martingale transforms goodness of fit tests in regression models this paper discusses two goodness of fit testing problems the first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model while the second pertains to fitting a parametric regression model when the error distribution is unknown for the first problem the paper contains tests based on a certain martingale type transform of residual empirical processes the advantage of this transform is that the corresponding tests are asymptotically distribution free for the second problem the proposed asymptotically distribution free tests are based on innovation martingale transforms a monte carlo study shows that the simulated level of the proposed tests is close to the asymptotic level for moderate sample sizes

a finite volume solution to the geophysical electromagnetic forward problem using unstructured grids abstractthe application of unstructured grids can improve the solution of total field electromagnetic problems because these grids allow efficient local refinement of the mesh at the locations of high field gradients unstructured grids also provide the flexibility required for representing arbitrary topography and subsurface interfaces we investigated the generalization of the standard yee s staggered scheme to unstructured tetrahedral voronoi grids using a finite volume approach we discretized the helmholtz equation for the electric field in the frequency domain and solved the problem to find the projection of the total electric field along the edges of the tetrahedral elements to compute the electric and magnetic fields at the observation points an interpolation technique was employed which uses the edge vector interpolation functions of the tetrahedral elements to verify the presented scheme two examples were evaluated which revealed the computation of the total and secondary fields due to ele

contour regression a general approach to dimension reduction we propose a novel approach to sufficient dimension reduction in regression based on estimating contour directions of small variation in the response these directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response leading to simple and general contour regression scr and gcr methodology in comparison with existing sufficient dimension reduction techniques this contour based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions while maintaining sqrt n consistency and computational ease moreover it proves robust to departures from ellipticity we establish population properties for both scr and gcr and asymptotic properties for scr simulations to compare performance with that of standard techniques such as ordinary least squares sliced inverse regression principal hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses we demonstrate the use of contour based methods on a data set concerning soil evaporation

a consistent nonparametric test of parametric regression functional form in fixed effects panel data models abstract we propose a consistent test for a linear functional form against a nonparametric alternative in a fixed effects panel data model we show that the test has a limiting standard normal distribution under the null hypothesis and show that the test is a consistent test we also establish the asymptotic validity of a bootstrap procedure which is used to better approximate the finite sample null distribution of the test statistic simulation results show that the proposed test performs well for panel data with a large number of cross sectional units and a finite number of observations across time

conformal hybrid finite difference time domain and finite volume time domain a hybrid method that combines the finite difference time domain fdtd and the finite volume time domain fvtd methods is presented the fvtd based on a conformal and unstructured grid is used in the near vicinity of the surface of a scatterer and the fdtd is used to model the fields in the surrounding area the two are coupled together through interpolation the vertex based fvtd allows for more convenient and accurate interpolations than a conformal fdtd method the hybrid method is validated through two examples the scattering by a pec cube and sphere by comparison with the direct fdtd solution and with an exact mei series solution for the spherical case

a consistent test for the functional form of a regression based on a difference of variance estimators in this paper we study the problem of testing the functional form of a given regression model a consistent test is proposed which is based on the difference of the least squares variance estimator in the assumed regression model and a nonparametric variance estimator the corresponding test statistic can be shown to be asymptotically normal under the null hypothesis and under fixed alternatives with different rates of convergence corresponding to both cases this provides a simple asymptotic test where the asymptotic results can also be used for the calculation of the type ii error of the procedure at any particular point of the alternative and for the construction of tests for precise hypotheses finally the finite sample performance of the new test is investigated in a detailed simulation study which also contains a comparison with the commonly used tests

high order fdtd methods via derivative matching for maxwell s equations with material interfaces this paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high order finite difference time domain fdtd schemes of computational electromagnetics cem with material interfaces in one 1d and two spatial dimensions 2d by making use of fictitious points systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage to arbitrarily high orders of accuracy in principle while often limited by numerical instability orders up to 16 and 12 are achieved respectively in 1d and 2d detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded fdtd methods as natural generalizations of the high order fdtd schemes the proposed derivative matching methods automatically reduce to the standard fdtd schemes when the material interfaces are absent an interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code another feature of the present approach is that it can be robustly implemented with other high accuracy time domain approaches such as the multiresolution time domain method and the local spectral time domain method to cope with material interfaces numerical experiments on both 1d and 2d problems are carried out to test the convergence examine the stability access the efficiency and explore the limitation of the proposed methods it is found that operating at their best capacity the proposed high order schemes could be over 2000 times more efficient than their fourth order versions in 2d in conclusion the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high order schemes for numerical solution of time domain maxwell s equations with material interfaces

bootstrap approximations in model checks for regression abstract let m m be a parametric model for an unknown regression function m for example m may consist of all polynomials or trigonometric polynomials with a given bound on the degree to check the full model m i e to test for h 0 m e m it is known that optimal tests should be based on the empirical process of the regressors marked by the residuals in this article we show that the distribution of this process may be approximated by the wild bootstrap the method is applied to simulated datasets as well as to real data

likelihood based sufficient dimension reduction we obtain the maximum likelihood estimator of the central subspace under conditional normality of the predictors given the response analytically and in simulations we found that our new estimator can preform much better than sliced inverse regression sliced average variance estimation and directional regression and that it seems quite robust to deviations from normality

an explicit fourth order orthogonal curvilinear staggered grid fdtd method for maxwell s equations the explicit fourth order staggered finite difference time domain scheme previously proposed for a cartesian grid is extended to maxwell s equations in an orthogonal curvilinear coordinate system and applied to electromagnetic wave problems a simple technique is also presented for generating orthogonal curvilinear grids that conform to the material boundaries and interfaces of the problem numerical experiments are presented to illustrate the efficiency and accuracy of the method

a constructive approach to the estimation of dimension reduction directions in this paper we propose two new methods to estimate the dimension reduction directions of the central subspace cs by constructing a regression model such that the directions are all captured in the regression mean compared with the inverse regression estimation methods e g j amer statist assoc 86 1991 328 332 j amer statist assoc 86 1991 316 342 j amer statist assoc 87 1992 1025 1039 the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable and have better performance than the inverse regression estimation methods for finite samples compared with the direct regression estimation methods e g j amer statist assoc 84 1989 986 995 ann statist 29 2001 1537 1566 j r stat soc ser b stat methodol 64 2002 363 410 which can only estimate the directions of cs in the regression mean the new methods can detect the directions of cs exhaustively consistency of the estimators and the convergence of corresponding algorithms are proved

an adaptive estimation of dimension reduction space summary searching for an effective dimension reduction space is an important problem in regression especially for high dimensional data we propose an adaptive approach based on semiparametric models which we call the conditional minimum average variance estimation mave method within quite a general setting the mave method has the following advantages most existing methods must undersmooth the nonparametric link function estimator to achieve a faster rate of consistency for the estimator of the parameters than for that of the nonparametric function in contrast a faster consistency rate can be achieved by the mave method even without undersmoothing the nonparametric link function estimator the mave method is applicable to a wide range of models with fewer restrictions on the distribution of the covariates to the extent that even time series can be included because of the faster rate of consistency for the parameter estimators it is possible for us to estimate the dimension of the space consistently the relationship of the mave method with other methods is also investigated in particular a simple outer product gradient estimator is proposed as an initial estimator in addition to theoretical results we demonstrate the efficacy of the mave method for high dimensional data sets through simulation two real data sets are analysed by using the mave approach

multilevel surface decomposition algorithm for rapid evaluation of transient near field to far field transforms a fast multilevel algorithm with reduced memory requirements for the evaluation of transient near field to far field transforms is presented the computational scheme is based on a hierarchical decomposition of an arbitrary shaped enclosing surface over which the near fields of an antenna or a scatterer are given for surface subdomains at the highest decomposition level the angular temporal far field patterns are calculated directly from the known near fields over a sparse angular grid of directions and a short temporal duration the multilevel computation comprises angular and temporal interpolations thus increasing angular resolution and temporal duration of radiation patterns while aggregating the subdomain contributions between successive decomposition levels these steps are repeated until obtaining the transient far field response of the whole enclosing surface the computational complexity of the proposed algorithm is substantially lower than that of the direct evaluation reduction in memory requirements is obtained by formulating the algorithm as a marching on in time windowed scheme this approach allows for embedding of the accelerated transforms within existing near field modeling tools

testing parametric assumptions of trends of a nonstationary time series the paper considers testing whether the mean trend of a nonstationary time series is of certain parametric forms a central limit theorem for the integrated squared error is derived and a hypothesis testing procedure is proposed the method is illustrated in a simulation study and is applied to assess the mean pattern of lifetime maximum wind speeds of global tropical cyclones from 1981 to 2006 we also revisit the trend pattern in the central england temperature series copyright 2011 oxford university press

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

flux limiting embedded boundary technique for electromagnetic fdtd a general approach for incorporating embedded boundaries into an electromagnetic finite difference time domain fdtd code is presented this algorithm is shown to satisfy gauss s law and enforces no magnetic monopoles while maintaining a globally second order result first order at physical boundaries with no added time step restriction theoretically predicted superior results are shown with an 11 time step reduction from the courant stability limit this is achieved through a physics based flux limiting scheme near physical boundaries stability local truncation error and energy conservation analysis are also provided

a finite volumes based 3 d low dispersion fdtd algorithm an algorithm extension to three dimensions is developed and presented for the highly phase coherent modified second order in time fourth order in space or m24 finite difference time domain fdtd algorithm a finite volumes approach in conjunction with yee s standard fdtd lattice is used for algorithm development the corresponding dispersion relation is also developed analyzed and compared to both the standard second order and fourth order fdtd algorithms as well as to two closely related high order phase coherent algorithms wideband algorithm attributes are also presented as well as sets of ready to use optimized algorithm coefficients

nonparametric stochastic frontiers a local maximum likelihood approach this paper proposes a new approach to handle nonparametric stochastic frontier sf models it is based on local maximum likelihood techniques the model is presented as encompassing some anchorage parametric model in a nonparametric way first we derive asymptotic properties of the estimator for the general case local linear approximations then the results are tailored to a sf model where the convoluted error term efficiency plus noise is the sum of a half normal and a normal random variable the parametric anchorage model is a linear production function with a homoscedastic error term the local approximation is linear for both the production function and the parameters of the error terms the performance of our estimator is then established in finite samples using simulated data sets as well as with a cross sectional data on us commercial banks the methods appear to be robust numerically stable and particularly useful for investigating a production process and the derived efficiency scores

exactly energy conserving semi implicit particle in cell formulation abstract we report a new particle in cell pic method based on the semi implicit approach the novelty of the new method is that unlike any of its semi implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly recent research has presented fully implicit methods where energy conservation is obtained as part of a non linear iteration procedure the new method referred to as energy conserving semi implicit method ecsim instead does not require any non linear iteration and its computational cycle is similar to that of explicit pic the properties of the new method are i it conserves energy exactly to round off for any time step or grid spacing ii it is unconditionally stable in time freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step iii it eliminates the constraint of the finite grid instability allowing the user to select any desired resolution without being forced to resolve the debye length iv the particle mover has a computational complexity identical to that of the explicit pic only the field solver has an increased computational cost the new ecsim is tested in a number of benchmarks where accuracy and computational performance are tested

a new test for the parametric form of the variance function in non parametric regression in the common non parametric regression model the problem of testing for the parametric form of the conditional variance is considered a stochastic process based on the difference between the empirical processes that are obtained from the standardized non parametric residuals under the null hypothesis of a specific parametric form of the variance function and the alternative is introduced and its weak convergence established this result is used for the construction of a kolmogorov smimov and a cramer von mises type of statistic for testing the parametric form of the conditional variance the consistency of a bootstrap approximation is established and the finite sample properties of this approximation are investigated by means of a simulation study in particular the new procedure is compared with some of the currently available methods for this problem

asymptotics for sliced average variance estimation in this paper we systematically study the consistency of sliced average variance estimation save the findings reveal that when the response is continuous the asymptotic behavior of save is rather different from that of sliced inverse regression sir sir can achieve sqrt n consistency even when each slice contains only two data points however save cannot be sqrt n consistent and it even turns out to be not consistent when each slice contains a fixed number of data points that do not depend on n where n is the sample size these results theoretically confirm the notion that save is more sensitive to the number of slices than sir taking this into account a bias correction is recommended in order to allow save to be sqrt n consistent in contrast when the response is discrete and takes finite values sqrt n consistency can be achieved therefore an approximation through discretization which is commonly used in practice is studied a simulation study is carried out for the purposes of illustration

a novel dual field time domain finite element domain decomposition method for computational electromagnetics a novel dual field time domain finite element domain decomposition method is presented for numerical simulation of electromagnetic phenomena the method divides the computation domain into several non overlapping subdomains and computes both the electric and magnetic fields in each subdomain by solving second order vector wave equations a leapfrog like scheme is employed in the time marching to update the alternating electric and magnetic fields adjacent subdomains are related to each other by the equivalent surface currents on the subdomain interfaces which are also updated in a similar fashion the method requires minimum communications between the subdomains thus is highly suitable for parallel computations the proposed domain decomposition method is particularly attractive for the numerical simulation of finite arrays and large scale electromagnetic problems numerical stability and dispersion error analyses are conducted and several radiation examples are presented to demonstrate the accuracy and efficiency of the method

statistics of cycles how loopy is your network we study the distribution of cycles of length h in large networks of size n 1 and find it to be an excellent ergodic estimator even in the extreme inhomogeneous case of scale free networks the distribution is sharply peaked around a characteristic cycle length h n our results suggest that h and the exponent might usefully characterize broad families of networks in addition to an exact counting of cycles in hierarchical nets we present a monte carlo sampling algorithm for approximately locating h and reliably determining our empirical results indicate that for small random scale free nets of degree exponent 1 1 and grows as the nets become larger

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

dimension reduction for conditional mean in regression in many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictors and less concerned with the other aspects of the conditional distribution in this paper we develop dimension reduction methods that incorporate this consideration we introduce the notion of the central mean subspace cms a natural inferential object for dimension reduction when the mean function is of interest we study properties of the cms and develop methods to estimate it these methods include a new class of estimators which requires fewer conditions than phd and which displays a clear advantage when one of the conditions for phd is violated cms also reveals a transparent distinction among the existing methods for dimension reduction ols phd sir and save we apply the new methods to a data set involving recumbent cows

the finite difference time domain fdtd and the finite volume time domain fvtd methods in solving maxwell s equations the finite difference time domain fdtd and its current generalizations have been demonstrated to be useful and powerful tools for the calculation of the radar cross section rcs of complicated objects the radiation of antennas in the presence of other structures and other applications the mathematical techniques for conformal fdtd have matured the primary impediments to its implementation are the complex geometries and material properties associated with the problem even under these circumstances fdtd is more flexible to implement because it is based on first principles instead of a clever mathematical trick this paper gives an account of some new results on conformal fdtd obtained by the authors and their associates at lockheed martin space company since 1988 the emphasis is on nonsmooth boundary condition simulation

on specification testing of ordered discrete choice models we discuss how to test the specification of an ordered discrete choice model against a general alternative two main approaches can be followed tests based on moment conditions and tests based on comparisons between parametric and nonparametric estimations following these approaches various statistics are proposed and their asymptotic properties are discussed the performance of the statistics is compared by means of simulations an easy to compute variant of the standard moment based statistic yields the best results in models with a single explanatory variable in models with various explanatory variables the results are less conclusive since the relative performance of the statistics depends on both the fit of the model and the type of misspecification that is considered

generalized likelihood ratio statistics and wilks phenomenon likelihood ratio theory has had tremendous success in parametric inference due to the fundamental theory of wilks yet there is no general applicable approach for nonparametric inferences based on function estimation maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting even if they exist they are hard to find and can not be optimal as shown in this paper we introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics a new s wilks phenomenon is unveiled we demonstrate that a class of the generalized likelihood statistics based on some appropriate nonparametric estimators are asymptotically distribution free and follow chi 2 distributions under null hypotheses for a number of useful hypotheses and a variety of useful models including gaussian white noise models nonparametric regression models varying coefficient models and generalized varying coefficient models we further demonstrate that generalized likelihood ratio statistics are asymptotically optimal in the sense that they achieve optimal rates of convergence given by ingster they can even be adaptively optimal in the sense of spokoiny by using a simple choice of adaptive smoothing parameter our work indicates that the generalized likelihood ratio statistics are indeed general and powerful for nonparametric testing problems based on function estimation

on directional regression for dimension reduction we introduce directional regression dr as a method for dimension reduction like contour regression dr is derived from empirical directions but achieves higher accuracy and requires substantially less computation dr naturally synthesizes the dimension reduction estimators based on conditional moments such as sliced inverse regression and sliced average variance estimation and in doing so combines the advantages of these methods under mild conditions it provides exhaustive and consistent estimate of the dimension reduction space we develop the asymptotic distribution of the dr estimator and from that a sequential test procedure to determine the dimension of the central space we compare the performance of dr with that of existing methods by simulation and find strong evidence of its advantage over a wide range of models finally we apply dr to analyze a data set concerning the identification of hand written digits

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

conformal fdtd methods to avoid time step reduction with and without cell enlargement during the last decades there have been considerable efforts to develop accurate and yet simple conformal methods for modelling curved boundaries within the finite difference time domain fdtd algorithm in an earlier publication we proposed the uniformly stable conformal usc approach as a general three dimensional extension of fdtd without the need to reduce the maximum stable time step the main idea of usc is the usage of virtually enlarged cells near to the boundary leading to an increased implementation effort in this paper we review the usc method and introduce a new simple and accurate conformal scheme which does not use such enlarged cells this simplified conformal sc scheme has the same number of operations and algorithmic logic as the standard staircase method and thus is easily realizable in existing fdtd codes like usc it leads to accurate results without time step reduction showing a nearly second order convergence in practice the method is verified and compared to other approaches by means of several numerical 2d and 3d examples

dimension reduction in regressions through cumulative slicing estimation in this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction in parallel to the classical slicing estimation we develop three methods that are termed respectively as cumulative mean estimation cumulative variance estimation and cumulative directional regression the strong consistency for p o n1 2 log n and the asymptotic normality for p o n1 2 are established where p is the dimension of the predictors and n is sample size such asymptotic results improve the rate p o n1 3 in many existing contexts of semiparametric modeling in addition we propose a modified bic type criterion to estimate the structural dimension of the central subspace its consistency is established when p o n1 2 extensive simulations are carried out for comparison with existing methods and a real data example is presented for illustration

convergent cartesian grid methods for maxwell s equations in complex geometries a convergent second order cartesian grid finite difference scheme for the solution of maxwell s equations is presented the scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly hence eliminating problems caused by staircasing and contrary to the popular yee scheme enforces the correct jump conditions on the field components across material interfaces a detailed analysis of the accuracy of the new embedding scheme is presented confirming its second order global accuracy furthermore the scheme is proven to be a bounded error scheme and thus convergent conditions for fully discrete stability is furthermore established this enables the derivation of bounds for fully discrete stability with cfl restrictions being almost identical to those of the much simpler yee scheme the analysis exposes that the effects of staircasing as well as a lack of properly enforced jump conditions on the field components have significant consequences for the global accuracy it is among other things shown that for cases in which a field component is discontinuous along a grid line as happens at general two and three dimensional material interfaces the yee scheme may exhibit local divergence and loss of global convergence to validate the analysis several one and two dimensional test cases are presented showing an improvement of typically 1 to 2 orders of accuracy at little or no additional computational cost over the yee scheme which in most cases exhibits first order accuracy c 2001 academic press

model checks for regression an innovation process approach in the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus smooth and directional goodness of fit tests since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain we propose to replace this process by its innovation martingale it turns out that the resulting tests are asymptotically distribution free under composite null models and may be readily performed a simulation study is included which indicates that the distributional approximations already work for small to moderate sample sizes

divergence preserving discrete surface integral methods for maxwell s curl equations using non orthogonal unstructured grids abstract several new discrete surface integral methods for solving maxwell s equations in the time domain are presented these methods which allow the use of general non orthogonal mixed polyhedral unstructured grids are direct generalizations of the canonical staggered grid finite difference method these methods are conservative in that they locally preserve divergence or charge employing mixed polyhedral cells hexahedral tetrahedral etc these methods allow more accurate modeling of non rectangular structures and objects because the traditional stair stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided numerical results demonstrating the accuracy of these new methods are presented

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

model checking for parametric single index models a dimension reduction model adaptive approach summary local smoothing testing based on multivariate non parametric regression estimation is one of the main model checking methodologies in the literature however the relevant tests suffer from the typical curse of dimensionality resulting in slow rates of convergence to their limits under the null hypothesis and less deviation from the null hypothesis under alternative hypotheses this problem prevents tests from maintaining the level of significance well and makes tests less sensitive to alternative hypotheses in the paper a model adaptation concept in lack of fit testing is introduced and a dimension reduction model adaptive test procedure is proposed for parametric single index models the test behaves like a local smoothing test as if the model were univariate it is consistent against any global alternative hypothesis and can detect local alternative hypotheses distinct from the null hypothesis at a fast rate that existing local smoothing tests can achieve only when the model is univariate simulations are conducted to examine the performance of our methodology an analysis of real data is shown for illustration the method can be readily extended to global smoothing methodology and other testing problems

model checking in regression via dimension reduction lack of fit checking for parametric and semiparametric models is essential in reducing misspecification the efficiency of most existing model checking methods drops rapidly as the dimension of the covariates increases we propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern consistency of the method is proved for parametric and semiparametric regression models a bootstrap implementation is also discussed simulation comparisons with several existing methods are made suggesting that the proposed methods are more efficient than the existing methods when the dimension increases air pollution data from chicago are used to illustrate the procedure

sufficient dimension reduction through discretization expectation estimation in the context of sufficient dimension reduction the goal is to parsimoniously recover the central subspace of a regression model many inverse regression methods use slicing estimation to recover the central subspace the efficacy of slicing estimation depends heavily upon the number of slices however the selection of the number of slices is an open and long standing problem in this paper we propose a discretization expectation estimation method which avoids selecting the number of slices while preserving the integrity of the central subspace this generic method assures root n consistency and asymptotic normality of slicing estimators for many inverse regression methods and can be applied to regressions with multivariate responses a bic type criterion for the dimension of the central subspace is proposed comprehensive simulations and an illustrative application show that our method compares favourably with existing estimators

development of a godunov method for maxwell s equations with adaptive mesh refinement in this paper we present a second order 3d method for maxwell s equations based on a godunov scheme with adaptive mesh refinement amr in order to achieve it we apply a limiter which better preserves extrema and boundary conditions based on a characteristic fields decomposition despite being more complex simplifications in the boundary conditions make the resulting method competitive in computer time consumption and accuracy compared to fdtd amr allows us to simulate systems with a sharp step in material properties with negligible rebounds and also large domains with accuracy in small wavelengths a godunov method is used to solve a conservative law s form of maxwell s equations suitable interpolation schemes and limiters allow solving maxwell s equations with amr a new numerical method for boundary conditions allows to simulate unbounded domains using amr allows solving big domain simulations in reasonable computational time

a spatial high order hexahedral discontinuous galerkin method to solve maxwell s equations in time domain in this paper we present a non dissipative spatial high order discontinuous galerkin method to solve the maxwell equations in the time domain the non intuitive choice of the space of approximation and the basis functions induce an important gain for mass stiffness and jump matrices in terms of memory this spatial approximation combined with a leapfrog scheme in time leads also to a fast explicit and accurate method a study of the dispersive error is carried out and a stability condition for the proposed scheme is established some comparisons with other schemes are presented to validate the new scheme and to point out its advantages finally in order to improve the efficiency of the method in terms of cpu time on general unstructured meshes a strategy of local time stepping is proposed

a class of difference schemes with flexible local approximation solutions of many physical problems have salient local features that are qualitatively known a priori for example singularities at point sources edge and corners boundary layers derivative jumps at material interfaces strong dipole field components near polarized spherical particles cusps of electronic wavefunctions at the nuclei electrostatic double layers around colloidal particles etc the known methods capable of providing flexible local approximation of such features include the generalized finite element partition of unity method special variational difference schemes in broken sobolev spaces and a few other specialized techniques in the proposed new class of flexible local approximation methods flame a desirable set of local approximating functions such as cylindrical or spherical harmonics plane waves harmonic polynomials etc defines a finite difference scheme on a chosen grid stencil one motivation is to minimize the notorious staircase effect at curved and slanted interface boundaries however the new approach has much broader applications as illustrative examples the paper presents arbitrarily high order 3 point schemes for the 1d schrodinger equation and a 1d singular equation schemes for electrostatic interactions of colloidal particles electromagnetic wave propagation and scattering plasmon resonances moreover many classical finite difference schemes including the collatz mehrstellen schemes are direct particular cases of flame

significance testing in nonparametric regression based on the bootstrap this paper proposes a test for selecting explanatory variables in nonparametric regression the test does not need to estimate the conditional expectation function given all the variables but only those which are significant under the null hypothesis this feature is computationally convenient and solves in part the problem of the curse of dimensionality when selecting regressors in a nonparametric context the proposed test statistic is based on functionals of a u process contiguous alternatives converging to the null at a rate n 1 2 can be detected the asymptotic null distribution of the statistic depends on certain features of the data generating process and asymptotic tests are difficult to implement except in rare circumstances we justify the consistency of two easy to implement bootstrap tests which exhibit good level accuracy for fairly small samples according to the reported monte carlo simulations these results are also applicable to test other interesting restrictions on nonparametric curves like partial linearity and conditional independence

subgraphs in random networks understanding the subgraph distribution in random networks is important for modeling complex systems in classic erdos networks which exhibit a poissonian degree distribution the number of appearances of a subgraph g with n nodes and g edges scales with network size as approximately n n g however many natural networks have a non poissonian degree distribution here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks characterized by an arbitrary degree sequence we find scaling rules for the commonly occurring case of directed scale free networks in which the outgoing degree distribution scales as p k approximately k gamma considering the power exponent of the degree distribution gamma as a control parameter we show that random networks exhibit transitions between three regimes in each regime the subgraph number of appearances follows a different scaling law approximately nalpha where alpha n g s 1 for gamma gamma c where s is the maximal outdegree in the subgraph and gamma c s 1 we find that certain subgraphs appear much more frequently than in erdos networks these results are in very good agreement with numerical simulations this has implications for detecting network motifs subgraphs that occur in natural networks significantly more than in their randomized counterparts