a staggered grid lagrangian eulerian remap code for 3 d mhd simulations abstract in this paper an approach to multidimensional magnetohydrodynamics mhd which correctly handles shocks but does not use an approximate riemann solver is proposed this approach is simple and is based on control volume averaging with a staggered grid the method builds on the older and often overlooked technique of on each step taking a fully 3 d lagrangian step and then conservatively remapping onto the original grid at the remap step gradient limiters are applied so that the scheme is monotonicity preserving for euler s equations this technique combined with an appropriately staggered grid and wilkins artificial viscosity can give results comparable to those from approximate riemann solvers we show how this can be extended to include a magnetic field maintaining the divergence free condition and pressure positivity and then present numerical test results where possible a comparison with other shock capturing techniques is presented and the advantages and disadvantages of the proposed scheme are clearly explained

a new form of the information matrix test a new form of the information matrix test is developed for a wide variety of statistical models the test is constructed against an explicit alternative with random parameter variation it is computed using a double length artificial regression instead of the more conventional outer product of the gradient regression which is known to have very poor finite sample properties in monte carlo experiments for the case of univariate linear regression models the new form performs remarkably well some approximate finite sample distributions are also calculated for this case and lend support to the use of the new form copyright 1992 by the econometric society

a low diffusive lagrange remap scheme for the simulation of violent air water free surface flows in 2002 despres and lagoutiere 17 proposed a low diffusive advection scheme for pure transport equation problems which is particularly accurate for step shaped solutions and thus suited for interface tracking procedure by a color function this has been extended by kokh and lagoutiere 28 in the context of compressible multifluid flows using a five equation model in this paper we explore a simplified variant approach for gas liquid three equation models the eulerian numerical scheme has two ingredients a robust remapped lagrange solver for the solution of the volume averaged equations and a low diffusive compressive scheme for the advection of the gas mass fraction numerical experiments show the performance of the computational approach on various flow reference problems dam break sloshing of a tank filled with water water water impact and finally a case of rayleigh taylor instability one of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers

information theory for maximum likelihood estimation of diffusion models abstract we develop an information theoretic framework for maximum likelihood estimation of diffusion models two information criteria that measure the divergence of a diffusion process from the true diffusion are defined the maximum likelihood estimator mle converges asymptotically to the limit that minimizes the criteria when sampling interval decreases as sampling span increases when both drift and diffusion specifications are correct the criteria become zero and the inverse curvatures of the criteria equal the asymptotic variance of the mle for misspecified models the minimizer of the criteria defines pseudo true parameters pseudo true drift parameters depend on approximate transition densities if used

improved fct algorithm for shock hydrodynamics the new ydfct algorithm is presented for the numerical solution of hydrodynamic flow problems with steep gradients this algorithm is an explicit finite difference scheme based on the flux corrected transport technique and it is an improvement of the etbfct and the xdfct algorithms the erosion of sharp edges the phase distortion of curved profiles and the terracing effect and velocity oscillations are eliminated or significantly reduced these improvements are obtained by following action of the limiter at edges more detailed linear numerical analysis of the difference scheme and considering the velocity gradient in the diffusion and antidiffusion coefficients properties of the new algorithm are also demonstrated by the solution of three test problems

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

testing for unobserved heterogeneity in exponential and weibull duration models abstract we examine the use of the likelihood ratio lr statistic to test for unobserved heterogeneity in duration models based on mixtures of exponential or weibull distributions we consider both the uncensored and censored duration cases the asymptotic null distribution of the lr test statistic is not the standard chi square as the standard regularity conditions do not hold instead there is a nuisance parameter identified only under the alternative and a null parameter value on the boundary of the parameter space as in cho and white 2007a we accommodate these and provide methods delivering consistent asymptotic critical values we conduct a number of monte carlo simulations comparing the level and power of the lr test statistic to an information matrix im test due to chesher 1984 and lagrange multiplier lm tests of kiefer 1985 and sharma 1987 our simulations show that the lr test statistic generally outperforms the im and lm tests we also revisit the work of van den berg and ridder 1998 on unemployment durations and of ghysels et al 2004 on interarrival times between stock trades and as it turns out affirm their original informal inferences

information ratio test for model misspecification in quasi likelihood inference in this article we focus on the circumstances in quasi likelihood inference that the estimation accuracy of mean structure parameters is guaranteed by correct specification of the first moment but the estimation efficiency could be diminished due to misspecification of the second moment we propose an information ratio ir statistic to test for model misspecification of the variance covariance structure through a comparison between two forms of information matrix the negative sensitivity matrix and the variability matrix we establish asymptotic distributions of the proposed ir test statistics we also suggest an approximation to the asymptotic distribution of the ir statistic via a perturbation resampling method moreover we propose a selection criterion based on the ir test to select the best fitting variance covariance structure from a class of candidates through simulation studies it is shown that the ir statistic provides a powerful statistical tool to detect different scenarios of misspecific

q analytic functions on quantum spaces in this article a different interpretation is given of the quantum plane introduced by manin and the q analytic functions on its two intervals are characterized the a1 q modules of q analytic functions defined in this article are in fact noncommutative associative algebras with unity which can be considered as the deformations of the algebras of analytic functions on the two intervals of r2 some results obtained by this approach are briefly mentioned

bootstrap critical values for tests based on generalized method of moments estimators monte carlo experiments have shown that tests based on generalized method ofmoments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used this paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions particular attention is given to the case of dependent data it is shown that with such data the bootstrap must sample blocks of data and that the formulae for the bootstrap versions of test statistics differ from the formulae that apply with the original data the results of monte carlo experiments on the numerical performance of the bootstrap show that it usually reduces the errors in level that occur when critical values based on first order asymptotic theory are used the bootstrap also provides an indication of the accuracy of critical values obtained from first order asymptotic theory

specification tests based on mcmc output abstract two test statistics are proposed to determine model specification after a model is estimated by an mcmc method the first test is the mcmc version of ios a test and its asymptotic null distribution is normal the second test is motivated from the power enhancement technique of fan et al 2015 it combines a component j 1 that tests a null point hypothesis in an expanded model and a power enhancement component j 0 obtained from the first test it is shown that j 0 converges to zero when the null model is correctly specified and diverges when the null model is misspecified also shown is that j 1 is asymptotically 2 distributed suggesting that the second test is asymptotically pivotal when the null model is correctly specified the main feature of the first test is that no alternative model is needed the second test has several properties first its size distortion is small and hence bootstrap methods can be avoided second it is easy to compute from mcmc output and hence is applicable to a wide range of models including latent variable models for which frequentist methods are difficult to use third when the test statistic rejects the null model and j 1 takes a large value the test suggests the source of misspecification the finite sample performance is investigated using simulated data the method is illustrated in a linear regression model a linear state space model and a stochastic volatility model using real data

asymptotic expansions of the information matrix test statistic the information matrix im test is shown to have a finite sample distribution which is poorly approximated by its asymptotic x 2 distribution in models and sample sizes commonly encountered in applied econometric research the quality of the x2 approximation depends upon the method chosen to compute the test failure to exploit restrictions on the covariance matrix of the test can lead to a test with appalling finite sample properties order o n 1 approximations to the exact distribution of an efficient form of the im test are reported these are developed from asymptotic expansions of the edgeworth and cornish fisher types they are compared with monte carlo estimates of the finite sample distribution of the test and are found to be superior to the usual x2 approximations in sample sizes of the magnitude found in applied micro econometric work the methods developed in the paper are applied to normal and exponential models and to normal regression models results are provided for the full im test and for heteroskedasticity and nonnormality diagnostic tests which are special cases of the im test in geieral the quality of alternative approximations is sensitive to covariate design however commonly used nonnormality tests are found to have distributions which to order o n 1 are invariant under changes in covariate design this leads to simple design and parameter invariant size corrections for nonnormality tests

the small sample performance of the information matrix test abstract this paper reviews the information matrix im test procedure see white 1982 it investigates the size performance of several variants of the im test statistic and in particular exposes the nr2 variant of the test as proposed by chesher 1983 and lancaster 1984 as being extremely poor alternative nr2 im test statistics are considered and it appears that substantial improvements can be made by incorporating expected values of third derivatives of the log density into the im test calculation procedure interestingly these are exactly the sort of calculations that the chesher 1983 and lancaster 1984 variant avoids

maximum likelihood estimation of the multivariate normal mixture model the hessian of the multivariate normal mixture model is derived and estimators of the information matrix are obtained thus enabling consistent estimation of all parameters and their precisions the usefulness of the new theory is illustrated with two examples and some simulation experiments the newly proposed estimators appear to be superior to the existing ones

extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics an extension of the piecewise parabolic method to treat multidimensional ideal magnetohydrodynamical equations is presented in this paper the multidimensional scheme is constructed from a one dimensional functioning code based on the dimensional splitting method originally suggested by strang the functioning code is built upon a nonlinear riemann solver for ideal mhd equations recently developed by the authors the correctness of the scheme is tested in the steepening of waves in both one and two dimensional situations and in various mhd shock tube problems which involve all the discontinuities in ideal mhd the robust character of the scheme is demonstrated in the shock tube problems and in the interaction between mhd shocks and a cloud the results of these problems show that the scheme keeps the principal advantages of a high order godunov scheme robust operation in the presence of very strong waves thin shock fronts with little attendant noise generation and thin contact discontinuity

duration response measurement error the impact of response measurement error in duration data is investigated using small parameter asymptotic approximations and compared with the effect of hazard function heterogeneity the approximations lead to a specification test to detect measurement error which is shown to be related to the class of information matrix tests it is shown that in a commonly used class of models the test statistic is exactly pivotal the second order asymptotic properties of the alternative forms of the test statistic are derived and the quality of the approximations and the performance of the test are investigated via monte carlo experimentation

bootstrap based critical values for the information matrix test abstract in finite samples the true size of white s information matrix test often differs greatly from its nominal size based on asymptotic critical values this paper shows how the bootstrap can be used to obtain improved finite sample critical values the results of monte carlo experiments show that for the cases investigated the bootstrap largely eliminates the problem of incorrect finite sample size moreover when size corrected critical values are used forms of the test that have small size distortions with asymptotic critical values can have much lower power than forms that have large size distortions with asymptotic critical values

pythagorean generalization of testing the equality of two symmetric positive definite matrices abstract we provide a new test for equality of two symmetric positive definite matrices that leads to a convenient mechanism for testing specification using the information matrix equality or the sandwich asymptotic covariance matrix of the gmm estimator the test relies on a new characterization of equality between two k dimensional symmetric positive definite matrices a and b the traces of a b 1 and b a 1 are equal to k if and only if a b using this simple criterion we introduce a class of omnibus test statistics for equality and examine their null and local alternative approximations under some mild regularity conditions a preferred test in the class with good omni directional power is recommended for practical work monte carlo experiments are conducted to explore performance characteristics under the null and local as well as fixed alternatives the test is applicable in many settings including gmm estimation svar models and high dimensional variance matrix settings

on the bootstrap and confidence intervals we derive an explicit formula for the first term in an unconditional edgeworth type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of studentized statistics the class includes sample mean k sample mean sample correlation coefficient maximum likelihood estimators expressible as functions of vector means etc we suggest that the bootstrap is really an empiric one term edgeworth inversion with the bootstrap simulations implicitly estimating the first term in an edgeworth expansion this view of the bootstrap is reinforced by our discussion of the iterated bootstrap which inverts an edgeworth expansion to arbitrary order by simulating simulations

lm tests of spatial dependence based on bootstrap critical values to test the existence of spatial dependence in an econometric model a convenient test is the lagrange multiplier lm test however evidence shows that in finite samples the lm test referring to asymptotic critical values may suffer from the problems of size distortion and low power which become worse with a denser spatial weight matrix in this paper residual based bootstrap methods are introduced for asymptotically refined approximations to the finite sample critical values of the lm statistics conditions for their validity are clearly laid out and formal justifications are given in general and in detail under several popular spatial lm tests using edgeworth expansions monte carlo results show that when the conditions are not fully met bootstrap may lead to unstable critical values that change significantly with the alternative whereas when all conditions are met bootstrap critical values are very stable approximate much better the finite sample critical values than those based on asymptotics and lead to significantly improved size and power the methods are further demonstrated using more general spatial lm tests in connection with local misspecification and unknown heteroskedasticity

a consistent bootstrap test for conditional density functions with time series data this paper presents a new test for evaluating conditional density functions for time series data thereby being applicable to forecasting problems we show that the test statistic is asymptotically distributed standard normal under the null hypothesis and diverges to infinity when the null hypothesis is false we use a bootstrap algorithm to approximate the distribution of the test statistic and show that the bootstrap distribution converges to the asymptotic distribution of the test statistic in probability an application to inflation forecasting is also presented to demonstrate the usefulness of the test

how to implement the bootstrap in static or stable dynamic regression models test statistic versus confidence region approach by combining two alternative formulations of a test statistic with two alternative resampling schemes we obtain four different bootstrap tests in the context of static linear regression models two of these are shown to have serious size and power problems whereas the remaining two are adequate and in fact equivalent the equivalence between the two valid implementations is shown to break down in dynamic regression models then the procedure based on the test statistic approach performs best at least in the ar 1 model similar finite sample phenomena are illustrated in the arma 1 1 model through a small scale monte carlo study and an empirical example

contracting in space an application of spatial statistics to discrete choice models abstract we develop tests for spatial error correlation and methods of estimation in the presence of such correlation for discrete choice models the tests which are based on the notion of a generalized residual are a set of orthogonality conditions that should be satisfied under the null when the restrictions are rejected the full model can be estimated by generalized method of moments these techniques are used to evaluate spatial patterns in retail gasoline contracts we examine whether the spatial configuration is random or whether there is a tendency towards clustering or dispersion of contract types the data consist of all contracts between integrated oil companies and their branded service stations in the city of vancouver six metrics or measures of closeness are examined euclidean distance competition along streets a combination of the first two nearest neighbors along streets nearest neighbors in euclidean distance and neighbors that share a common marked boundary

on the number of bootstrap simulations required to construct a confidence interval abstract the purpose of this document is to make two points about the effect of the number of bootstrap simulations b on percentile t bootstrap confidence intervals the first point concerns coverage probability the second distance of the simulated critical point form the true critical point derived with b infinity in both cases the author has in mind applications to smooth statistics such as the studentized mean of a sample drawn from a continuous distribution he indicates the change that have to be made if the distribution of the statistic is not smooth additional keywords exponentive functions

empirically relevant critical values for hypothesis tests a bootstrap approach tests of statistical hypotheses can be based on either of two critical values the type i critical value or the size corrected critical value the former usually depends on unknown population parameters and cannot be evaluated exactly in applications but it can often be estimated very accurately by using the bootstrap the latter does not depend on unknown population parameters but is likely to yield a test with low power the critical values used in most monte carlo studies of the powers of tests are neither type i nor size corrected they are irrelevant to empirical research

the power of bootstrap and asymptotic tests the bootstrap discrepancy measures the difference in rejection probabilities between a bootstrap test and one based on the true distribution the order of magnitude of the bootstrap discrepancy is the same under the null hypothesis and under non null processes described by pitman drift if the test statistic is not an exact pivot critical values depend on which data generating process dgp is used to determine the null distribution we propose using the dgp which minimizes the bootstrap discrepancy we also show that under an asymptotic independence condition the power of both bootstrap and asymptotic tests can be estimated cheaply by simulation

likelihood ratio specification tests misspecification tests for parametric models f y that examine data for failure of moment conditions implied by the maintained parametric distribution are interpreted as score tests of h 0 0 in the context of a parametric family of distributions r y this family contains the maintained distribution as a special case 0 and has the property that only in that special case do the chosen moment conditions hold a likelihood ratio test of h 0 0 therefore constitutes an alternative test of the validity of the moment conditions this test admits a bartlett correction unlike conventional moment tests for which adjustments based on second order asymptotic theory may behave badly the dependence of the bartlett correction and of the o n 1 2 local power of the test on the way in which r y is constructed is studied in many cases the correction can be made to vanish leading to a specification test whose distribution is chi square to order o p n 2

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

misspecification tests for binomial and beta binomial models the ios test of presnell and boss j am stat assoc 2004 99 465 216 227 is a general purpose goodness of fit test based on the ratio of in sample and out of sample likelihoods for large samples the ios statistic can be approximated by a multiplicative contrast between two estimates of the information matrix and in this way the ios test is connected to white s econometrica 1982 50 1 26 information matrix test or im test which is based directly on the difference of two estimates of the information matrix in this paper we compare the performance of ios to that of the im test and of other goodness of fit tests for binomial and beta binomial models in both examples and simulations our findings suggest that ios is strongly competitive not only against the im test but also against tests designed for specific binomial and beta binomial models

bootstrap methods for markov processes the block bootstrap is the best known bootstrap method for time series data when the analyst does not have a parametric model that reduces the data generation process to simple random sampling however the errors made by the block bootstrap converge to zero only slightly faster than those made by first order asymptotic approximations this paper describes a bootstrap procedure for data that are generated by a markov process or a process that can be approximated by a markov process with sufficient accuracy the procedure is based on estimating the markov transition density nonparametrically bootstrap samples are obtained by sampling the process implied by the estimated transition density conditions are given under which the errors made by the markov bootstrap converge to zero more rapidly than those made by the block bootstrap

comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems two versions of flux corrected transport and two versions of total variation diminishing schemes are tested for several one and two dimensional hydrodynamic and magnetohydrodynamic problems two of the schemes ydfct and tvdlf are tested extensively for the first time the results give an insight into the limitations of the methods their relative strengths and weaknesses some subtle points of the algorithms and the effects of selecting different options for certain methods are emphasised

the ios test for model misspecification a new test of model misspecification is proposed based on the ratio of in sample and out of sample likelihoods the test is broadly applicable and in simple problems approximates well known intuitive methods using jackknife influence curve approximations it is shown that the test statistic can be viewed asymptotically as a multiplicative contrast between two estimates of the information matrix both of which are consistent under correct model specification this approximation is used to show that the statistic is asymptotically normally distributed although it is suggested that p values be computed using the parametric bootstrap the resulting methodology is demonstrated with various examples and simulations involving both discrete and continuous data

q analytic functions fractals and generalized analytic functions we introduce a new class of complex functions of complex argument which we call q analytic functions these functions satisfy q cauchy riemann equations and have real and imaginary parts as q harmonic functions we show that q analytic functions are not the analytic functions however some of these complex functions fall in the class of generalized analytic functions as a main example we study the complex q binomial functions and their integral representation as a solution of the d bar problem in terms of these functions the complex q analytic fractal satisfying the self similar q difference equation is derived a new type of quantum states as q analytic coherent states and corresponding q analytic fock bargmann representation are constructed as an application we solve quantum q oscillator problem in this representation and show that the wave functions of quantum states are given by complex q binomials

formulations of artificial viscosity for multi dimensional shock wave computations in this paper we present a new formulation of the artificial viscosity concept physical arguments for the origins of this term are given and a set of criteria that any proper functional form of the artificial viscosity should satisfy is enumerated the first important property is that by definition a viscosity must always be dissipative transferring kinetic energy into internal energy and must never act as a false pressure the artificial viscous force should be galilean invariant and vary continuously as a function of the criterion used to determine compression and expansion and remain zero for the latter case these requirements significantly constrain the functional form that the artificial viscous force can have in addition an artificial viscosity should be able to distinguish between shock wave and adiabatic compression and not result in spurious entropy production when only the latter is present it must therefore turn off completely for self similiar motion where only a uniform stretching and or a rigid rotation occurs an additional important but more subtle condition where the artificial viscosity should produce no effect is along the direction tangential to a convergent shock front since the velocity is only discontinuous in the normal direction our principal result is the development of a new formulation of an edge centered artificial viscosity that is to be used in conjunction with a staggered spatial placement of variables that meets all of these standards and without the need for problem dependent numerical coefficients that have in the past made the artificial viscosity method appear somewhat arbitrary our formulation and numerical results are given with respect to two spatial dimensions but all of our arguments carry over directly to three dimensions a central feature of our development is the implementation of simple advection limiters in a straightforward manner in more than one dimension to turn off the artificial viscosity for the above mentioned conditions and to substantially reduce its effect when strong velocity gradients are absent

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class