimum eigenvalue problem the importance of trs is due to the fact that it provides the step in trust region minimization algorithms the semidefinite framework is studied as an interesting instance of semidefinite programming as well as a tool for viewing known algorithms and deriving new algorithms for trs in particular a dual simplex type method is studied that solves trs as a parametric eigenvalue problem this method uses the lanczos algorithm for the smallest eigenvalue as a black box therefore the essential cost of the algorithm is the matrix vector multiplication and thus sparsity can be exploited a primal simplex type method provides steps for the so called hard case extensive numerical tests for large sparse problems are discussed these tests show that the cost of the algorithm is 1 n times the cost of finding a minimum eigenvalue using the lanczos algorithm where 0 n 1 is a fraction which decreases as the dimension increases

diagnostics and robust estimation when tranforming the regression model and the response in regression analysis the response is often transformed to remove heteroscedasticity and or skewness when a model already exists for the untransformed response then it can be preserved by applying the same transform to both the model and the response this methodology which we call transform both sides has been applied in several recent papers and appears highly useful in practice when a parametric transformation family such as the power transformations is used then the transformation can be estimated by maximum likelihood the maximum likelihood estimator however is very sensitive to outliers in this article we propose diagnostics to indicate cases influential for the transformation or regression parameters we also propose a robust bounded influence estimator similar to the krasker welsch regression estimator

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

a consistent 3d corotational beam element for nonlinear dynamic analysis of flexible structures abstract the purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3d flexible frames the novelty of the formulation lies in the use of the corotational framework i e the decomposition into rigid body motion and pure deformation to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix as a consequence cubic interpolations are adopted to formulate both inertia and internal local terms in the derivation of the dynamic terms an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained to enhance the efficiency of the iterative procedure an approximate expression of the tangent dynamic matrix is adopted four numerical examples are considered to assess the performance of the new formulation against the one suggested by simo and vu quoc 1988 48 it was observed that the proposed formulation proves to combine accuracy with efficiency in particular the present approach achieves the same level of accuracy as the formulation of simo and vu quoc but with a significantly smaller number of elements

an enhanced co rotational approach for large displacement analysis of plates this paper presents a new co rotational approach for the large displacement analysis of plates employing 4 noded quadrilateral flat shell elements the proposed approach benefits from i a simple local co rotational system invariant to the element nodal ordering ii the choice of the two smallest components of the nodal normal vector as global rotational degrees of freedom and iii the use of hierarchic freedoms that are unaffected by the co rotational transformations for higher order accuracy important additional benefits that arise from the aforementioned features include symmetry of the tangent stiffness matrix and complete insensitivity of the large displacement transformations to the size of the incremental step the applicability of the new approach to moderately thick as well as thin plates is illustrated by considering two alternative local formulations based on the reissner mindlin and discrete kirchhoff hypotheses several examples are finally presented which demonstrate the accuracy step insensitivity and computational benefits of the proposed co rotational approach for large displacement analysis of plate structures copyright 2005 john wiley sons ltd

transformations and influential cases in regression we describe a diagnostic method for assessing the degree to which individual cases and groups of cases influence the box cox likelihood estimate of the transformation parameter for the response variable in linear regression models we compare the method to a method proposed by atkinson 1982 and sketch the extension to explanatory variables we present two examples

the score statistic for regression transformation summary the score statistic for regression transformation using a parametric family is developedfurther a simple formula for the approximate variance matrix of score statistics basedon asymptotic theory is applied to yield the score statistic t s for regression transforma tion this is compared to atkinson s t d statistic for the same problem and yields animprovement to its standardization simulations indicate that the significance levels ofthe proposed score statistic t s are very close to their nominal values some key words power transformation regression score statistic simulation tests for normality 1 introduction the work of box cox 1964 has been the basis of many investigations into theuse of transformations in regression analysis and the current state of the topic is wellsummarized in the monographs of cook weisberg 1982 and atkinson 1985 theprincipal aim of the original work was to transform a response or dependent variable sothat it would satisfy the normality and other standard assumptions of regression analysis the authors used a parametric family of transformations to achieve this and placedemphasis on estimating its parameters in subsequent work andrews 1971 was moreconcerned with testing transformation parameters while atkinson 1973 introducedanother statistic for this purpose from consideration of both andrews s statistic and scoreor c a tests the present paper develops a standardized score statistic in the case of ascalar transformation parameter in effect it is found to provide the standardization ofatkinson s statistic an aspect which atkinson 1973 believed to be theoretically intract able and avoided by using an approximate regression argument

minimizing a quadratic over a sphere a new method the sequential subspace method ssm is developed for the problem of minimizing a quadratic over a sphere in our scheme the quadratic is minimized over a subspace which is adjusted in successive iterations to ensure convergence to an optimum when a sequential quadratic programming iterate is included in the subspace convergence is locally quadratic numerical comparisons with other recent methods are given

iterative methods for nearly singular linear systems iterative methods are developed and studied for near singular linear systems cx b our approach called the transformed minimal residual algorithm tmres is derived from any convergent iterative scheme sxk 1 txk b associated with a splitting c s t in each step of tmres the transformed residual s 1 b cx is minimized over a krylov space generated by s 1 t the original iterative scheme typically converges slowly when c is nearly singular while a krylov space generated by s 1 t often contains a much better approximation to a solution tmres is algebraically equivalent to the generalized minimal residual algorithm gmres preconditioned by s 1 although there are numerical differences since a different matrix s 1 c is used to generate the krylov space in preconditioned gmres special attention is given to sparsity and convergence issues related to linear systems of the form bf aa tr sigma bf i bf x bf b where sigma ge 0

a simulation experiment for comparing tests of regression transformation abstract an example is given of the use of graphical methods in the analysis of a simulation experiment comments are made on the design of such studies

a class of locally and globally robust regression estimates abstract we present a new class of regression estimates called generalized estimates these estimates are defined by minimizing the scale of the weighted residuals with weights that penalize high leverage observations like the estimates the generalized estimates utilize for their definition two loss functions 1 and 2 which together with the weights can be chosen to achieve simultaneously high breakdown point finite gross error sensitivity and high efficiency we recommend however choosing these functions so as to control the bias behavior of the estimate for a large range of possible contaminations and then boosting the efficiency by a simple least squares reweighting step the generalized estimate with loss functions 1 and 2 is related to the hill ryan gm estimate with a loss function which is a linear combination of 1 and r in fact both estimates have the same influence function and asymptotic distribution under the central model we show that a certain generalized estima

k clustering as a detection tool for influential subsets in regression this article describes a new methodology for the detection of influential subsets in regression the method is based on an adaptation of computational and graphical techniques used in cluster analysis and makes use of some general properties of influential subsets but it is independent of any specific measure of influence for small to moderate data sets the proposed method is computationally efficient compared to existing search methods and it identifies subset candidates that merit attention according to some or all measures of joint influence that have appeared in the literature to date examples are given illustrating the method applied to two data sets previously analyzed in published studies

a global convergence theory for the celis dennis tapia trust region algorithm for constrained optimization a global convergence theory for a class of trust region algorithms for solving the equality constrained optimization problem is presented this theory is sufficiently general that it holds for any algorithm that generates steps giving at least a fraction of cauchy decrease in the quadratic model of the constraints and that uses the augmented lagrangian as a merit function this theory is used to establish global convergence of the 1984 celis dennis tapia algorithm with a different scheme for updating the penalty parameter the behavior of the penalty parameter is also discussed

two graphical displays for outlying and influential observations in regression summary the paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression these procedures are presented as half normal plots with envelopes derived from simulation in order to avoid overinterpretation of the data analysis of a well known data set leads to the use of a data transformation a simple test for which is commended and to some comments on the relationship with robust regression the widespread availability of sophisticated computer software has made the fitting of multiple regression equations painless but the very ease of these procedures may cause insufficient care to be given to checking and scrutiny of the data transcription punching and data manipulation errors may lead to bad values both of the observations y and of the independent or explanatory variables x it is the purpose of the present paper to describe and exemplify two plots which provide checks against such bad values it is argued that these plots and a test for transformations should accompany any thorough regression analysis bad values of the response or outliers have long been detected by a variety of plots of residuals bad values of the explanatory variables are less easily detected even when they lead to an extreme point in the design space since the fitted equation will pass close to such an influential observation the residual may not be especially large even after allowance has been made for the small variance of the fitted value at such a point to detect such behaviour a quantity is needed which exhibits the dependence of the fitted model on each point or group of points discussions of such quantities are given by hoaglin welsch 1978 and more recently by belsley kuh welsch 1980 2 1 by cook weisberg 1980 and by pregibon 1981 the quantity used here is a modification of a statistic proposed by cook 1977 which is derived in 2 two half normal plots are presented in 3 as an aid to interpretation envelopes to the plots are generated by simulation examples of the plots are given in 4 both for simulated data and for the stack loss data given by brownlee 1965 p 454 transformations of this data set are discussed in 5 the paper concludes with some comments on the relationship with robust

transformations and influential observations in minimum sum of absolute errors regression the box cox power transformation model is considered for minimum sum of absolute errors msae regression a long tailed error distribution specifically the laplace distribution is included and could accommodate observations that in the normal case are outlying or unduly influencing a choice of transformation the log likelihood procedure of box and cox 1964 for obtaining the optimal transformation parameter is adapted for laplace errors and msae regression graphical methods for detecting the influence of individual observations on the choice of transformation are described application to examples illustrates that this approach can provide valuable additional information to the data analyst

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

on the spherical quasi convexity of quadratic functions abstract in this paper the spherical quasi convexity of quadratic functions on spherically convex sets is studied several conditions characterizing the spherical quasi convexity of quadratic functions are presented in particular conditions implying spherical quasi convexity of quadratic functions on the spherical positive orthant are given some examples are provided as applications of the obtained results

a comparison of asymptotically equivalent test statistics for regression transformation summary a simulation comparison is made of six asymptotically equivalent test statistics for transformation of the response in regression the tests typically have observed sizes up to twice the nominal size a likelihood ratio statistic a score statistic and a wald statistic behave very similarly both at the null hypothesis and in terms of power values of all the statistics are highly positively correlated the greater part of any differences between the statistics is concentrated in their standard deviations to test hypotheses about parametric families of transformation box cox 1964 use a likelihood ratio test more recently several other asymptotically equivalent tests have been suggested in the present paper we present empirical comparisons of six tests in terms of size power and diagnostic efficacy the interesting relevance of these results to small sample comparisons of score wald and likelihood ratio tests is briefly discussed the notation and background of the paper follow those of box cox 1964 a vector of n response values y is linearly related with an initial constant term to p 1 explanatory variables whose values and an initial column of ones are contained in an n xp matrix x the box cox family of transformations indexed by a scalar parameter a is employed to produce the transformed response variable y the aim is to choose a by maximum likelihood so that y follows the linear model y a x 3 e 1 1 where e is a vector of errors which are mutually independent with normal distributions of zero mean and constant variance a2 and 3 is a vector of coefficients the estimate a satisfies the equation

solving the trust region subproblem using the lanczos method the approximate minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming methods when the number of variables is large the most widely used strategy is to trace the path of conjugate gradient iterates either to convergence or until it reaches the trust region boundary in this paper we investigate ways of continuing the process once the boundary has been encountered the key is to observe that the trust region problem within the currently generated krylov subspace has a very special structure which enables it to be solved very efficiently we compare the new strategy with existing methods the resulting software package is available as hsl vf05 within the harwell subroutine library

geometrically nonlinear formulation for the curved shell elements this paper presents a geometrically nonlinear formulation using total lagrangian approach for the three dimensional curved shell elements the basic element geometry is constructed using the coordinates of the middle surface nodes and the mid surface nodal point normals the element displacement field is described using three translations of the mid surface nodes and the two rotations about the local axes the existing shell element formulations are restricted to small nodal rotations between two successive load increments the element formulation presented here removes such restrictions this is accomplished by retaining nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties the formulation presented here is very general and yet can be made specific by selecting proper nonlinear functions representing the effects of nodal rotations the element properties are derived and presented in detail numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements

asymptotic post buckling analysis of rectangular plates by hc finite elements the present paper extends the finite element perturbation approach already presented for pin jointed and framed structures15 to rectangular thin plates koiter s asymptotic strategy2 is coupled with a high continuity finite element discretization of the plate 22 the consistency of the discrete model is discussed from the kinematical and numerical points of view and several numerical tests are reported it appears that use of the hc elements makes the perturbation algorithm insensitive to the locking phenomenon occurring in the evaluation of the postbuckling behaviour it also allows the use of very fine discretization meshes at low computational cost

a trust region algorithm for equality constrained optimization a trust region algorithm for equality constrained optimization is proposed that employs a differentiable exact penalty function under certain conditions global convergence and local superlinear convergence results are proved

robust response transformations based on optimal prediction nonlinear regression problems can often be reduced to linearity by transforming the response variable e g using the box cox family of transformations the classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion assuming homoscedastic normal errors for the transformed response these estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic this article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution for this purpose a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an m scale this concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients a finite sample estimate of this criterion based on a robust version of s

finite rotation analysis and consistent linearization using projectors abstract a systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis this procedure is a generalization of the work presented in computers and structures volume 30 pp 257 267 the basis of our approach is the element independent co rotational algorithm where the element rigid body motion translations and rotations is separated from the deformational part of its total motion the variation of this co rotational relation results in a projector matrix with the property that a consistent internal force vector is invariant under its action the consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector this results in an unsymmetric tangent matrix whose anti symmetric part depends on the out of balance force vector in this paper we prove that using the symmetric part of the tangent matrix the newton iteration retains its quadratic rate of convergence this approach has been used to solve a number of large rotation test example problems the results demonstrate that it is possible to analyze structures undergoing large rotations within a general co rotational framework using simple and economical finite elements the resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre and post processors to the element routines

diagnostic regression analysis and shifted power transformations diagnostic displays for outlying and influential observations are reviewed in some examples apparent outliers vanish after a power transformation of the data interpretation of the score statistic for transformations as regression on a constructed variable makes diagnostic methods available for detection of the influence of individual observations on the transformation methods for the power transformation are exemplified and extended to the power transformation after a shift in location for which there are two constructed variables the emphasis is on plots as diagnostic tools

element behavior in post critical plane frame analysis depending on the type of uni modal cuspoid catastrophe which governs the local behavior of a structure at a simple critical point correct prediction of the post critical path requires an accurat

on the choice of the linear element for corotational triangular shells the corotational formulation for triangular thin shell elements presented in a eriksson c pacoste element formulation and numerical techniques for stability problems in shells comput methods

evaluation of the constant strain triangle with drilling rotations the performance of the constant strain triangle with added drilling rotations is evaluated by solving a variety of plane test problems numerical results confirm that the new element is always superior to the standard constant strain triangle and that it is of similar accuracy to the best available alternative triangular elements of other authors it is however less accurate than some rectangular elements which include drilling rotations

more on score tests for transformation in regression summary lawrance s 1987 results concerning tests for transformation in regression are extended to models where response and mean may both be transformed it is also suggested i that the methods of lawrance and of atkinson 1982 lead to statistics with near perfect correlation and ii that observed and expected informations may have considerably different effects as standardizations of the score statistic

linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method abstract in the present study we apply the natural mode method and formulate an appropriate linear and geometrically nonlinear theory which is implemented on a model three node multilayered triangular facet element which incorporates the effect of transverse shear deformation and is intended for the nonlinear analysis of large and complex isotropic and composite structures in this context we discuss the derivation of the elastic and geometrical elemental stiffnesses which are based on appropriate kinematic as well as physical idealizations which constitute basic elements of the method of intelligent physical lumping subsequently we present the ariban scheme accumulation of the rigid body and natural modes for geometrically nonlinear analysis it is emphasized that both the triangular facet element and the nonlinear algorithm are developed for the analysis of large and complex structures for which higher order formal finite elements cannot provide answers inexpensivelly in addition the structure of the algorithm and its matrix language are ideally suited for modern parallel computers we conclude our study with numerical examples for isotropic and composite plates all the numerical experiments show the accuracy and potential of the developed methodology for extensive structural engineering computations

global convergence of ssm for minimizing a quadratic over a sphere in an earlier paper minimizing a quadratic over a sphere siam j optim 12 2001 188 208 we presented the sequential subspace method ssm for minimizing a quadratic over a sphere this method generates approximations to a minimizer by carrying out the minimization over a sequence of subspaces that are adjusted after each iterate is computed we showed in this earlier paper that when the subspace contains a vector obtained by applying one step of newton s method to the first order optimality system ssm is locally quadratically convergent even when the original problem is degenerate with multiple solutions and with a singular jacobian in the optimality system in this paper we prove nonlocal convergence of ssm to a global minimizer whenever each ssm subspace contains the following three vectors i the current iterate ii the gradient of the cost function evaluated at the current iterate and iii an eigenvector associated with the smallest eigenvalue of the cost function hessian for nondegenerate problems the convergence rate is at least linear when vectors i iii are included in the ssm subspace

estimation for the box cox transformation model without assuming parametric error distribution box and cox proposed a power transformation for the response variable that yields a linear regression model with normal error and constant variance inference procedures for the regression coefficients and transformation parameter under this model setting have been studied extensively in this article we propose a simple semiparametric estimation method for the box cox transformation model with no specific parametric assumption on the distribution of the error term the resulting estimators are strongly consistent and asymptotically normal their covariance matrix can be estimated through a novel resampling method without involving nonparametric function estimates of the underlying unknown density function for the error term the new proposal is illustrated with a well known dataset in the literature of transformation and its efficiency and robustness are closely examined through numerical studies

a simplified co rotational method for quadrilateral shell elements in geometrically nonlinear analysis summary this paper presents a simplified co rotational formulation for quadrilateral shell elements inheriting the merit of element independence from the traditional co rotational approach in literature with the objective of application to nonlinear analysis of civil engineering structures the authors further simply the formulation of the geometrical stiffness using the small strain assumption which is valid in the co rotational approach with the warping effects considered as eccentricities compared with the traditional element independent co rotational method the projector is neglected both in the tangent stiffness matrix and the internal force vector for simplicity in formulation meanwhile a quadrilateral flat shell element allowing for drilling rotations is adopted and incorporated into this simplified co rotational algorithm for geometrically nonlinear analysis involved with large displacements and large rotations several benchmark problems are presented to confirm the efficiency and accuracy of the proposed method for practical applications

semiparametric box cox power transformation models for censored survival observations the accelerated failure time model specifies that the logarithm of the failure time is linearly related to the covariate vector without assuming a parametric error distribution in this paper we consider the semiparametric box cox transformation model which includes the above regression model as a special case to analyse possibly censored failure time observations inference procedures for the transformation and regression parameters are proposed via a resampling technique prediction of the survival function of future subjects with a specific covariate vector is also provided via pointwise and simultaneous interval estimates all the proposals are illustrated with datasets from two clinical studies

path following analysis of thin walled structures and comparison with asymptotic post critical solutions a path following non linear elastic analysis for structures composed of assemblages of flat slender elastic panels is presented the proposed path following method employs fem technology and a kinematical model to analyse these structures using a koiter asymptotic approach as a result it is possible to verify the accuracy achieved by the asymptotic method the proposed mixed path following formulation is both efficient and robust with regards to the locking extrapolation phenomenon that strongly affects compatible formulations the use of an hc finite element makes it possible to avoid the problem of the finite rotations in the space maintaining a high degree of continuity and making the numeric formulation simple and efficient copyright 2002 john wiley sons ltd

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types

new tools for residual analysis techniques are presented for stepwise selection of observations in order of discrepancy from a linear model and for assigning a p value to each selected observation a general class of criteria for discrepancy is defined and leading members of the class are discussed two ways to define the sequence of p values for a general selection criterion are discussed and their relative advantages are compared the techniques are illustrated on several data sets using only the computationally simpler of the two approaches to p values

biased and unbiased cross validation in density estimation abstract nonparametric density estimation requires the specification of smoothing parameters the demands of statistical objectivity make it highly desirable to base the choice on properties of the data set in this article we introduce some biased cross validation criteria for selection of smoothing parameters for kernel and histogram density estimators closely related to one investigated in scott and factor 1981 these criteria are obtained by estimating l 2 norms of derivatives of the unknown density and provide slightly biased estimates of the average squared l 2 error or mean integrated squared error these criteria are roughly the analog of wahba s 1981 generalized cross validation procedure for orthogonal series density estimators we present the relationship of the biased cross validation procedure to the least squares cross validation procedure which provides unbiased estimates of the mean integrated squared error both methods are shown to be based on u statistics we compare the two metho