bootstrap j tests of nonnested linear regression models the j test for nonnested regression models often overrejects very severely as an asymptotic test we provide a theoretical analysis which explains why and when it performs badly this analysis implies that except in certain extreme cases the j test will perform very well when bootstrapped using several methods to speed up the simulations we obtain extremely accurate monte carlo results on the finite sample performance of the bootstrapped j test these results fully support the predictions of our theoretical analysis even in contexts where the analysis is not strictly applicable

non regular maximum likelihood problems four non regular estimation problems are reviewed and discussed one the unbounded likelihood problem involves distributions with infinite spikes for which maximum likelihood can fail to give consistent estimators a comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case an application to the box cox shifted power transform is given the other three problems occur when the true parameter lies in some special subregion in one the constrained parameter problem the subregion is a boundary the other two the embedded model and the indeterminate parameters problems occur when the model takes on a special form in the subregion these last two problems have previously been investigated separately we show that they are equivalent in some situations both often arise in non linear models and we give a directed graph approach which allows for their occurrence in nested model building it is argued that many non regular problems can be handled systematically without having to resort to elaborate technical assumptions relatively uncomplicated methods may be used provided that the underlying nature of the non regularity is understood

comparison of local power of alternative tests of non nested regression models the paper derives and compares the local power of three different methods of testing non nested regression models that are available in the literature it shows that the asymptotic power of the orthodox f test against local alternatives is strictly less than that of cox s non nested test or the j test recently proposed by davidson and mackinnon 5 unless the number of non overlapping variables of the alternative hypothesis over the null hypothesis is unity in which case all three tests are shown to be asymptotically equivalent the final section of the paper gives results of monte carlo experiments designed to check the validity of the theoretical findings of the paper and also to shed light on the small sample properties of the cox test and the orthodox test

improved conditioning of finite element matrices using new high order interpolatory bases the condition number of finite element matrices constructed from interpolatory bases will grow as the polynomial degree of the basis functions is increased the worst case scenario for this growth rate is exponential and in this paper we demonstrate through computational example that the traditional set of uniformly distributed interpolation points yields this behavior we propose a set of nonuniform interpolation points which yield a much improved polynomial growth rate of condition number these points can be used to construct several types of popular hexahedral basis functions including the 0 form standard lagrangian 1 form curl conforming and 2 form divergence conforming varieties we demonstrate through computational example the benefits of using these new interpolatory bases in finite element solutions to maxwell s equations in both the frequency and time domain

large scale 3d geoelectromagnetic modeling using parallel adaptive high order finite element method abstractwe have investigated the use of the adaptive high order finite element method fem for geoelectromagnetic modeling because high order fem is challenging from the numerical and computational points of view most published finite element studies in geoelectromagnetics use the lowest order formulation solution of the resulting large system of linear equations poses the main practical challenge we have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block diagonal and auxiliary space preconditioners the solver was found to be efficient for high finite element orders unstructured and nonconforming locally refined meshes a wide range of frequencies large conductivity contrasts and number of degrees of freedom dofs furthermore the presented linear solver is in essence algebraic i e it acts on the matrix vector level and thus requires no information about the discretization boundary conditions or physical source used making it readily ef

a high order mixed vector finite element method for solving the time dependent maxwell equations on unstructured grids we present a mixed vector finite element method for solving the time dependent coupled ampere and faraday laws of maxwell s equations on unstructured hexahedral grids that employs high order discretization in both space and time the method is of arbitrary order accuracy in space and up to 4th order accurate in time making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods in addition the method correctly models both the jump discontinuities and the divergence free properties of the electric and magnetic fields is charge and energy conserving conditionally stable and free of spurious modes several computational experiments are performed to demonstrate the accuracy efficiency and benefits of the method

some aspects of testing non nested hypotheses abstract this paper examines some aspects of testing non nested hypotheses an inequality between the cox and atkinson statistics is noted and the necessary and sufficient condition for the atkinson test to be consistent is derived a new test procedure is also outlined the rest of the paper illustrates the various test statistics their properties and relationships for competing linear regression models

regularity and separation from potential barriers for a non local phase field system abstract we show that solutions of a two phase model involving a non local interactive term become more regular immediately after the moment they separate from the pure phases this result allows us to prove stronger convergence to equilibria a new proof of the separation property is also given

modeling of electromagnetic absorption scattering problems using hp adaptive finite elements a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for affine elements is presented the proposed method is illustrated and verified with a series of 2d experiments including elements with curved boundaries and nonhomogeneous media

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

existence of global solutions to the caginalp phase field system with dynamic boundary conditions and singular potentials our aim in this article is to prove the global in time existence of solutions to a caginalp phase field system with dynamic boundary conditions and a singular potential the main difficulty is to prove that the solutions are strictly separated from the singular values of the potential this is achieved by studying an auxiliary elliptic problem

the phase field transition system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity abstract the paper establishes the existence estimate uniqueness and regularity for the solution of a nonlinear parabolic system a two phase caginalp type system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity it extends the already studied types of boundary conditions which makes the mathematical model to be richer and more flexible to describe the real physical phenomena including phase separation

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

a comparison of nonnested tests for misspecified models using the method of approximate slopes abstract comparisons of the cox wald and j tests are conducted under a standard framework and in a misspecified setting the data generation process includes a regressor that is not in either model most power comparisons have been carried out for local alternatives but comparisons under a nonlocal alternatives framework using the method of approximate slopes developed by bahadur 1960 1967 are made in this paper monte carlo experiments are conducted and the cox test is shown to have the highest small sample power and approximate slope for most of the cases considered the results from response surface regressions provide strong evidence that the approximate slope is a good predictor of the small power of nonnested tests it is also useful for directly comparing the small sample power of one degree of freedom tests of nonnested hypotheses

regularity conditions for cox s test of non nested hypotheses abstract in this article we provide for the first time general regularity conditions and a rigorous proof of the asymptotic normality of cox s statistic for testing separate families of hypotheses the cox test for choosing between competing linear regression models is discussed as an example

some robust exact results on sample autocorrelations and tests of randomness abstract several exact results on the second moments of sample autocorrelations for both gaussian and non gaussian series are presented general formulae for the means variances and covariances of sample autocorrelations are given for the case where the variables in a sequence are exchangeable bounds for the variances and covariances of sample autocorrelations from an arbitrary random sequence are derived exact and explicit formulae for the variances and covariances of sample autocorrelations from a gaussian white noise are given it is observed that the latter results hold for all spherically symmetric distributions a simulation experiment with gaussian series indicates that normalizing each sample autocorrelation with its exact mean and variance instead of the usual approximate moments can improve considerably the accuracy of the asymptotic n 0 1 distribution to obtain critical values for tests of randomness the exact second moments of rank autocorrelations are also studied

analysis of an iterative scheme of fractional steps type associated to the reaction diffusion equation endowed with a general nonlinearity and cauchy neumann boundary conditions abstract the paper studies the existence uniqueness regularity and the approximation of solutions to the reaction diffusion equation endowed with a general nonlinear regular potential and cauchy neumann boundary conditions the convergence and error estimate results for an iterative scheme of fractional steps type associated to the nonlinear parabolic equation are also established the advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of nonlinear parabolic equation

analysis of a two phase field model for the solidification of an alloy abstract in this paper we present some theoretical results for a system of nonlinear partial differential equations that provide a phase field model for the solidification melting of a metallic alloy it is assumed that two different kinds of crystallization are possible consequently the unknowns are the temperature and the phase field functions u and v the time derivatives u t and v t appear in the equation for the heat equation on the other hand the equations for u and v contain nonlinear terms where we find

on the existence uniqueness and regularity of solutions to the phase field system with a general regular potential and a general class of nonlinear and non homogeneous boundary conditions abstract this paper studies a caginalp phase field transition system endowed with a general regular potential as well as a general class in both unknown functions of nonlinear and non homogeneous depending on time and space variables boundary conditions we first prove the existence uniqueness and regularity of solutions to the allen cahn equation subject to the nonlinear and non homogeneous dynamic boundary conditions the existence uniqueness and regularity of solutions to the caginalp system in this new formulation are also proved this extends previous works concerned with regular potential and nonlinear boundary conditions allowing the present mathematical model to better approximate the real physical phenomena especially phase transitions

exact permutation tests for non nested non linear regression models abstract this paper proposes exact distribution free permutation tests for the specification of a non linear regression model against one or more possibly non nested alternatives the new tests may be validly applied to a wide class of models including models with endogenous regressors and lag structures these tests build on the well known j test developed by davidson and mackinnon 1981 several tests for model specification in the presence of alternative hypotheses econometrica 49 781 793 and their exactness holds under broader assumptions than those underlying the conventional j test the j type test statistics are used with a randomization or monte carlo resampling technique which yields an exact and computationally inexpensive inference procedure a simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions the test procedure developed is illustrated by an application to inflation dynamics

numerical evaluation of hierarchical vector finite elements on curvilinear domains in 2 d when using the finite element method computational efficiency may be improved by using higher order elements typical 2 d triangular rectilinear elements cannot exactly model curved geometries negating the advantage of higher order elements when such geometries are modeled curvilinear elements can be applied to such problems and have significantly better computational efficiency than rectilinear elements when higher order elements are used results are shown for elemental basis orders ranging from ct ln through full fifth order in rectilinear and curvilinear domains

tests of non nested regression models small sample adjustments and monte carlo evidence abstract it is known that the small sample significance levels of cox type tests of non nested regression models can be much greater than the nominal level adjustments designed to overcome this problem are discussed and two tests are proposed monte carlo evidence on the performance of the tests derived in this paper the davidson mackinnon j test and the fisher mcaleer test is presented the f test applied to the comprehensive model is also included in the simulation experiments

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

the encompassing principle and its application to testing nonnested hypotheses the encompassing principle is used to develop a testing framework which unifies the literature on non nested testing allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist as well as embracing nested hypothesis testing the concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative the analysis is illustrated by an application to two non nested linear regression models and it is shown that the conventional f test as well as all the one degree of freedom non nested tests has an encompassing interpretation and that the f test is a complete parametric encompassing test

testing nested or non nested hypotheses this paper presents a test procedure for nested or non nested hypotheses the test statistic is based on the difference between two estimators of the pseudo true value as defined for instance by sawa this statistic is similar to the usual wald statistic in the case of nested hypotheses and it can be replaced by an asymptotically equivalent one deduced from the score function

tests of non nested regression models some results on small sample behaviour and the bootstrap the most popular procedures for testing a regression model against a single non nested alternative can be substantially oversized in small samples also when a regression model is to be tested in the presence of several non nested alternatives the null model is sometimes accepted only if testing against each alternative in turn produces no significant outcomes this approach leads to an implicit overall test with a significance level that is not known even asymptotically it is shown that the bootstrap can be used to control significance levels in both types of situation power estimates for various tests using bootstrap critical values are also obtained and compared

an o p3 hp version fem in two dimensions preconditioning and post processing abstract the bernstein polynomials have been known for over a century and are widely used in the spline literature computer aided geometric design and computer graphics however the realization that the bernstein basis has favorable properties allowing the efficient implementation of high order methods for the approximation of partial differential equations is a relatively recent development for instance it is known ainsworth et al 2011 that the bernstein basis can be exploited to compute all of the entries in the load vector in o p 3 operations even in the case of non linear problems on curvilinear elements for a degree p approximation moreover the element matrices can be assembled in o 1 operations per entry we show that properties of the bernstein polynomials can also be exploited to obtain o p 3 complexity procedures for all of the main components needed to implement a high order finite element code including computation of the residuals needed for an iterative solution method evaluating the action of a preconditioner for the global mass matrices and visualization and post processing of the resulting finite element approximations the construction of a preconditioner for the mass matrix whose condition number does not degenerate with the order p at a cost of o p 3 operations is one of the main contributions of the present work the preconditioner is based on an abstract additive schwarz method recently developed by the authors the preconditioner can be implemented at a cost of o p 3 operations by exploiting properties of the bernstein polynomials in particular we present an algorithm which allows one to invert the interior block of the element mass matrix in o p 3 operations numerical examples are provided to illustrate the applicability of the bernstein basis to challenging non linear reaction diffusion problems non linear wave propagation of solitons and to robust approximation of problems exhibiting boundary layers

phase field systems with nonlinear coupling and dynamic boundary conditions we consider phase field systems of caginalp type on a three dimensional bounded domain the order parameter fulfills a dynamic boundary condition while the relative temperature is subject to a homogeneous boundary condition of dirichlet neumann or robin type moreover the two equations are nonlinearly coupled through a quadratic growth function here we extend several results which have been proven by some of the authors for the linear coupling more precisely we demonstrate the existence and uniqueness of global solutions then we analyze the associated dynamical system and we establish the existence of global as well as exponential attractors we also discuss the convergence of given solutions to a single equilibrium

hierarchic hp edge element families for maxwell s equations on hybrid quadrilateral triangular meshes we construct and study a set of hierarchic basis functions for the galerkin discretisation of the space h curl 169 suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non uniform order polynomial approximation we investigate the conditioning and dispersive behaviour of the elements in addition numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time harmonic maxwell s equations that have singularities

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

corrigendum to existence of global solutions to the caginalp phase field system with dynamic boundary conditions and singular potentials j math anal appl 343 2008 557 566

convergence to equilibrium for the cahn hilliard equation with dynamic boundary conditions this paper is concerned with the asymptotic behavior of solution to the cahn hilliard equation 0 1 u t u u u3 x t r subject to the following dynamic boundary conditions 0 2 s u u hs gsu 1 sut t 0 x 0 t 0 x and the initial condition 0 3 u t 0 u0 x x where is a bounded domain in rn n 3 with smooth boundary and s 0 s 0 gs 0 hs are given constants is the tangential laplacian operator and is the outward normal direction to the boundary this problem has been considered in the recent paper by racke and zheng adv differential equations 8 1 2003 83 where the global existence and uniqueness were proved in a very recent manuscript by pruss racke and zheng konstanzer schrift math inform 189 2003 the results on existence of global attractor and maximal regularity of solution have been obtained in this paper convergence of solution of this problem to an equilibrium as time goes to infinity is proved

conditioning of hierarchic p version nedelec elements on meshes of curvilinear quadrilaterals and hexahedra the conditioning of a set of hierarchic basis functions for p version edge element approximation of the space h curl is studied theoretical bounds are obtained on the location of the eigenvalues and on the growth of the condition numbers for the mass curl curl and stiffness matrices that naturally arise from galerkin approximation of maxwell s equations the theory is applicable to meshes of curvilinear quadrilaterals or hexahedra in two and three dimensions respectively including the case in which the local order of approximation is nonuniform throughout the theory is illustrated with numerical examples that show that the theoretical asymptotic bounds are sharp and are attained within the range of practical computation

alternative procedures and associated tests of significance for non nested hypotheses this paper attempts to synthesize various procedures for testing non nested hypotheses within the framework of artificial nesting and establishes the result that different tests correspond to different treatments of its identification problem numerical and a priori identification methods are distinguished we derive two modified likelihood ratio tests that are asymptotically equivalent to the cox test and explain the relationship between them the tests are consistent this abstract was borrowed from another version of this item

the distributions of the j and cox non nested tests in regression models with weakly correlated regressors abstract this paper examines the asymptotic null distributions of the j and cox non nested tests in the framework of two linear regression models with nearly orthogonal non nested regressors the analysis is based on the concept of near population orthogonality npo according to which the non nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn new distributional results emerge under npo the j and cox tests tend to two different random variables asymptotically each of which is expressible as a function of a nuisance parameter c a n 0 1 variate and a 2 q variate where q is the number of non nested regressors in the alternative model the monte carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under npo by plugging consistent estimates of c into the relevant asymptotic expressions an empirical example illustrates the plug in procedure

aspects of an adaptive hp finite element method adaptive strategy conforming approximation and efficient solvers the main components needed for an adaptive hp version finite element algorithm are discussed an adaptive hp refinement strategy effective methods for constructing conforming hp approximations and efficient solvers for the large ill conditioned systems of linear equations together these provide the methodology for an effective adaptive hp version algorithm the presentation emphasizes the links between the differing components showing how the algorithms may be implemented efficiently in practice the main principles are illustrated by use of concrete examples so that a non expert may develop their own adaptive hp code the performance of the whole algorithm is illustrated for some representative problems taken from linear elasticity

frequency and time domain electromagnetic scattering simulations employing higher order edge elements finite elements are often used for electromagnetic scattering simulations where the main goal is the accurate predicting of the radar cross section or scattering width output edge element discretizations are popular as they are known to eliminate the problems of spurious modes and allow the easy implementation of boundary conditions and material interfaces this work employs a technique which uses higher order edge elements for scattering problems set in both the frequency and time domains in three and two dimensions respectively such approximations are attractive as they are known to give a higher level of accuracy for a given number of degrees of freedom when compared to lower order approximations appropriate solution techniques are proposed for the system of linear equations which arises in each case numerical examples demonstrate the effectiveness of the proposed procedures