nonparametric inference based on conditional moment inequalities abstract this paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and or equalities the parameters need not be identified confidence sets and tests are introduced the correct uniform asymptotic size of these procedures is established the false coverage probabilities and power of the cs s and tests are established for fixed alternatives and some local alternatives finite sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model the recommended cs test uses a cramer von mises type test statistic and employs a generalized moment selection critical value

distribution theory for the studentized mean for long short and negative memory time series abstract we consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory short memory negative intermediate memory or is the first difference of such a process the rate of growth of this variance depends crucially on the type of memory and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically we also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size extending known results to the case of flat top tapers we adopt the fixed proportion bandwidth perspective in our empirical section presenting two methods for estimating the limiting critical values both the subsampling method and a plug in approach simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean both methods perform well although the subsampling method appears to be better sized and provide a viable framework for conducting inference for the mean in summary we supply a unified asymptotic theory that covers all different types of memory under a single umbrella

conformal mapping based coordinate generation method for flows in periodic configurations abstract a conformal mapping based coordinate generation method for periodic configurations has been developed a channel of an arbitrary shape in the physical plane representing internal configurations is mapped into a straight channel in the computational plane and a wall of an arbitrary shape in the physical plane representing external configurations is mapped into a straight wall in the computational plane the parameters of the transformations have to be determined through a method of successive approximations a simple iteration scheme that converges quite rapidly even with a poor initial guess is presented solutions for different configurations are displayed to illustrate the capabilities of the method

testing optimal kernel choice in har inference abstract the paper investigates the optimal kernel choice in heteroskedasticity and autocorrelation robust tests based on the fixed b asymptotics in parallel with the optimality of the quadratic spectral kernel under the asymptotic mean squared error criterion of the point estimator of the long run variance as considered in andrews 1991 we show that the optimality of the quadratic spectral kernel continues to hold under the testing oriented criterion of sun philips and jin 2008 which takes a weighted average of the probabilities of type i and type ii errors of the fixed b asymptotic test

implicit spectrally accurate method for moving boundary problems using immersed boundary conditions concept a fully implicit spectral algorithm for the analysis of moving boundary problem is described the algorithm is based on the concept of immersed boundary conditions ibc i e the computational domain is fixed while the time dependent physical domain is submerged inside the computational domain and is described in the context of the diffusion type problems the physical conditions along the edges of the physical domain are treated as internal constraints the method eliminates the need for adaptive grid generation that follows evolution of the physical domain and provides sharp resolution of the location of the boundary various tests confirm the spectral accuracy in space and the first and second order accuracy in time the computational cost advantage of the ibc method as compared with the more traditional algorithm based on the mapping concept is demonstrated

asymptotic f and t tests in an efficient gmm setting abstract this paper considers two step efficient gmm estimation and inference where the weighting matrix and asymptotic variance matrix are based on the series long run variance estimator we propose a simple and easy to implement modification to the trinity of test statistics in the two step efficient gmm setting and show that the modified test statistics are all asymptotically f distributed under the so called fixed smoothing asymptotics the modification is multiplicative and involves the j statistic for testing over identifying restrictions this leads to convenient asymptotic f tests whose critical values i e the standard f critical values are readily available from standard statistical tables and programming environments for testing a single restriction with a one sided alternative an asymptotic t test theory using the standard t distribution as the reference distribution is also developed

three dimensional front tracking we describe a three dimensional front tracking algorithm discuss its numerical implementation and present studies to validate the correctness of this approach based on the results of the two dimensional computations we expect three dimensional front tracking to significantly improve computational efficiencies for problems dominated by discontinuities in some cases for which the interface computations display considerable numerical sensitivity we expect a greatly enhanced capability

the error in rejection probability of simple autocorrelation robust tests a new class of autocorrelation robust test statistics is introduced the class of tests generalizes the kiefer vogelsang and bunzel 2000 test in a manner analogous to anderson and darling s 1952 generalization of the cramer von mises goodness of fit test in a gaussian location model the error in rejection probability of the new tests is found to be o t 1 log t where t denotes the sample size

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

a penalized neumann control approach for solving an optimal dirichlet control problem for the navier stokes equations we introduce a penalized neumann boundary control approach for solving an optimal dirichlet boundary control problem associated with the two or three dimensional steady state navier stokes equations we prove the convergence of the solutions of the penalized neumann control problem the suboptimality of the limit and the optimality of the limit under further restrictions on the data we describe the numerical algorithm for solving the penalized neumann control problem and report some numerical results

testing dependence among serially correlated multicategory variables the contingency table literature on tests for dependence among discrete multicategory variables is extensive standard tests assume however that draws are independent and only limited results exist on the effect of serial dependency a problem that is important in areas such as economics finance medical trials and meteorology this article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions the tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite order markov processes for three way or higher order tables we propose new tests of joint and marginal independence monte carlo experiments show that the proposed tests have good finite sample properties an empirical application to microeconomic survey data on firms forecasts of changes to their production and prices demonstrates the importance of correcting fo

simple and powerful gmm over identification tests with accurate size abstract based on the series long run variance estimator we propose a new class of over identification tests that are robust to heteroscedasticity and autocorrelation of unknown forms we show that when the number of terms used in the series long run variance estimator is fixed the conventional j statistic after a simple correction is asymptotically f distributed we apply the idea of the f approximation to the conventional kernel based j tests simulations show that the j tests based on the finite sample corrected j statistic and the f approximation have virtually no size distortion and yet are as powerful as the standard j tests

robust m tests without consistent estimation of the asymptotic covariance matrix we extend the kvb approach of kiefer vogelsang and bunzel 2000 to constructing robust m tests without consistent estimation of the asymptotic covariance matrix we demonstrate that when model parameters have to be estimated the normalizing matrix computed using a full sample estimator is able to eliminate the nuisance parameters when there is no estimation effect but not otherwise to circumvent the problem of estimation effect we propose using recursive estimators to compute the normalizing matrix and show that the resulting m test is asymptotically pivotal this m test is thus robust not only to heteroscedasticity and serial correlations of unknown form but also to the presence of an estimation effect as examples we consider robust tests for serial correlations and robust information matrix tests the former tests extend that of lobato 2001 and are applicable to model residuals for testing higher order moments we find that the latter tests are also robust when a lower order moment is miss

estimation and inference in semiparametric quantile factor models we propose an estimation methodology for a semiparametric quantile factor panel model we provide tools for inference that are robust to the existence of moments and to the form of weak cross sectional dependence in the idiosyncratic error term we apply our method to crsp daily data

measurement error in linear autoregressive models time series data are often subject to measurement error usually the result of needing to estimate the variable of interest although it is often reasonable to assume that the measurement error is additive i e the estimator is conditionally unbiased for the missing true value the measurement error variances often vary as a result of changes in the population process over time and or changes in sampling effort in this article we address estimation of the parameters in linear autoregressive models in the presence of additive and uncorrelated measurement errors allowing heteroscedasticity in the measurement error variances we establish the asymptotic properties of naive estimators that ignore measurement error and propose an estimator based on correcting the yule walker estimating equations we also examine a pseudo likelihood method based on normality assumptions and computed using the kalman filter we review other techniques that have been proposed including two that require no information about

a simple and trustworthy asymptotic t test in difference in differences regressions abstract we propose an asymptotically valid t test that uses student s t distribution as the reference distribution in a difference in differences regression for the asymptotic variance estimation we adopt the clustering by time approach to accommodate cross sectional dependence this approach often assumes the clusters to be independent across time but we allow them to be temporally dependent the proposed t test is based on a special heteroscedasticity and autocorrelation robust har variance estimator we target the type i and type ii errors and develop a testing oriented method to select the underlying smoothing parameter by capturing the estimation uncertainty of the har variance estimator the t test has more accurate size than the corresponding normal test and is just as powerful as the latter compared to the nonstandard test developed in the literature the standard t test is just as accurate but much more convenient to use model based and empirical data based monte carlo simulations show that the t test works quite well in finite samples

convergence of adaptive finite element methods for general second order linear elliptic pdes we prove convergence of adaptive finite element methods afems for general nonsymmetric second order linear elliptic pdes thereby extending the result of morin nochetto and siebert it siam j numer anal 38 2000 pp 466 488 it siam rev 44 2002 pp 631 658 the proof relies on quasi orthogonality which accounts for the bilinear form not being a scalar product together with novel error and oscillation reduction estimates which now do not decouple we show that afems are a contraction for the sum of energy error plus oscillation numerical experiments including oscillatory coefficients and both coercive and noncoercive convection diffusion pde illustrate the theory and yield optimal meshes

over determined formulation of the immersed boundary conditions method abstract the over determined formulation of the immersed boundary conditions ibc method is proposed the method relies on the fourier expansions in the periodic direction and chebyshev expansions in the transverse direction the boundaries of the physical domain are immersed inside a regular computational domain and the boundary conditions enter the algorithm in the form of constraints construction of these constraints provides degrees of freedom in excess of that required to formulate a closed system of algebraic equations use of the additional degrees of freedom that leads to an over determined system is explored in order to improve the accuracy of the ibc method and to expand its applicability to more extreme geometries the over constraint formulation has been tested on three model problems that lead to the laplace biharmonic and navier stokes equations and thus cover the most commonly encountered types of operators in all cases tested the over determined formulation was found to improve the performance of the ibc method

a nonstandard empirical likelihood for time series standard blockwise empirical likelihood bel for stationary weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions this aspect can be difficult and impacts coverage accuracy as an alternative this paper proposes a new version of bel based on a simple though non standard data blocking rule which uses a data block of every possible length consequently the method involves no block selection and is also anticipated to exhibit better coverage performance its non standard blocking scheme however induces non standard asymptotics and requires a significantly different development compared to standard bel we establish the large sample distribution of log ratio statistics from the new bel method for calibrating confidence regions for mean or smooth function parameters of time series this limit law is not the usual chi square one but is distribution free and can be reproduced through straightforward simulations numerical studies indicate that the proposed method generally exhibits better coverage accuracy than standard bel

generalized empirical likelihood tests in time series models with potential identification failure abstract we introduce test statistics based on generalized empirical likelihood methods that can be used to test simple hypotheses involving the unknown parameter vector in moment condition time series models the test statistics generalize those in guggenberger and smith 2005 generalized empirical likelihood estimators and tests under partial weak and strong identification econometric theory 21 4 667 709 from the i i d to the time series context and are alternatives to those in kleibergen 2005a testing parameters in gmm without assuming that they are identified econometrica 73 4 1103 1123 and otsu 2006 generalized empirical likelihood inference for nonlinear and time series models under weak identification econometric theory 22 3 513 527 the main feature of these tests is that their empirical null rejection probabilities are not affected much by the strength or weakness of identification more precisely we show that the statistics are asymptotically distributed as chi square under both classical asymptotic theory and weak instrument asymptotics of stock and wright 2000 gmm with weak identification econometrica 68 5 1055 1096 we also introduce a modification to otsu s 2006 statistic that is computationally more attractive a monte carlo study reveals that the finite sample performance of the suggested tests is very competitive

a direct spectral method for determination of flows over corrugated boundaries a completely spectral algorithm for analysis of flows over corrugated boundaries is proposed the algorithm treats the flow problem as an internal rather then a boundary value problem where the flow conditions are specified along a line in the interior of the computational domain the method eliminates the need for a coordinate generation and or premapping required for regularization of the computational domain in standard implementations of spectral discretizations various tests confirm the spectral accuracy of the algorithm

testing for common deterministic trend slopes we propose tests for hypotheses on the parameters for deterministic trends the model framework assumes a multivariate structure for trend stationary time series variables we derive the asymptotic theory and provide some relevant critical values monte carlo simulations suggest which tests are more useful in practice than others we apply our tests to examine real gdp convergence for a sample of seven european countries

an asymptotic analysis of likelihood based diffusion model selection using high frequency data abstract we provide a new asymptotic analysis of model selection procedure that compares likelihoods of two candidate diffusion models our asymptotic analysis relies on two dimensional asymptotic expansions with shrinking sampling interval and increasing sampling span t and clarifies the different roles of drift and diffusion functions in the selection of diffusion models in particular we show that the model with superior diffusion function specification is always preferred to the competing model regardless of their drift specifications if is sufficiently small relative to t the specifications of drift functions matter only when the models have an identical diffusion specification

numerical simulation of unsteady nonisothermal capillary interfaces a family of algorithms for simulation of unsteady nonisothermal capillary interfaces has been developed the algorithms are based on a coordinate transformation method the time dependent unknown physical domain is mapped onto a rectangular computational domain with the explicit form of the mapping function not being known four types of temporal discretization are used leading to the first order accurate one step implicit method second order accurate crank nicolson and trapezoidal methods and second order accurate two step implicit method in all cases second order finite difference approximations were used for spatial discretizations various tests demonstrated that the algorithms deliver theoretically predicted accuracy even for very large interfacial distortions the crank nicolson and trapezoidal methods have been found to be conditionally stable and thus are not recommended

a posteriori error analysis of optimal control problems with control constraints we derive a unifying framework for the a posteriori error analysis of control constrained linear quadratic optimal control problems we consider finite element discretizations with discretized and nondiscretized control a fundamental error equivalence drastically simplifies the a posteriori error analysis for optimal control problems it basically remains to apply error estimators for the linear state and adjoint problem we give several examples including stabilized discretizations and investigate the quality of the estimators and the performance of the adaptive iteration by selected numerical experiments

an adaptive finite element algorithm with reliable and efficient error control for linear parabolic problems an efficient and reliable a posteriori error estimate is derived for linear parabolic equations which does not depend on any regularity assumption on the underlying elliptic operator an adaptive algorithm with variable time step sizes and space meshes is proposed and studied which at each time step delays the mesh coarsening until the final iteration of the adaptive procedure allowing only mesh and time step size refinements before it is proved that at each time step the adaptive algorithm is able to reduce the error indicators and thus the error below any given tolerance within a finite number of iteration steps the key ingredient in the analysis is a new coarsening strategy numerical results are presented to show the competitive behavior of the proposed adaptive algorithm

a noisy principal component analysis for forward rate curves abstract principal component analysis pca is the most common nonparametric method for estimating the volatility structure of gaussian interest rate models one major difficulty in the estimation of these models is the fact that forward rate curves are not directly observable from the market so that non trivial observational errors arise in any statistical analysis in this work we point out that the classical pca analysis is not suitable for estimating factors of forward rate curves due to the presence of measurement errors induced by market microstructure effects and numerical interpolation our analysis indicates that the pca based on the long run covariance matrix is capable to extract the true covariance structure of the forward rate curves in the presence of observational errors moreover it provides a significant reduction in the pricing errors due to noisy data typically found in forward rate curves

let s fix it fixed b asymptotics versus small b asymptotics in heteroskedasticity and autocorrelation robust inference in the presence of heteroscedasticity and autocorrelation of unknown forms the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter depending on whether this lag truncation parameter is speci ed to grow at a slower rate than or the same rate as the sample size we obtain two types of asymptotic approximations the small b asymptotics and the xed b asymptotics using techniques for probability distribution approximation and high order expansions this paper shows that the xed b asymptotic approximation provides a higher order re nement to the rst order small b asymptotics this result provides a theoretical justi cation on the use of the xed b asymptotics in empirical applications on the basis of the xed b asymptotics and higher order small b asymptotics the paper introduces a new and easy to use asymptotic f test that employs a nite sample corrected wald statistic and uses an f distribution as the reference distribution finally the paper develops a bandwidth selection rule that is testing optimal in that the bandwidth minimizes the type ii error of the asymptotic f test while controlling for its type i error monte carlo simulations show that the asymptoticf test with the testing optimal bandwidth works very well in nite samples

fixed smoothing asymptotics in a two step generalized method of moments framework fixed smoothing asymptotics this paper develops the fixed smoothing asymptotics in a two step generalized method of moments gmm framework under this type of asymptotics the weighting matrix in the second step gmm criterion function converges weakly to a random matrix and the two step gmm estimator is asymptotically mixed normal nevertheless the wald statistic the gmm criterion function statistic and the lagrange multiplier statistic remain asymptotically pivotal it is shown that critical values from the fixed smoothing asymptotic distribution are high order correct under the conventional increasing smoothing asymptotics when an orthonormal series covariance estimator is used the critical values can be approximated very well by the quantiles of a noncentral f distribution a simulation study shows that statistical tests based on the new fixed smoothing approximation are much more accurate in size than existing tests

adaptive finite element methods with convergence rates adaptive finite element methods for numerically solving elliptic equations are used often in practice only recently 12 17 have these methods been shown to converge however this convergence analysis says nothing about the rates of convergence of these methods and therefore does in principle not guarantee yet any numerical advantages of adaptive strategies versus non adaptive strategies the present paper modifies the adaptive method of morin nochetto and siebert 17 for solving the laplace equation with piecewise linear elements on domains in 2 by adding a coarsening step and proves that this new method has certain optimal convergence rates in the energy norm which is equivalent to the h1 norm namely it is shown that whenever s 0 and the solution u is such that for each n 1 it can be approximated to accuracy o n s in the energy norm by a continuous piecewise linear function on a triangulation with n cells using complete knowledge of u then the adaptive algorithm constructs an approximation of the same type with the same asymptotic accuracy while using only information gained during the computational process moreover the number of arithmetic computations in the proposed method is also of order o n for each n 1 the construction and analysis of this adaptive method relies on the theory of nonlinear approximation

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

adaptive finite element methods for optimal control of partial differential equations basic concept a new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by elliptic partial differential equations the lagrangian formalism yields the first order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive galerkin finite element method the mesh design in the resulting reduced models is controlled by residual based a posteriori error estimates these are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error in this case the computed state and costate variables can be used as sensitivity factors multiplying the local cell residuals in the error estimators this results in a generic and simple algorithm for mesh adaptation within the optimization process this method is developed and tested for simple boundary control problems in semiconductor models

nonparametric rank tests for non stationary panels we develop a set of nonparametric rank tests for non stationary panels based on multivariate variance ratios which use untruncated kernels as such the tests do not require the choice of tuning parameters associated with bandwidth or lag length and also do not require choices with respect to numbers of common factors the tests allow for unrestricted cross sectional dependence and dynamic heterogeneity among the units of the panel provided simply that a joint functional central limit theorem holds for the panel of differenced series we provide a discussion of the relationships between our setting and the settings for which first and second generation panel unit root tests are designed in monte carlo simulations we illustrate the small sample performance of our tests when they are used as panel unit root tests under the more restrictive dgps for which panel unit root tests are typically designed and for more general dgps we also compare the small sample performance of our nonparametric tests to parametric rank tests finally we provide an empirical illustration by testing for income convergence among countries

structural break models under mis specification implications for forecasting abstract this paper revisits the least squares estimator of the linear regression with a structural break we view the model as an approximation to the true data generating process whose exact nature is unknown but perhaps changing over time either continuously or with some jumps this view is widely held in the forecasting literature and under this view the time series dependence property of all the observed variables is unstable as well we establish that the rate of convergence of the estimator to a properly defined limit is at most the cube root of t where t is the sample size which is much slower than the standard super consistent rate we also provide an asymptotic distribution of the estimator and that of the gaussian quasi likelihood ratio statistic for a certain class of true data generating processes we relate our finding to current forecast combination methods and propose a new averaging scheme our method compares favourably with various contemporary forecasting methods in forecasting a number of macroeconomic series

a posteriori error estimates for control problems governed by stokes equations in this paper we derive a posteriori error estimates for the finite element approximation of distributed optimal control problems governed by the stokes equations we obtain a posteriori error estimators for both the state and the control approximation in the l2 norm and the h1 norm these estimates can be used to construct reliable adaptive finite element approximation for the control problems

spectral density and spectral distribution inference for long memory time series via fixed b asymptotics this paper studies taper based estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework and makes several theoretical contributions i we treat multiple frequencies jointly ii we allow for long range dependence or anti persistence at differing frequencies iii we allow for tapers that are only piecewise smooth or discontinuous including flat top and truncation tapers iv we study higher order accuracy through the limit distribution s laplace transform v we develop a taper based estimation theory for the spectral distribution and show how confidence bands can be constructed simulation results produce quantiles and document the finite sample size properties of the estimators and a few empirical applications demonstrate the utility of the new methods

a test of the null of integer integration against the alternative of fractional integration abstract this paper proposes a test of the null of integer integration against the alternative of fractional integration the null of integer integration is satisfied if the series is either i 0 or i 1 we reject the null if the kpss test rejects i 0 and a unit root test rejects i 1 we suggest a new unit root test a lower tail kpss test applied to the differenced data to use in this procedure we provide critical values under standard asymptotics and fixed b asymptotics we prove the consistency of this testing procedure against i d alternatives with 0 d 1 and simulation evidence on the size and power of the test in finite samples is provided

gridless spectral algorithm for stokes flow with moving boundaries a gridless spectrally accurate algorithm for the stokes flow with moving boundaries is presented the algorithm uses fixed computational domain with boundaries of the flow domain moving inside the computational domain the spatial discretization is based on the fourier expansions in the streamwise direction and the chebyshev expansions in the transverse direction temporal discretization uses one and two steps implicit formulations the boundary conditions on the moving boundaries are imposed using the immersed boundary conditions concept numerical tests confirm the spectral accuracy in space and theoretically predicted accuracy in time different variants of the solution procedure are presented and their relative advantages are discussed

spectrally accurate algorithm for the analysis of flows in two dimensional vibrating channels a spectral algorithm based on the immersed boundary conditions ibc concept has been developed for the analysis of flows in channels bounded by vibrating walls the vibrations take the form of travelling waves of arbitrary profile the algorithm uses a fixed computational domain with the flow domain immersed in its interior boundary conditions enter the algorithm in the form of constraints the spatial discretization uses a fourier expansion in the stream wise direction and a chebyshev expansion in the wall normal direction use of the galileo transformation converts the unsteady problem into a steady one an efficient solver which takes advantage of the structure of the coefficient matrix has been used it is demonstrated that the method can be extended to more extreme geometries using the overdetermined formulation various tests confirm the spectral accuracy of the algorithm

should we go one step further an accurate comparison of one step and two step procedures in a generalized method of moments framework abstract according to conventional asymptotic theory the two step generalized method of moments gmm estimator and test perform at least as well as the one step estimator and test in large samples the conventional asymptotic theory completely ignores the estimation uncertainty in the weighting matrix and as a result it may not reflect finite sample situations well in this paper we employ the more accurate fixed smoothing asymptotic framework to compare the performances of the one step and two step procedures we show that the two step procedures outperform the one step procedures only when the squared long run canonical correlation coefficients between two blocks of transformed moment conditions are larger than the thresholds established in this paper the thresholds depend on the criteria of interest a monte carlo study lends support to our asymptotic results

randomization tests under an approximate symmetry assumption this paper develops a theory of randomization tests under an approximate symmetry assumption randomization tests provide a general means of constructing tests that control size in nite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis here by exhibits symmetry we mean that the distribution remains invariant under a group of transformations in this paper we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis an important application of this idea is in settings where the data may be grouped into a xed number of clusters with a large number of observations within each cluster in such settings we show that the distribution of the observed data satises our approximate symmetry requirement under weak assumptions in particular our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster but also across clusters this approach enjoys several advantages over other approaches in these settings among other things it leads to a test that is asymptotically similar which as shown in a simulation study translates into improved power at many alternatives finally we use our results to revisit the analysis of angrist and lavy 2009 who examine the impact of a cash award on exam performance for low achievement students in israel

adaptive finite element method for elliptic optimal control problems convergence and optimality in this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints we use variational discretization concept to discretize the control variable and piecewise linear and continuous finite elements to approximate the state variable based on the well established convergence theory of afem for elliptic boundary value problems we rigorously prove the convergence and quasi optimality of afem for optimal control problems with respect to the state and adjoint state variables by using the so called perturbation argument numerical experiments confirm our theoretical analysis

simple robust testing of regression hypotheses in this paper we consider the problem of hypothesis testing in models with errors that have serial correlation or heteroskedasticity of unknown form this situation is often encountered in regression models applied to economic time series data it is a classic textbook result that while ordinary least squares ols estimates of regression parameters remain consistent and asymptotically normal when errors are heteroskedastic or autocorrelated provided usual regularity conditions hold and no lagged dependent variables are in the model standard tests are no longer valid if the true form of serial correlation heteroskedasticity were known then generalized least squares gls provides efficient estimates and standard inference can be conducted on the gls transformed model but in practice the form of serial correlation heteroskedasticity is often unknown and this has led to the development of techniques that permit valid asymptotic inference without having to specify a model of the serial correlation or heteroskedasticity the most common approach is to estimate the variance covariance matrix of the ols estimates nonparametrically using spectral methods heteroskedasticity and autocorrelation consistent hac estimators and construct standard tests using the asymptotic normality of the ols estimates hac estimators have been extensively analyzed in the econometrics literature and important contributions are given by andrews 1991 andrews and monahan 1992 gallant 1987 hansen 1992 newey and west 1987 robinson 1991 1998 and white 1984 among others the benefit of hac estimator tests is asymptotically valid inference that is robust to general forms of serial correlation heteroskedasticity in the errors we propose an alternative method of constructing robust test statistics we apply a nonsingular data dependent stochastic transformation to the ols estimates the asymptotic distribution of the transformed estimates does not depend on nuisance parameters then test statistics that are asymptotically invariant to nuisance parameters asymptotic pivotal statistics are constructed the resulting test statistics have nonstandard asymptotic distributions that only depend on the number of restrictions being tested and critical values are easy to simulate using standard techniques the main advantage of our approach compared to standard approaches is that estimates of the variance covariance matrix are not explicitly required to construct the tests this is potentially important for two reasons first with the exception of the estimator proposed by robinson 1998 2 consistent nonparametric estimates of variance covariance matrices in models with serial

an optimal adaptive finite element method although existing adaptive finite element methods for solving second order elliptic equations often perform better in practical computations than nonadaptive ones usually they are not even proven to converge only recently in the work of dorfler siam j numer anal 33 1996 pp 1106 1124 and that of morin nochetto and siebert siam j numer anal 38 2000 pp 466 488 adaptive methods were constructed for which convergence could be demonstrated however convergence alone does not imply that the method is more efficient than its nonadaptive counterpart in numer math 97 2004 pp 219 268 binev dahmen and devore added a coarsening step to the routine of morin nochetto and siebert and proved that the resulting method is quasi optimal in the following sense if the solution is such that for some s 0 the error in energy norm of the best continuous piecewise linear approximations subordinate to any partition with n triangles is mathcal o n s then given an eps 0 the adaptive method produces an approximation with an error less than eps subordinate to a partition with mathcal o eps 1 s triangles in only mathcal o eps 1 s operations in this paper employing a different type of adaptive partition we develop an adaptive method with properties similar to those of binev dahmen and devore s method but unlike their method our coarsening routine will be based on a transformation to a wavelet basis and we expect it to have better quantitative properties furthermore all our results are valid uniformly in the size of possible jumps of the diffusion coefficients since the algorithm uses solely approximations of the right hand side we can even allow right hand sides in h 1 omega that lie outside l 2 omega at least when they can be sufficiently well approximated by piecewise constants in our final adaptive algorithm all tolerances depend on an a posteriori estimate of the current error instead of an a priori one this can be expected to provide quantitative advantages

quasi optimal convergence rate for an adaptive finite element method we analyze the simplest and most standard adaptive finite element method afem with any polynomial degree for general second order linear symmetric elliptic operators as is customary in practice the afem marks exclusively according to the error estimator and performs a minimal element refinement without the interior node property we prove that the afem is a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops this geometric decay is instrumental to derive the optimal cardinality of the afem we show that the afem yields a decay rate of the energy error plus oscillation in terms of the number of degrees of freedom as dictated by the best approximation for this combined nonlinear quantity

efficient estimation of heterogeneous coefficients in panel data models with common shocks this paper investigates efficient estimation of heterogeneous coefficients in panel data models with common shocks which have been a particular focus of recent theoretical and empirical literature we propose a new two step method to estimate the heterogeneous coefficients in the first step the maximum likelihood ml method is first conducted to estimate the loadings and idiosyncratic variances the second step estimates the heterogeneous coefficients by using the structural relations implied by the model and replacing the unknown parameters with their ml estimates we establish the asymptotic theory of our estimator including consistency asymptotic representation and limiting distribution the two step estimator is asymptotically efficient in the sense that it has the same limiting distribution as the infeasible generalized least squares gls estimator intensive monte carlo simulations show that the proposed estimator performs robustly in a variety of data setups

the cross quantilogram measuring quantile dependence and testing directional predictability between time series this paper proposes the cross quantilogram to measure the quantile dependence between two time series we apply it to test the hypothesis that one time series has no directional predictability to another time series we establish the asymptotic distribution of the cross quantilogram and the corresponding test statistic the limiting distributions depend on nuisance parameters to construct consistent confidence intervals we employ the stationary bootstrap procedure we show the consistency of this bootstrap also we consider the self normalized approach which is shown to be asymptotically pivotal under the null hypothesis of no predictability we provide simulation studies and two empirical applications first we use the cross quantilogram to detect predictability from stock variance to excess stock return compared to existing tools used in the literature of stock return predictability our method provides a more complete relationship between a predictor and stock return second we investigate the systemic risk of individual financial institutions such as jp morgan chase goldman sachs and aig this article has supplementary materials online

optimal bandwidth selection in heteroskedasticity autocorrelation robust testing the paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors the studentization is based on robust standard errors with truncation lag m bt for some constant b 2 0 1 and sample size t it is shown that the nonstandard xed b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the nite sample distributions than the standard small b limit distribution we further show that for typical economic time series the optimal bandwidth that minimizes a weighted average of type i and type ii errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long run variance estimator a plug in procedure for implementing this optimal bandwidth is suggested and simulations not reported here con rm that the new plug in procedure works well in nite samples

heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects abstract this paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms we propose a bivariate kernel covariance estimator that nests existing estimators as special cases our estimator improves upon existing estimators in terms of robustness efficiency and adaptiveness for distributional approximations we considered two types of asymptotics the increasing smoothing asymptotics and the fixed smoothing asymptotics under the former asymptotics the wald statistic based on our covariance estimator converges to a chi square distribution under the latter asymptotics the wald statistic is asymptotically equivalent to a distribution that can be well approximated by an f distribution simulation results show that our proposed testing procedure works well in finite samples

estimation of longrun variance of continuous time stochastic process using discrete sample abstract this paper develops the methodology and asymptotic theory for the estimation of longrun variance of continuous time process we analyze the asymptotic bias and variance of the longrun variance estimator in continuous time and provide the optimal bandwidth balancing them off and minimizing the asymptotic mean squared error in the paper we present not only how to consistently estimate the longrun variance of continuous time process but also how to choose bandwidth optimally with data dependent procedures using discrete samples our framework is also useful to analyze the high frequency behaviors of usual longrun variance estimators for discrete time series in particular we show that they all diverge to infinity as the sampling frequency increases the relevance and usefulness of our continuous time framework and asymptotic theory are demonstrated by illustration and simulation

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

controlling the size of autocorrelation robust tests autocorrelation robust tests are notorious for suffering from size distortions and power problems we investigate under which conditions the size of autocorrelation robust tests can be controlled by an appropriate choice of critical value

error estimates for the numerical approximation of dirichlet boundary control for semilinear elliptic equations we study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control the control is the trace of the state on the boundary of the domain which is assumed to be a convex polygonal open set in mathbb r 2 piecewise linear finite elements are used to approximate the control as well as the state we prove that the error estimates are of order o h 1 1 p for some p 2 which is consistent with the w 1 1 p p gamma regularity of the optimal control

schwarz christoffel methods for conformal mapping of regions with a periodic boundary abstract numerical conformal mapping methods for regions with a periodic boundary have been developed these methods are based on the generalized schwarz christoffel equation and can deal with boundary curves of arbitrary forms i e made up of one or more rectifiable jordan curves high order quadrature rules have been implemented in order to increase accuracy of the mapping this is of particular relevance to highly accurate grid generation techniques required by for example implementation of high order compact finite difference discretization schemes

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

a fixed bandwidth view of the pre asymptotic inference for kernel smoothing with time series data this paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms based on the xed bandwidth asymptotic variance and the pre asymptotic variance we propose a heteroskedasticity and autocorrelation robust har variance estimator that achieves double robustness it is asymptotically valid regardless of whether the temporal dependence is present or not and whether the kernel smoothing bandwidth is held constant or allowed to decay with the sample size using the har variance estimator we construct the studentized test statistic and examine its asymptotic properties under both the xed smoothing and increasing smoothing asymptotics the xed smoothing approximation and the associated convenient t approximation achieve extra robustness it is asymptotically valid regardless of whether the truncation lag parameter governing the covariance weighting grows at the same rate as or a slower rate than the sample size finally we suggest a simulation based calibration approach to choose smoothing parameters that optimize testing oriented criteria simulation shows that the proposed procedures work very well in nite samples

local a posteriori error estimates for convex boundary control problems in this paper we derive some improved a posteriori error estimates for finite element approximation of neumann boundary control problems we first establish local upper a posteriori error estimates for both the state and the control approximation of the general convex boundary control problems we then derive local upper and lower a posteriori error estimates for a class of control problems that frequently appear in applications

spectrally accurate algorithm for moving boundary problems for the navier stokes equations a spectral algorithm based on the immersed boundary conditions ibc concept is developed for simulations of viscous flows with moving boundaries the algorithm uses a fixed computational domain with flow domain immersed inside the computational domain boundary conditions along the edges of the time dependent flow domain enter the algorithm in the form of internal constraints spectral spatial discretization uses fourier expansions in the stream wise direction and chebyshev expansions in the normal to the wall direction up to fourth order implicit temporal discretization methods have been implemented it has been demonstrated that the algorithm delivers the theoretically predicted accuracy in both time and space performances of various linear solvers employed in the solution process have been evaluated and a new class of solver that takes advantage of the structure of the coefficient matrix has been proposed the new solver results in a significant acceleration of computations as well as in a substantial reduction in memory requirements

error estimates for discontinuous galerkin time stepping schemes for robin boundary control problems constrained to parabolic pdes we consider fully discrete finite element approximations of a robin optimal boundary control problem constrained by linear parabolic pdes with rough initial data conforming finite element methods for spatial discretization combined with discontinuous time stepping galerkin schemes are being used for the space time discretization error estimates are proved under weak regularity hypotheses for the state adjoint and control variables computational examples validating our expected rates of convergence are also provided

heteroskedasticity autocorrelation robust standard errors using the bartlett kernel without truncation in this paper we analyze heteroskedasticity autocorrelation hac robust tests constructed using the bartlett kernel without truncation we show that while such an hac estimator is not consistent asymptotically valid testing is still possible we show that tests using the bartlett kernel without truncation are exactly equivalent to recent hac robust tests proposed by kiefer vogelsang and bunzel 2000 econometrica 68 pp 695 714

schwarz christoffel mappings a general approach abstract a general method is developed for constructing equations of the schwarz christoffel type these equations define conformal transformations between regions of the complex plane each of whose boundaries may consist of straight or continuously curved line segments and corners the more familiar types of schwarz christoffel equations are rederived and some new types are obtained

robust trend inference with series variance estimator and testing optimal smoothing parameter abstract the paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model the trends are estimated by the ols estimator and the long run variance lrv matrix is estimated by a series type estimator with carefully selected basis functions regardless of whether the number of basis functions k is fixed or grows with the sample size the wald statistic converges to a standard distribution it is shown that critical values from the fixed k asymptotics are second order correct under the large k asymptotics a new practical approach is proposed to select k that addresses the central concern of hypothesis testing the selected smoothing parameter is testing optimal in that it minimizes the type ii error while controlling for the type i error simulations indicate that the new test is as accurate in size as the nonstandard test of vogelsang and franses 2005 and as powerful as the corresponding wald test based on the large k asymptotics the new test therefore combines the advantages of the nonstandard test and the standard wald test while avoiding their main disadvantages power loss and size distortion respectively

the immersed boundary method a projection approach a new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion like previous methods a boundary force is applied at the immersed surface to satisfy the no slip constraint this extra constraint can be added to the incompressible navier stokes equations by introducing regularization and interpolation operators the current method gives prominence to the role of the boundary force acting as a lagrange multiplier to satisfy the no slip condition this role is analogous to the effect of pressure on the momentum equation to satisfy the divergence free constraint the current immersed boundary method removes slip and non divergence free components of the velocity field through a projection the boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger cfl numbers compared to some past methods symmetry and positive definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field examples show that the current formulation achieves second order temporal accuracy and better than first order spatial accuracy in l 2 norms for one and two dimensional test problems results from two dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies

a unifying theory of tests of rank the general principles underlying tests of matrix rank are investigated it is demonstrated that statistics for such tests can be seen as implicit functions of null space estimators in turn the asymptotic behaviour of the null space estimators is shown to determine the asymptotic behaviour of the statistics through a plug in principle the theory simplifies the asymptotics under a variety of alternatives of empirical relevance as well as misspecification clarifies the relationships between the various existing tests makes use of important results in the numerical analysis literature and motivates numerous new tests a brief monte carlo study illustrates the results

robustifying multivariate trend tests to nonstationary volatility abstract this article studies inference of multivariate trend model when the volatility process is nonstationary within a quite general framework we analyze four classes of tests based on least squares estimation one of which is robust to both weak serial correlation and nonstationary volatility the existing multivariate trend tests which either use non robust standard errors or rely on non standard distribution theory are generally non pivotal involving the unknown time varying volatility function in the limit two step residual based i i d bootstrap and wild bootstrap procedures are proposed for the robust tests and are shown to be asymptotically valid simulations demonstrate the effects of nonstationary volatility on the trend tests and the good behavior of the robust tests in finite samples

the completion of locally refined simplicial partitions created by bisection recently in found comput math 7 2 2007 245 269 we proved that an adaptive finite element method based on newest vertex bisection in two space dimensions for solving elliptic equations which is essentially the method from sinum 38 2000 466 488 by morin nochetto and siebert converges with the optimal rate the number of triangles n in the output partition of such a method is generally larger than the number m of triangles that in all intermediate partitions have been marked for bisection because additional bisections are needed to retain conforming meshes a key ingredient to our proof was a result from numer math 97 2004 219 268 by binev dahmen and devore saying that n n 0 cm for some absolute constant c where n 0 is the number of triangles from the initial partition that have never been bisected in this paper we extend this result to bisection algorithms of n simplices with that generalizing the result concerning optimality of the adaptive finite element method to general space dimensions

convergence and quasi optimality of an adaptive finite element method for elliptic robin boundary control problem abstract in this paper we focus on the convergence and quasi optimality of an adaptive finite element method for elliptic robin boundary control problems we use piecewise linear finite elements to approximate the state and the adjoint state variables and the variational discretization to approximate the control variable under mild assumption on the initial mesh we prove the contraction property for the sum of the energy errors of the state and adjoint state and the scaled error estimator on two consecutive adaptive loops the resulting linear convergence yields the quasi optimal convergence rate for the afem algorithm applied to our problem additionally some numerical results are provided to support our theoretical analysis