spatially dependent polya tree modeling for survival data with the proliferation of spatially oriented time to event data spatial modeling in the survival context has received increased recent attention a traditional way to capture a spatial pattern is to introduce frailty terms in the linear predictor of a semiparametric model such as proportional hazards or accelerated failure time we propose a new methodology to capture the spatial pattern by assuming a prior based on a mixture of spatially dependent polya trees for the baseline survival in the proportional hazards model thanks to modern markov chain monte carlo mcmc methods this approach remains computationally feasible in a fully hierarchical bayesian framework we compare the spatially dependent mixture of polya trees mpt approach to the traditional spatial frailty approach and illustrate the usefulness of this method with an analysis of iowan breast cancer survival data from the surveillance epidemiology and end results seer program of the national cancer institute our method provides better goodness of fit over the traditional alternatives as measured by log pseudo marginal likelihood lpml the deviance information criterion dic and full sample score fss statistics

vibration of arbitrarily shaped triangular plates with elastically restrained edges abstract a solution method is proposed for the vibration analysis of arbitrarily shaped triangular plates with elastically restrained edges an arbitrarily shaped triangular plate is first mapped into a right angled isosceles triangular plate and subsequently stretched to form a square plate by padding to it another right angled isosceles triangular plate of near zero thickness the displacement function is then expressed as a two dimensional fourier cosine series supplemented by several one dimensional series introduced to improve the convergence and accuracy of the displacement solution regardless of the shapes and boundary conditions of the triangular plate the final stiffness and mass matrices can always be calculated analytically which makes the current solution method highly efficient in implementations numerical examples are presented to verify the applicability of the proposed method to triangular plates of different shapes and perhaps more importantly different boundary conditions the current method can be easily extended to plates with heterogeneous material properties variable thickness non uniform elastic restraints etc

frequency analysis of corner point supported mindlin plates by a finite difference energy method abstract the first known solution of the title problem is presented a method based on the variational procedure in conjunction with a finite difference method is used to examine the free vibration characteristics numerical studies show that the convergence is relatively slow requiring a finer mesh model in view of the symmetry of the geometry of the plate and the symmetry in the distribution of the point supports only one quarter of the plate is examined three mode types are developed to account for the full plate detailed results are given for the frequencies and mode shapes of the first six modes of each symmetry class and the effect of transverse shear deformation and rotary inertia is analyzed the validity of the results is partially demonstrated by comparing them with existing solutions based on the classical thin plate theory

eigenvalue analysis of doubly connected plates with different configurations this paper deals with the vibration and buckling analyses of the first order shear deformable rhombic and square plates using a p type variational method the formulation includes rotary inertia and transverse shear terms the full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements the symmetry about x and y axes with regards to load and boundary conditions are exploited buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method

an analytical solution for the free vibration analysis of rectangular plates resting on symmetrically distributed point supports abstract a general analytical solution is obtained for the free vibration of rectangular plates supported on their lateral surface by symmetrically distributed point supports highly accurate eigenvalues are provided for a square plate supported at various points along the diagonal results are compared with earlier findings obtained by a finite element method it is shown that the method may be extended to solve various other problems the tabulation of eigenvalues appears to be the most comprehensive yet made for a square plate with point supports on the diagonals

identifiability and rates of estimation for scale parameters in location mixture models in this paper we consider the problem of identifiability and estimation for the scale parameter 0 in the location mixture model 0 x y where x has a known distribution independent of the y whose distribution is unknown identification of 0 is ensured by constraining y based on the tail behavior of the distribution for x rates for estimation are described for those x which can be written as a square summable series of exponential variables as a special case our analysis shows that the structural parameters in the weibull semiparametric mixture heckman and singer are not estimable at the usual parametric op 1 xn rate the exact relationship between identifying constraints and achievable rates is explained 1 introduction heckman and singer 1984 studied economic theories concerning continuous durations of occupancy of states in order to properly estimate structural parameters in the presence of population heterogeneity they proposed the use of a semiparametric mixture model as a method for modeling duration data the model they proposed was the weibull semiparametric mixture

stable bundles and integrable systems on considere la geometrie symplectique des fibres cotangents aux espaces de modules de fibres vectoriels stables sur une surface de riemann on montre que ce sont des systemes dynamiques hamiltoniens algebriquement completement integrables

cross section regression with common shocks this paper considers regression models for cross section data that exhibit cross section dependence due to common shocks such as macroeconomic shocks the paper analyzes the properties of least squares ls estimators in this context the results of the paper allow for any form of cross section dependence and heterogeneity across population units the probability limits of the ls estimators are determined and necessary and sufficient conditions are given for consistency the asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling the t wald and f statistics are found to have asymptotic standard normal x 2 and scaled x 2 distributions respectively under the null hypothesis when the conditions required for consistency of the parameter under test hold however the absolute values of t wald and f statistics are found to diverge to infinity under the null hypothesis when these conditions fail confidence intervals exhibit similarly dichotomous behavior hence common shocks are found to be innocuous in some circumstances but quite problematic in others models with factor structures for errors and regressors are considered using the general results conditions are determined under which consistency of the ls estimators holds and fails in models with factor structures the results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units

large amplitude dynamic analysis of simply supported skew plates by a variational method abstract large amplitude free vibration analysis of simply supported thin isotropic skew plates has been presented the large deformation is imparted statically by subjecting the plate under uniform transverse pressure the mathematical formulation is based on the variational principle in which the displacement fields are assumed as a combination of orthogonal polynomial or transcendental functions each satisfying the corresponding boundary conditions of the plate the large amplitude dynamic problem is addressed by solving the corresponding static problem first and subsequently with the resultant displacement field the problem is formulated the vibration frequencies are obtained from the solution of a standard eigenvalue problem entire computational work is carried out in a normalized square domain obtained through an appropriate domain mapping technique results of the reduced problem revealed excellent agreement with other studies and a typical comparison of the actual problem is also carried out successfully results are furnished in dimensionless amplitude frequency plane in the form of backbone curves and pictorial representations of some vibration mode shapes are made

a variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness a new variable kinematic ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented carrera s unified formulation and the versatile pb 2 ritz method are properly combined to build a powerful yet simple modeling and solution framework the proposed technique allows to generate arbitrarily accurate ritz solutions from a large variety of refined two dimensional plate theories by expanding so called ritz fundamental nuclei of the plate mass and stiffness matrices theoretical development of the present methodology is described in detail convergence and accuracy of the method are examined through several examples on thin moderately thick and very thick plates of rectangular skew trapezoidal and general quadrilateral shapes with an arbitrary combination of clamped free and simply supported edges present results are compared with existing three dimensional solutions from open literature maximum and average differences of various higher order plate theories and three dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters

sieve estimation of panel data models with cross section dependence abstract in this paper we consider the problem of estimating semiparametric panel data models with cross section dependence where the individual specific regressors enter the model nonparametrically whereas the common factors enter the model linearly we consider both heterogeneous and homogeneous regression relationships when both the time and cross section dimensions are large we propose sieve estimators for the nonparametric regression functions by extending pesaran s 2006 common correlated effect cce estimator to our semiparametric framework asymptotic normal distributions for the proposed estimators are derived and asymptotic variance estimators are provided monte carlo simulations indicate that our estimators perform well in finite samples

the g generalized hitchin systems and prym varieties in this article we consider the generalized hitchin systems introduced by bottacin and markman for an arbitrary reductive complex group g they have the structure of lagrangian fibrations pr u by generalized prym varieties over sets u parametrizing families of weyl invariant curves the g generalized hitchin systems satisfy a rank two condition and one can find invariant varieties x which distinguish these systems it is then shown that there is a correspondence between these integrable systems and the varieties x k d h which are equipped with an appropriate two form with values in the cartan subalgebra h

transverse vibration of simply supported elliptical and circular plates using boundary characteristic orthogonal polynomials in two variables abstract the first four frequencies and mode shapes have been computed for elliptical and circular plates of uniform thickness with simply supported edges by employing orthogonal polynomials in the rayleigh ritz method in general this is found to give better results than traditional methods successive approximations have been worked out to ensure convergence comparisons have been made with existing results in some cases calculations have been done for several values of b a i e the ratio of the semi major and semi minor axes mode shapes have been used to obtain three dimensional plots of plates in displaced configurations

panel data models with spatially correlated error components abstract in this paper we consider a panel data model with error components that are both spatially and time wise correlated the model blends specifications typically considered in the spatial literature with those considered in the error components literature we introduce generalizations of the generalized moments estimators suggested in kelejian and prucha 1999 a generalized moments estimator for the autoregressive parameter in a spatial model international economic review 40 509 533 for estimating the spatial autoregressive parameter and the variance components of the disturbance process we then use those estimators to define a feasible generalized least squares procedure for the regression parameters we give formal large sample results for the proposed estimators we emphasize that our estimators remain computationally feasible even in large samples

free vibration analysis of a flat plate using the hierarchical finite element method abstract the hierarchical finite element method is used to determined the natural frequencies and modes of a flat rectangular plate ten different boundary conditions including free edges and point supports are considered in this paper extensive results are presented for each case including the variation of frequency with the aspect ratio and the poisson ratio and these are shown to be in very good agreement with the work of other investigators this confirms both the applicability and accuracy of solution of the hfem to problem of this type

estimating multiplicative and additive hazard functions by kernel methods we propose new procedures for estimating the component functions in both additive and multiplicativen onparametricm arker dependenht azard models we work with a full counting process framework that allows for left truncation and right censoring and time varying covariates our procedures are based on kernel hazard estimation as developed by nielsen and linton and on the idea of marginal integration we provide a central limit theorem for the marginal integration estimator we then define estimators based on finite step backfitting in both additive and multiplicative cases and prove that these estimators are asymptotically normal and have smaller variance than the marginal integration method

on the asymptotic properties of estimators of models containing limited dependent variables for the tobit model with independent observations amemiya 1 has established the strong consistency and asymptotic normality of a stationary point 9 of the log likelihood the likelihood for dependent observations may be computationally intractable so the behavior of 9 in the presence of serially correlated observations is of interest under a relaxation of amemiya s assumption of independence we prove that 9 is strongly consistent and asymptotically normal and give an expression for the limiting covariance matrix

transverse vibration of skew plates with variable thickness abstract the rayleigh ritz method has been used to study the transverse vibrations of skew plates of variable thickness with different combinations of boundary conditions at the four edges the two dimensional thickness variation is taken as the cartesian product of linear variations along the two concurrent edges of the plate the first three frequencies and mode shapes have been computed by using successive approximations convergence of results is ensured by working out several approximations until the results converge to four significant digits in special cases comparisons have been made with results that are available in the literature mode shapes have also been plotted for some selected cases

kernel estimation in a nonparametric marker dependent hazard model we introduce a new kernel hazard estimator in a nonparametric model where the stochastic hazard depends on the current value of time and on the current value of a time dependent covariate or marker we establish the pointwise and global convergence of our estimator

semiparametric estimation of a proportional hazard model with unobserved heterogeneity the proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity this paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically the baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known finite dimensional parametric families existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family thus the estimators presented here are more general than existing ones

moving least square ritz method for vibration analysis of plates this paper presents a novel numerical method the moving least square ritz method mls ritz for free vibration analysis of classical thin plates the proposed method utilizes the strength of the moving least square approach to define the ritz trial function for the transverse displacement of the plates a set of points is pre selected on the calculation domain of a plate that forms the basis for the mls ritz trial function the edge support conditions of the plate are satisfied by forcing the boundary points to meet the geometric boundary conditions of the plate via a point substitution technique virtual points points outside the plate domain are introduced for clamped edges to improve the convergence and accuracy of the calculations square and right angled isosceles triangular plates of various combinations of edge support conditions are selected to examine the validity and accuracy of the mls ritz method extensive convergence studies are carried out to investigate the influence of the mls mesh size the mls support radius the number of gaussian integration points and the shape of the mls weight function on the proposed method comparing with the existing ritz methods the mls ritz method is highly stable and accurate and is extremely flexible for dealing with plates of arbitrary shapes and boundary conditions

do validation for kernel density estimation bandwidth selection in kernel density estimation is one of the fundamental model selection problems of mathematical statistics the study of this problem took major steps forward with the articles of hall and marron 1987 and hall and johnstone 1992 since then the focus seems to have been on various versions of implementing the so called plug in method aimed at estimating the minimum mean integrated squared error mise the most successful of these efforts still seems to be the plug in method of sheather and jones 1991 or park and marron 1990 that we also use as a benchmark in this article in this article we derive a new theorem deriving the asymptotic theory for linear combinations of bandwidths obtained from different selectors as for example direct and indirect cross validation and plug in where we take advantage of recent advances in the study of indirect cross validation see hart and yi 1998 hart and lee 2005 and savchuk hart and sheather 2008 2010 we conclude that the slow

axisymmetric vibration of circular plates and its analog in elliptical plates using characteristic orthogonal polynomials the axisymmetric vibration of circular plates and its analog in elliptic plates with clamped simply supported and free boundary conditions are investigated using boundary characteristic orthogonal polynomials in the rayleigh ritz method modified polar coordinates are employed to analyze the vibration of elliptical plates with circular plates as a special case axisymmetric vibration of circular plates and its analog in elliptical plates with concentric nodal elipses require only one dimensional shape functions in the rayleigh ritz method the first six natural frequencies and the parameters associated with nodal ellipses are tabulated

vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in the semi analytical finite strip method abstract a semi analytical finite strip method mapping arbitrarily shaped plates into a natural co ordinate plane using serendipity functions is presented the product of normalized beam characteristic orthogonal polynomials and hermitian polynomials form the displacement function for the strip in the natural co ordinate domain flexural free vibration analysis of various shaped plates is performed results show that as long as the plate is modelled by high enough degree mapping functions for the specific applications requested the flexural frequencies obtained are in excellent agreement with those found in the literature

numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the rayleigh ritz method unilateral buckling is a contact problem whereby buckling is confined to take place in only one lateral direction for plate structures this can occur when a thin steel plate is juxtaposed with a rigid concrete medium and the steel may only buckle locally away from the concrete core this paper investigates the use of simple and orthogonal polynomials in the rayleigh ritz method for unilateral plate buckling the orthogonal polynomials used are the classical chebyshev types 1 and 2 legrende hermite and laguerre the study presents a comparison between the efficiency of the polynomial based displacement functions with regard to elastic bilateral and unilateral plate buckling where efficiency is measured as a function of their convergence characteristics some buckling solutions for plates with varying boundary conditions and in plane shear loads are also provided as an illustration copyright 1999 john wiley sons ltd

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

free vibration of thick layered rectangular plates with point supports by finite layer method in this paper the free vibration of thick isotropic and laminated composite rectangular plates with point supports is analyzed by the finite layer method a new set of two dimensional basic functions which satisfies the kinematic boundary conditions at the edges of the plate and the zero displacement conditions at point supports is developed to describe the variation of three dimensional displacements in the plane of a thin finite layer one dimensional linear or quadratic shape functions are adopted to describe the variation of the displacements through the thickness layer the governing eigenvalue equation of the plate is derived via the conventional displacement method numerical results for the three dimensional vibration of rectangular plates with point supports are presented herein for the first time the eigenfrequencies of simply supported rectangular plates with a central point support are studied in detail by considering the variations of aspect ratio side to thickness ratio properties of materials number of laminates and stacking sequences comparison with known thin plate and mindlin plate solutions is carried out to verify the applicability and accuracy of the proposed method

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

profile quasi maximum likelihood estimation of partially linear spatial autoregressive models abstract we propose profile quasi maximum likelihood estimation of spatial autoregressive models that are partially linear the rate of convergence of the spatial parameter estimator depends on some general features of the spatial weight matrix of the model the estimators of other finite dimensional parameters in the model have the regular n rate of convergence and the estimator of the nonparametric component is consistent but with different restrictions on the choice of bandwidth parameter associated with different natures of the spatial weights monte carlo simulations verify our theory and indicate that our estimators perform reasonably well in finite samples

flexural vibration of skew plates using boundary characteristic orthogonal polynomials in two variables abstract the first five frequencies have been determined for the transverse vibration of a rectangular or a skew plate under different boundary conditions by using boundary characteristic orthogonal polynomials in two variables the given plate is first mapped into a square plate over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by using the gram schmidt process the rayleigh ritz method is then used to determine the frequencies for all possible combination of the boundary conditions and with different skew angles comparison has been made with known results

transverse vibrations of a trapezoidal cantilever plate of variable thickness n atural frequencies of a trapezoidal cantilever plate of variable thickness which model an aircraft wing structure approximately are determined using energy techniques characteristic orthogonal polynomials in two variables are constructed to describe the structural deflections which are used in the rayleigh ritz method to obtain the natural frequencies the fundamental natural frequencies for different parameter values are also obtained using a deflection function containing an optimized exponent the first technique can be used to obtain the natural frequencies and corresponding mode shapes for the preliminary design of aircraft wing structures

modeling spatial survival data using semiparametric frailty models we propose a new class of semiparametric frailty models for spatially correlated survival data specifically we extend the ordinary frailty models by allowing random effects accommodating spatial correlations to enter into the baseline hazard function multiplicatively we prove identifiability of the models and give sufficient regularity conditions we propose drawing inference based on a marginal rank likelihood no parametric forms of the baseline hazard need to be assumed in this semiparametric approach monte carlo simulations and the laplace approach are used to tackle the intractable integral in the likelihood function different spatial covariance structures are explored in simulations and the proposed methods are applied to the east boston asthma study to detect prognostic factors leading to childhood asthma

estimation of spatial autoregressive panel data models with fixed effects this paper establishes asymptotic properties of quasi maximum likelihood estimators for sar panel data models with fixed effects and sar disturbances a direct approach is to estimate all the parameters including the fixed effects because of the incidental parameter problem some parameter estimators may be inconsistent or their distributions are not properly centered we propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions for the model with individual effects only the direct approach does not yield a consistent estimator of the variance parameter unless t is large but the estimators for other common parameters are the same as those of the transformation approach we also consider the estimation of the model with both individual and time effects

vibration of skew plates resting on point supports abstract this paper deals with the vibrations of skew plates resting on point supports the spline element method is used to demonstrate the accuracy of the method several examples are solved and results are compared with those obtained by other approximate methods the effects of skew angles and locations of point supports on natural frequencies of isotropic skew plates are also investigated

efficient gmm estimation of spatial dynamic panel data models with fixed effects abstract in this paper we derive the asymptotic properties of gmm estimators for the spatial dynamic panel data model with fixed effects when n is large and t can be large but small relative to n the gmm estimation methods are designed with the fixed individual and time effects eliminated from the model and are computationally tractable even under circumstances where the ml approach would be either infeasible or computationally complicated the ml approach would be infeasible if the spatial weights matrix is not row normalized while the time effects are eliminated and would be computationally intractable if there are multiple spatial weights matrices in the model also consistency of the mle would require t to be large and not small relative to n if the fixed effects are jointly estimated with other parameters of interest the gmm approach can overcome all these difficulties we use exogenous and predetermined variables as instruments for linear moments along with several levels of their neighboring variables and additional quadratic moments we stack up the data and construct the best linear and quadratic moment conditions an alternative approach is to use separate moment conditions for each period which gives rise to many moments estimation we show that these gmm estimators are n t consistent asymptotically normal and can be relatively efficient we compare these approaches on their finite sample performance by monte carlo

simple estimation of a duration model with unobserved heterogeneity this paper presents a simple estimator of the shape parameter in a weibull duration model with unobserved heterogeneity the estimator is consistent and asymptotically normal under mild conditions and a consistent estimator of the asymptotic variance is available a monte carlo study indicates that the asymptotic distribution of the estimator provides a good approximation to the finite sample distribution the estimation strategy can be extended to a model with regressors and to a log logistic model with unobserved heterogeneity the advantages of the estimator are that it is easy to calculate and that its asymptotic distribution can be derived copyright 1990 by the econometric society

vibration of shear deformable rectangular plates using a spline function rayleigh ritz approach the prediction of the natural frequencies of vibration of rectangular plates or orthotropic laminates is described through the use of b spline functions as trial functions in a rayleigh ritz approach through thickness shear deformation effects are included in the analysis and hence assumptions have to be made for the spatial variation over the plate middle surface of each of the lateral deflection and the two rotation components two versions of the spline function rayleigh ritz approach are described in one of these the deflection and rotations are represented by functions of the same polynomial order whilst in the other a lower order representation is used for each rotation component in one of the co ordinate directions it is shown in a number of applications that the former version leads to shear locking behaviour whilst the latter version avoids this behaviour and is suitable for the analysis of both thick and thin plates

transverse vibrations of thin elastic plates with concentrated masses and internal elastic supports abstract the fundamental frequency of vibration of a plate carrying concentrated masses and with internal elastic supports is determined the case of an orthotropic rectangular plate elastically restrained against rotation along the four edges is tackled first by using simple polynomial approximations and the galerkin method then vibrations of clamped and simply supported isotropic plates of regular polygonal shape are studied by using the conformal mapping technique coupled with the variational method finally the case of a circular plate elastically restrained against translation and rotation is considered

smoothing parameter selection in nonparametric regression using an improved akaike information criterion summary many different methods have been proposed to construct nonparametric estimates of a smooth regression function including local polynomial convolution kernel and smoothing spline estimators each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set in this paper an improved version of a criterion based on the akaike information criterion aic termed aicc is derived and examined as a way to choose the smoothing parameter unlike plug in methods aicc can be used to choose smoothing parameters for any linear smoother including local quadratic and smoothing spline estimators the use of aicc avoids the large variability and tendency to undersmooth compared with the actual minimizer of average squared error seen when other classical approaches such as generalized cross validation or the aic are used to choose the smoothing parameter monte carlo simulations demonstrate that the aicc based smoothing parameter is competitive with a plug in method assuming that one exists when the plug in method works well but also performs well when the plug in approach fails or is unavailable

the free flexural vibration of right triangular isotropic and orthotropic plates abstract a simple straighforward rayleigh ritz analysis is given for the determination of an eigenproblem for the free flexural vibration of thin right triangular plates having any combination of the classical free simply supported or clamped boundary conditions simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals the analysis is developed for specially orthotropic plates but numerical results are given primarily for the isotropic case

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

determination of the steady state response of a viscoelastically point supported rectangular plate the steady state response to a sinusoidally varying force is determined for a viscoelastically point supported square or rectangular plate for this purpose the transverse deflection of the plate is written in a series of the product of the deflection functions of beams parallel to the edges and the response equation is derived by the generalized galerkin method the natural boundary conditions of the plate which cannot be satisfied by the beam functions at the edges and the corners are appropriately compensated by suitable additions to the residual forces and moments the method is applied to a square plate supported at four points symmetrically located at the corners or on the diagonals the steady state response of the plate to a point force acting at the centre is calculated numerically and the effects of the point supports on the vibration are studied

the singularity of the information matrix of the mixed proportional hazard model this paper presents new identification conditions for the mixed proportional hazard model in particular the baseline hazard is assumed to be bounded away from 0 and near t 0 these conditions ensure that the information matrix is nonsingular the paper also presents an estimator for the mixed proportional hazard model that converges at rate n 1 2

application of a new differential quadrature methodology for free vibration analysis of plates a new methodology is introduced in the differential quadrature dq analysis of plate problems the proposed approach is distinct from other dq methods by employing the multiple boundary conditions in a different manner for structural and plate problems the methodology employs the displacement within the domain as the only degree of freedom whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently in order to demonstrate the capability of the new methodology all cases of free vibration analysis of rectangular isotropic plates in which the conventional dq methods have had some sort of difficulty to arrive at a converged or accurate solution are carried out excellent convergence behaviour and accuracy in comparison with exact results and or results obtained by other approximate methods were obtained the analogous dq formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised it must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods copyright 2002 john wiley sons ltd

limit theory for panel data models with cross sectional dependence and sequential exogeneity abstract the paper derives a general central limit theorem clt and asymptotic distributions for sample moments related to panel data models with large n the results allow for the data to be cross sectionally dependent while at the same time allowing the regressors to be only sequentially rather than strictly exogenous the setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and or from the presence of common factors the latter leads to the need for random norming the limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied we prove such a central limit theorem by first extending results for stable convergence in hall and heyde 1980 to non nested martingale arrays relevant for our applications we illustrate our result by establishing a generalized estimation theory for gmm estimators of a fixed effect panel model without imposing i i d or strict exogeneity conditions we also discuss a class of maximum likelihood ml estimators that can be analyzed using our clt

semiparametric gmm estimation of spatial autoregressive models abstract we propose semiparametric gmm estimation of semiparametric spatial autoregressive sar models under weak moment conditions in comparison with the quasi maximum likelihood based semiparametric estimator of su and jin 2010 we allow for both heteroscedasticity and spatial dependence in the error terms we derive the limiting distributions of our estimators for both the parametric and nonparametric components in the model and demonstrate the estimator of the parametric component has the usual n asymptotics when the error term also follows an sar process we propose an estimator for the parameter in the sar error process and derive the joint asymptotic distribution for both spatial parameters consistent estimates for the asymptotic variance covariance matrices of both the parametric and nonparametric components are provided monte carlo simulations indicate that our estimators perform well in finite samples

three dimensional elasticity solutions to vibration of cantilevered skewed trapezoids an accurate three dimensional elasticity model for determining the free vibration response of skewed trapezoidal plates is presented the method is formulated on the basis of a linear small strain three dimensional elasticity theory with the ritz minimization procedure the solution method uses sets of uniquely defined one and twodimensional polynomial functions to approximate the trial displacements in the thickness and surface directions respectively these functions are orthogonally generated and have been proven to be highly efficient and numerically stable the proposed technique yields natural frequencies and mode shapes for a wide range of cantilevered skewed trapezoidal plates of arbitrary planform the accuracy of these results whenever possible is validated through comparison with the analytical and experimental data parametric investigations on the vibration behavior of cantilevered trapezoidal plates with respect to different thickness ratios skew angles and chord ratios have been carried out for the first time the presence of surface parallel symmetric thickness modes for these plates is demonstrated in vivid three dimensional mode shape plots

application of two dimensional orthogonal plate function to flexural vibration of skew plates abstract a set of two dimensional orthogonal plate functions is used as an admissible deflection function for the study of the flexural vibration of skew plates by the rayleigh ritz method from a prescribed starting function satisfying the boundary conditions the higher terms in the two dimensional orthogonal plate functions are generated by using the gram schmidt orthogonalization process the method is applied to obtain results for a few particular rhombic plates with different support conditions at various skew angles where possible the numerical results presented are compared with the values obtained by other numerical methods in the literature the results should be of considerable value and practical significance in design applications

vibration analysis of skew fibre reinforced composite laminated plates the vibration of skew laminated composite plates with simply supported and clamped edges is studied the skew plate is mapped into a unit square by linear transformation orthogonal polynomials are used with the ritz method to determine the natural frequencies the effects of skew angle and lamination scheme on natural frequencies are studied results are tabulated for different lamination schemes and compared to available studies in the literature

the free flexural vibration of isotropic and orthotropic general triangular shaped plates abstract the rayleigh ritz method is used with simple polynomials as admissible functions to obtain an eigenvalue equation for the free flexural vibration of thin isotropic and specially orthotropic general triangular plates the plates may have any combination of the classical free simply supported or clamped boundary conditions the convergence and accuracy of the solution is illustrated and numerical results are presented for a variety of isotropic plates and for orthotropic cantilever plates

qml estimation of dynamic panel data models with spatial errors abstract we propose quasi maximum likelihood qml estimation of dynamic panel models with spatial errors when the cross sectional dimension n is large and the time dimension t is fixed we consider both the random effects and fixed effects models and prove consistency and derive the limiting distributions of the qml estimators under different assumptions on the initial observations we propose a residual based bootstrap method for estimating the standard errors of the qml estimators monte carlo simulation shows that both the qml estimators and the bootstrap standard errors perform well in finite samples under a correct assumption on initial observations but may perform poorly when this assumption is not met

buckling and vibration of polar orthotropic circular plate resting on winkler foundation buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory the plate is resting on winkler type foundation an approximate solution has been obtained by ritz method which employs basis functions based upon static deflection of polar orthotropic plates the effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter flexibility parameter in plane force and nodal diameter the critical buckling load for clamped and simply supported plates have been obtained a comparison of results with those available in literature has been presented

quasi maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and t are large this paper investigates the asymptotic properties of quasi maximum likelihood estimators for spatial dynamic panel data with xed eects when both the number of individuals n and the number of time periods t are large we consider the case where t is asymptotically large relative to n the case where t is asymptotically proportional to n and the case where n is asymptotically large relative to t in the case where t is asymptotically large relative to n the estimators are p nt consistent and asymptotically normal with the limit distribution centered around 0 when n is asymptotically proportional to t the estimators are p nt consistent and asymptotically normal but the limit distribution is not centered around 0 and when n is large relative to t the estimators are consistent with rate t and have a degenerate limit distribution the estimators of the xed eects are p t consistent and asymptotically normal we also propose a bias correction for our estimators we show that when t grows faster than n 1 3 the correction will asymptotically eliminate the bias and yield a centered con dence interval

kernel estimation of hazard functions when observations have dependent and common covariates abstract we propose a hazard model where dependence between events is achieved by assuming dependence between covariates this model allows for correlated variables specific to observations as well as macro variables which all observations share this setup better fits many economic and financial applications where events are not independent nonparametric estimation of the hazard function is then studied kernel estimators proposed in nielsen and linton 1995 and linton et al 2003 are shown to have similar asymptotic properties compared with the i i d case mixing conditions ensure the asymptotic results follow these results depend on adjustments to bandwidth conditions simulations are conducted which verify the impact of dependence on estimators bandwidth selection accounting for dependence is shown to improve performance in an empirical application trade intensity in high frequency financial data is estimated

separating coordinates for the generalized hitchin systems and the classical r matrices we exhibit natural darboux coordinates for the generalized hitchin systems studied by bottacin and markman these systems are defined on spaces of stable pairs consisting of a vector bundle and a form valued meromorphic endomorphism of the bundle in special cases genus zero genus one the bundles are rigid and one has the rational trigonometric and elliptic gaudin systems explicit formulae are given in these cases

semiparametric estimation of a panel data proportional hazards model with fixed effects this paper considers a panel duration model that has a proportional hazards specification with fixed effects the paper shows how to estimate the baseline and integrated baseline hazard functions without assuming that they belong to known finite dimensional families of functions existing estimators assume that the baseline hazard function belongs to a known parametric family therefore the estimators presented here are more general than existing ones this paper also presents a method for estimating the parametric part of the proportional hazards model with dependent right censoring under which the partial likelihood estimator is inconsistent the paper presents some monte carlo evidence on the small sample performance of the new estimators

a boundary perturbation method for circularly periodic plates with a core fundamental frequencies of vibrating circularly periodic plates with a circular core have been determined analytically a boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem the method is then applied to wavy and polygonal plates with clamped and simply supported outer boundary conditions clamped simply supported and free circular cores are considered approximate analytical formulations of the fundamental frequency for such plates with core are obtained

nonlinearity and temporal dependence nonlinearities in the drift and diffusion coefficients influence temporal dependence in diffusion models we study this link using three measures of temporal dependence mixing mixing and mixing stationary diffusions that are mixing have mixing coefficients that decay exponentially to zero when they fail to be mixing they are still mixing and mixing but coefficient decay is slower than exponential for such processes we find transformations of the markov states that have finite variances but infinite spectral densities at frequency zero the resulting spectral densities behave like those of stochastic processes with long memory finally we show how state dependent poisson sampling alters the temporal dependence

natural frequencies of rectangular plates with free edges abstract this note presents vibration analysis of isotropic rectangular plates with free edges by the rayleigh ritz method with b spline functions to show the accuracy of the present method the results are compared with existing results based on other numerical methods and found to be in good agreement accurate frequencies of rectangular plates are analyzed for different aspect ratios and boundary conditions the effects of poisson s ratio on natural frequencies of square plates with free edges are also investigated

mixtures of polya trees for flexible spatial frailty survival modelling mixtures of polya trees offer a very flexible nonparametric approach for modelling time to event data many such settings also feature spatial association that requires further sophistication either at the point level or at the lattice level in this paper we combine these two aspects within three competing survival models obtaining a data analytic approach that remains computationally feasible in a fully hierarchical bayesian framework using markov chain monte carlo methods we illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the surveillance epidemiology and end results program of the national cancer institute our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions ignore spatial association or both

large panels with common factors and spatial correlation this paper considers the statistical analysis of large panel data sets where even after condi tioning on common observed eects the cross section units might remain dependently distrib uted this could arise when the cross section units are subject to unobserved common eects and or if there are spill over eects due to spatial or other forms of local dependencies the paper provides an overview of the literature on cross section dependence introduces the con cepts of time speci c weak and strong cross section dependence and shows that the commonly used spatial models are examples of weak cross section dependence it is then established that the common correlated eects cce estimator of panel data model with a multifactor error structure recently advanced by pesaran 2006 continues to provide consistent estimates of the slope coe cient even in the presence of spatial error processes small sample properties of the cce estimator under various patterns of cross section dependence including spatial forms are investigated by monte carlo experiments results show that the cce approach works well in the presence of weak and or strong cross sectionally correlated errors we also explore the role of certain characteristics of spatial processes in determining the performance of cce estimators such as the form and intensity of spatial dependence and the sparseness of the spatial weight

application of the spline element method to analyze vibration of annular sector plates abstract this paper deals with the vibrations of isotropic annular sector plates with arbitrary boundary conditions using the spline element method to demonstrate the accuracy of the methods several examples are solved and results are compared with those obtained by analytical methods and by other numerical methods good accuracy is obtained frequencies of annular sector plates with free edges and with point supports are presented

flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables a set of characteristic orthogonal polynomials in two variables is used as deflection functions to obtain the natural frequencies and mode shapes of polygonal plates by the rayleigh ritz method the set of orthogonal polynomials is constructed by employing the gram schmidt orthogonalization procedure the first six natural frequencies are numerically evaluated for triangular plates of different configurations by using these orthogonal functions and the corresponding mode shapes are plotted results are compared with those obtained previously by other methods