three dimensional vibration of a buckled elastica supported by spherical hinges abstract in this paper we study the effect of extensibility on the vibration characteristics of a spatial buckled rod elastica under edge thrust and supported by spherical hinges at the ends the nonlinear equations of motion are written within the framework of director theory the elastica in question admits only plane deformations there are three types of vibration modes in plane symmetric out of plane and anti symmetric twisting out of plane most of the natural frequencies decrease as the end shortening increases except the first in plane mode without a nodal point this mode is inadmissible in an inextensible elastica this may be considered a flaw in the inextensible elastica model when dynamic behavior is concerned in the limit case when the static deformation is small a small deformation theory taking into account axial extensibility is formulated and compared with the elastica model the natural frequency of the first in plane mode derived from small deformation theory agrees very well with the one calculated from the extensible elastica model in the post buckling range however all others are found to be independent of end shortening this obviously unreasonable result is due to the limitation of small deformation theory

asymptotic optimality of cl and generalized cross validation in ridge regression with application to spline smoothing the asymptotic optimality of mallows c l and generalized cross validation is demonstrated in the setting of ridge regression an application is made to spline smoothing in nonparametric regression a counterexample is given to help understand why sometimes gcv may not be asymptotically optimal the coefficient of variation for the eigenvalues of the information matrix must be large in order to guarantee the optimality of gcv the proff is based on the connection between gcv and stein s unbiased risk estimate

on the linear normal modes of planar pre stressed curved beams the natural frequencies and mode shapes of planar shear undeformable beams around their curved pre stressed post buckling configurations are investigated neglecting rotary inertia effects two mechanical models are considered depending on the assumed boundary conditions in the buckling and post buckling phases with the first model the beam is considered inextensible because it is hinged at one end and is acted upon by an axial compressive force on the other end a sliding hinge in the second case the beam is assumed inextensible in the pre stressed phase same boundary conditions as above whereas it is extensible in the subsequent free linear dynamic phase because the sliding hinged boundary is changed into a stationary hinged end linear vibrations are governed by partial differential equations with non constant coefficients and the solutions for the frequencies and mode shapes are found employing two approximate approaches a fully numerical method based on a finite element formulation and a semi analytical method based on a weak formulation galerkin method the main results are compared and a close agreement in the outcomes is found the leading mechanical differences in the linear normal modes of the two pre stressed curved beam models are discussed

elliptic integral solutions of plane elastica with axial and shear deformations abstract closed form solutions are derived for elastica with axial and shear deformations using elliptic integrals the theories used here are the timoshenko beam theory of finite displacements with finite strains and that with small strains elliptic integral solutions are further transformed to normal forms to obtain accurate solutions as a result both of the closed form solutions are expressed in normal forms from the first to the third kind of elliptic integrals with these solutions two kinds of structures are analyzed to examine the effect of shear deformations along with the accuracy of the approximate theory of finite displacements with small strains

nonlinear large deflection problems of beams with gradient a biparametric perturbation method for beams with gradient due to the combined influences introduced by loads and gradient the first derivative item in euler bernoulli equation can not be neglected thus making the solution of the problem be a nonlinear large deflection one in this paper we use a new perturbation method with two small parameters one describes the loads effect and another describes the geometrical nature of the problem to solve the nonlinear large deflection problem of beams with gradient under the two different boundary conditions we derive the first and second order approximate analytical solution of the deflection the rotation and the arc length of the beam as well as the internal forces of the beam at the end the results indicate that the choice of two independent parameters may describe comprehensively the nonlinear effects caused by loads and gradient which enables the approximate solution to be precise enough to be used for the analysis of large deflection beam with gradient

efficiency for regularization parameter selection in penalized likelihood estimation of misspecified models it has been shown that akaike information criterion aic type criteria are asymptotically efficient selectors of the tuning parameter in nonconcave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available we relax this assumption to prove that aic itself is asymptotically efficient and we study its performance in finite samples in classical regression it is known that aic tends to select overly complex models when the dimension of the maximum candidate model is large relative to the sample size simulation studies suggest that aic suffers from the same shortcomings when used in penalized regression we therefore propose the use of the classical corrected aic aic c as an alternative and prove that it maintains the desired asymptotic properties to broaden our results we further prove the efficiency of aic for penalized likelihood methods in the context of generalized linear models with no dispersion parameter similar result

model selection principles in misspecified models summary model selection is of fundamental importance to high dimensional modelling featured in many contemporary applications classical principles of model selection include the bayesian principle and the kullback leibler divergence principle which lead to the bayesian information criterion and akaike information criterion respectively when models are correctly specified yet model misspecification is unavoidable in practice we derive novel asymptotic expansions of the two well known principles in misspecified generalized linear models which give the generalized bayesian information criterion and generalized akaike information criterion a specific form of prior probabilities motivated by the kullback leibler divergence principle leads to the generalized bayesian information criterion with prior probability gbicp which can be naturally decomposed as the sum of the negative maximum quasi log likelihood a penalty on model dimensionality and a penalty on model misspecification directly numerical studies demonstrate the advantage of the new methods for model selection in both correctly specified and misspecified models

least squares model averaging this paper considers the problem of selection of weights for averaging across least squares estimates obtained from a set of models existing model average methods are based on exponential akaike information criterion aic and bayesian information criterion bic weights in distinction this paper proposes selecting the weights by minimizing a mallows criterion the latter an estimate of the average squared error from the model average fit we show that our new mallows model average mma estimator is asymptotically optimal in the sense of achieving the lowest possible squared error in a class of discrete model average estimators in a simulation experiment we show that the mma estimator compares favorably with those based on aic and bic weights the proof of the main result is an application of the work of li 1987

frequentist model average estimators the traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance without acknowledging the additional uncertainty introduced by model selection this often means underreporting of variability and too optimistic confidence intervals we build a general large sample likelihood apparatus in which limiting distributions and risk properties of estimators post selection as well as of model average estimators are precisely described also explicitly taking modeling bias into account this allows a drastic reduction in complexity as competing model averaging schemes may be developed discussed and compared inside a statistical prototype experiment where only a few crucial quantities matter in particular we offer a frequentist view on bayesian model averaging methods and give a link to generalized ridge estimators our work also leads to new model selection criteria the methods are illustrated with real data applications

behaviour of the extensible elastica solution the general form of the virtual work expression for the large strain euler bernoulli beam theory is derived using the nominal strain biot s tensor from the equilibrium equations derived from the virtual work expression it turns out that a linear relation between biot s stress tensor and the biot nominal strain tensor forms the differential equation used to derive the elastica solution moreover in the differential equation one additional term enters which is related to the extensibility of the beam axis as a special application the well known problem of an axially loaded beam is analysed due to the extensibility of the beam axis it is shown that the buckling load of the extensible elastica solution depends on the slenderness and it is of interest that for small slenderness the bifurcation point becomes unstable this means the bifurcation point changes from being supercritical which always hold for the inextensible case i e the classical elastica solution to being a subcritical point in addition higher order singularities are found as well as nonbifurcating isolated branches

semiparametric model averaging prediction for dichotomous response abstract model averaging has attracted abundant attentions in the past decades as it emerges as an impressive forecasting device in econometrics social sciences and medicine so far most developed model averaging methods focus only on either parametric models or nonparametric models with a continuous response in this paper we propose a semiparametric model averaging prediction smap method for a dichotomous response the idea is to approximate the unknown score function by a linear combination of one dimensional marginal score functions the weight parameters involved in the approximation are obtained by first smoothing the nonparametric marginal scores and then applying the parametric model averaging via a maximum likelihood estimation the proposed smap provides greater flexibility than parametric models while being more stable than a fully nonparametric approach theoretical properties are investigated in two practical scenarios i covariates are conditionally independent given the response and ii the conditional independence assumption does not hold in the first scenario we show that smap puts weight one to the true model and hence the model averaging estimators are consistent in the second scenario in which a true model may not exist smap is shown to be asymptotically optimal in the sense that its kullback leibler loss is asymptotically identical to that of the best but infeasible model averaging estimator empirical evidences from simulation studies and a real data analysis are presented to support and illustrate our methods

large deformation and stability of an extensible elastica with an unknown length abstract a beam resting on spatially fixed supports may slide relatively to these as soon as external forces are applied consequently the length of the portion of the reference configuration which is currently located between the supports depends on the loading and therefore is not known in advance in the present paper the problem of a slender beam under a uniformly distributed force is investigated which is clamped at one side but may slide through another clamping device in axial direction at the opposite side in combination with a suitable coordinate transformation by which the numerical treatment is simplified a finite element approach is utilized to determine the equilibrium shape for the maximum critical load that can be imposed on the beam in the course of this the influence of the extensibility of the beam axis is studied a theory based on reissner s geometrically exact relations for the plane deformation of beams is adapted such that it allows constitutive relations on stress strain level to be integrated consistently in addition to the classical equations of the extensible elastica a constitutive model derived from the st venant kirchhoff material of non linear continuum mechanics is studied the results obtained in this survey are finally compared to those from the linear beam theory which turns out to be incapable of describing the problem under consideration in a satisfactory manner

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

isogeometric analysis for nonlinear planar kirchhoff rods weighted residual formulation and collocation of the strong form abstract high order shape functions used in isogeometric analysis allow the direct solution not only to the weighted residual formulation of the strong form opening the door to new integration schemes e g reduced gauss lobatto quadrature integration at superconvergent sites but also to collocation approaches e g using greville or superconvergent collocation points the goal of the present work is to compare these different methods through the application to the planar kirchhoff rod a fourth order rotation free formulation used to model slender beams under large deformations robustness of the geometrically nonlinear solution is improved using the mixed integration point mip newton a method that combines the advantages of displacement and mixed formulations based on the observations of the convergence plots convergence order estimates are provided for each discretization method advantages and weaknesses in terms of robustness and computation cost are also discussed for a set of benchmarks

a self concordant interior point approach for optimal control with state constraints we propose an infeasible interior point method for pointwise state constrained optimal control problems with linear elliptic pdes a smoothed constraint violation functional is used to develop a self concordant barrier approach in an infinite dimensional setting we provide a detailed convergence analysis in function space for this approach the quality of the smoothing is described by a parameter by fixing this parameter we obtain a perturbed version of the original problem we establish complexity estimates and convergence rates for the methods that we propose to solve a given perturbed problem we also estimate the distance between the optimal solution of the perturbed problem and the optimal solution of the original problem moreover our approach yields a rigorous measure for the proximity of the actual iterate to the minimizer of the perturbed and the original problems we report on numerical experiments to illustrate efficiency and mesh independence

the intricate global structure of buckled states of compressible columns singularity theory and global multiparameter bifurcation theory are combined to show that nonbifurcating buckled states of compressible nonlinearly elastic columns lie on branches having detailed qualitative properties these properties distinguish the branches globally together with a delicate asymptotic analysis they are used to show that the global disposition of solution branches both bifurcating and not is strikingly different from that for incompressible columns

a model averaging approach for high dimensional regression this article considers high dimensional regression problems in which the number of predictors p exceeds the sample size n we develop a model averaging procedure for high dimensional regression problems unlike most variable selection studies featuring the identification of true predictors our focus here is on the prediction accuracy for the true conditional mean of y given the p predictors our method consists of two steps the first step is to construct a class of regression models each with a smaller number of regressors to avoid the degeneracy of the information matrix the second step is to find suitable model weights for averaging to minimize the prediction error we estimate the model weights using a delete one cross validation procedure departing from the literature of model averaging that requires the weights always sum to one an important improvement we introduce is to remove this constraint we derive some theoretical results to justify our procedure a theorem is proved showing that del

parsimonious model averaging with a diverging number of parameters model averaging generally provides better predictions than model selection but the existing model averaging methods cannot lead to parsimonious models parsimony is an especially important propert

weighted average least squares estimation of generalized linear models abstract the weighted average least squares wals approach introduced by magnus et al 2010 in the context of gaussian linear models has been shown to enjoy important advantages over other strictly bayesian and strictly frequentist model averaging estimators when accounting for problems of uncertainty in the choice of the regressors in this paper we extend the wals approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models glms we study the large sample properties of the wals estimator for glms under a local misspecification framework and the finite sample properties of this estimator by a monte carlo experiment the design of which is based on a real empirical analysis of attrition in the first two waves of the survey of health aging and retirement in europe share

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

on the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach abstract in finite element methods that are based on position and slope coordinates a representation of axial and bending deformation by means of an elastic line approach has become popular such beam and plate formulations based on the so called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories examining the existing planar absolute nodal coordinate element which uses a curvature proportional bending strain expression it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and even more serious the normal force is incorrect a correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived the strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the st venant kirchhoff material therefore the strain energy is derived for the latter case and compared to classical nonlinear rod theories the error in the original absolute nodal coordinate formulation is documented by numerical examples the numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications the numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre curved static and dynamic problems including buckling and eigenvalue analysis the resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy momentum conservation

the focused information criterion a variety of model selection criteria have been developed of general and specific types most of these aim at selecting a single model with good overall properties for example formulated via average prediction quality or shortest estimated overall distance to the true model the akaike the bayesian and the deviance information criteria along with many suitable variations are examples of such methods these methods are not concerned however with the actual use of the selected model which varies with context and application the present article takes the view that the model selector should instead focus on the parameter singled out for interest in particular a model that gives good precision for one estimand may be worse when used for inference for another estimand we develop a method that for a given focus parameter estimates the precision of any submodel based estimator the framework is that of large sample likelihood inference using an unbiased estimate of limiting risk we propose a foc

regularization parameter selections via generalized information criterion we apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators this approach relies heavily on the choice of regularization parameter which controls the model complexity in this paper we propose employing the generalized information criterion encompassing the commonly used akaike information criterion aic and bayesian information criterion bic for selecting the regularization parameter our proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches we show that the bic type selector enables identification of the true model consistently and the resulting estimator possesses the oracle property in the terminology of fan and li 2001 in contrast however the aic type selector tends to overfit with positive probability we further show that the aic type selector is asymptotically loss efficient while the bic type selector is not

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail

least squares model averaging by mallows criterion abstract this paper is in response to a recent paper by hansen 2007 who proposed an optimal model average estimator with weights selected by minimizing a mallows criterion the main contribution of hansen s paper is a demonstration that the mallows criterion is asymptotically equivalent to the squared error so the model average estimator that minimizes the mallows criterion also minimizes the squared error in large samples we are concerned with two assumptions that accompany hansen s approach the first is the assumption that the approximating models are strictly nested in a way that depends on the ordering of regressors often there is no clear basis for the ordering and the approach does not permit non nested models which are more realistic from a practical viewpoint second for the optimality result to hold the model weights are required to lie within a special discrete set in fact hansen noted both difficulties and called for extensions of the proof techniques we provide an alternative proof which shows that the result on the optimality of the mallows criterion in fact holds for continuous model weights and under a non nested set up that allows any linear combination of regressors in the approximating models that make up the model average estimator these results provide a stronger theoretical basis for the use of the mallows criterion in model averaging by strengthening existing findings