asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

a localized re initialization equation for the conservative level set method the conservative level set methodology for interface transport is modified to allow for localized level set re initialization this approach is suitable to applications in which there is a significant amount of spatial variability in level set transport the steady state solution of the modified re initialization equation matches that of the original conservative level set provided an additional eikonal equation is solved which can be done efficiently through a fast marching method fmm implemented within the context of the accurate conservative level set method acls desjardins et al 2008 6 the fmm solution of this eikonal equation comes at no additional cost a metric for the appropriate amount of local re initialization is proposed based on estimates of local flow deformation and numerical diffusion the method is compared to standard global re initialization for two test cases yielding the expected results that minor differences are observed for zalesak s disk and improvements in both mass conservation and interface topology are seen for a drop deforming in a vortex finally the method is applied to simulation of a viscously damped standing wave and a three dimensional drop impacting on a shallow pool negligible differences are observed for the standing wave as expected for the last case results suggest that spatially varying re initialization provides a reduction in spurious interfacial corrugations improvements in the prediction of radial growth of the splashing lamella and a reduction in conservation errors as well as a reduction in overall computational cost that comes from improved conditioning of the pressure poisson equation due to the removal of spurious corrugations

diagnostic tests for homoskedasticity in spatial cross sectional or panel models abstract we propose an adjusted quasi score aqs method for constructing tests for homoskedasticity in spatial econometric models we first obtain an aqs function by adjusting the score type function from the given model to achieve unbiasedness and then develop an outer product of martingale difference opmd estimate of its variance in standard problems where a genuine quasi score vector is available the aqs opmd method leads to finite sample improved tests over the usual methods more importantly in non standard problems where a genuine quasi score is not available and the usual methods fail the proposed aqs opmd method provides feasible solutions the aqs tests are formally derived and asymptotic properties examined for three representative models spatial cross sectional static and dynamic panel models monte carlo results show that the proposed aqs tests have good finite sample properties

central limit theorems for quadratic forms with time domain conditions we establish the central limit theorem for quadratic forms t s 1 n b t s p m n x t x s of the bivariate appell polynomials p m n x t x s under time domain conditions these conditions relate the weights b t and the covariances of the sequences p m n x t x s and x t the time domain approach together with the spectral domain approach developed earlier yields a general set of conditions for central limit theorems

a remark on computing distance functions we propose a new method for the reconstruction of the signed distance function in the context of level set methods the new method is a modification of the algorithm which makes use of the pde equation for the distance function introduced by m sussman p smereka and s osher 1994 j comput phys 119 146 it is based mainly on the use of a truly upwind discretization near the interface comparison with the previous algorithm shows a definite improvement when used with a first order upwind scheme the method provides first order accuracy for the signed distance function in the whole computational domain and second order accuracy in the location of the interface a second order version of the method is also presented

on the bootstrap for moran s i test for spatial dependence this paper is concerned with the use of the bootstrap for statistics in spatial econometric models with a focus on the test statistic for moran s i test for spatial dependence we show that for many statistics in spatial econometric models the bootstrap can be studied based on linear quadratic lq forms of disturbances by proving the uniform convergence of the cumulative distribution function for lq forms to that of a normal distribution we show that the bootstrap is generally consistent for test statistics that can be approximated by lq forms including moran s i possible asymptotic refinements of the bootstrap are most commonly studied using edgeworth expansions for spatial econometric models we may establish asymptotic refinements of the bootstrap based on asymptotic expansions of lq forms when the disturbances are normal we prove the existence of the usual edgeworth expansions for lq forms when the disturbances are not normal we establish an asymptotic expansion of lq forms based on martingales these results are applied to show the second order correctness of the bootstrap for moran s i test

a numerical method for computing minimal surfaces in arbitrary dimension in this paper we propose a numerical method for computing minimal surfaces with fixed boundaries the level set method is used to evolve a codimension 1 surface with fixed codimension 2 boundary in r n under mean curvature flow for n 3 the problem has been approached in d l chopp 1993 and l t cheng d l chopp computing minimal surfaces via level set curvature flow j comput phys 106 1 1993 77 91 and l t cheng the level set method applied to geometrically based motion materials science and image processing ucla cam report 00 20 using the level set method but with a more complicated boundary conditions the method we present can be generalized straightforward to arbitrary dimension and the framework in which it is presented is dimension independent examples are shown for n 2 3 4

crystal growth and dendritic solidification we present a numerical method which computes the motion of complex solid liquid boundaries in crystal growth the model we solve includes physical effects such as crystalline anisotropy surface tension molecular kinetics and undercooling the method is based on two ideas first the equations of motion are recast as a single history dependent boundary integral equation on the solid liquid boundary a fast algorithm is used to solve the integral equation efficiently second the boundary is moved by solving a hamiltonjacobi type equation on a fixed domain formulated by osher and sethian for a function in which the boundary is a particular level set this equation is solved by finite difference schemes borrowed from the technology of hyperbolic conservation laws the two ideas are combined by constructing a smooth extension of the normal velocity off the moving boundary in a way suggested by the physics of the problem our numerical experiments show the evolution of complex crystalline shapes development of large spikes and corners dendrite formation and side branching and pieces of solid merging and breaking off freely

finite element methods on very large dynamic tubular grid encoded implicit surfaces the simulation of physical processes on interfaces and a variety of applications in geometry processing and geometric modeling are based on the solution of partial differential equations on curved and evolving surfaces frequently an implicit level set type representation of these surfaces is the most effective and computationally advantageous approach this paper addresses the computational problem of how to solve partial differential equations on highly resolved level sets with an underlying very high resolution discrete grid these high resolution grids are represented in a very efficient dynamic tubular grid encoding format for a narrow band a reaction diffusion model on a fixed surface and surface evolution driven by a nonlinear geometric diffusion approach by isotropic or truly anisotropic curvature motion are investigated as characteristic model problems the proposed methods are based on semi implicit finite element discretizations directly on these narrow bands require only standard numerical quadrature and allow for large time steps to combine large time steps with a very thin and thus storage inexpensive narrow band suitable transparent boundary conditions on the boundary of the narrow band and a nested iteration scheme in each time step are investigated this nested iteration scheme enables the discrete interfaces to move in a single time step significantly beyond the domain of the narrow band of the previous time step furthermore algorithmic tools are provided to assemble finite element matrices and to apply matrix vector operators via fast cache coherent access to the dynamic tubular grid encoded data structure the consistency of the presented approach is evaluated and various numerical examples show its application potential

dynamic spatial panel models networks common shocks and sequential exogeneity this paper considers a class of generalized methods of moments gmm estimators for general dynamic panel models allowing for weakly exogenous covariates and cross sectional dependence due to spatial lags unspecified common shocks and time varying interactive effects we significantly expand the scope of the existing literature by allowing for endogenous time varying spatial weight matrices without imposing explicit structural assumptions on how the weights are formed an important area of application is in social interaction and network models where our specification can accommodate data dependent network formation we consider an exemplary social interaction model and show how identification of the interaction parameters is achieved through a combination of linear and quadratic moment conditions for the general setup we develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions this is an important ingredient to a tractable asymptotic distribution of our estimators in general the asymptotic distribution of our estimators is found to be mixed normal due to random norming however the asymptotic distribution of our test statistics is still chi square

large sample properties of the matrix exponential spatial specification with an application to fdi this paper studies large sample properties of the matrix exponential spatial specification mess we find that the quasi maximum likelihood estimator qmle for the mess is consistent under heteroskedasticity a property not shared by the qmle of the sar model for the general model that has mess in both the dependent variable and disturbances labeled mess 1 1 the qmle can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two mess processes are commutative we also consider the generalized method of moments estimator gmme in the homoskedastic case we derive a best gmme that is as efficient as the maximum likelihood estimator under normality and can be asymptotically more efficient than the qmle under non normality in the heteroskedastic case an optimal gmme can be more efficient than the qmle asymptotically the qml approach for the mess model has the computational advantage over that of a sar model the computational simplicity carries over to mess models with any finite order of spatial matrices no parameter range needs to be imposed in order for the model to be stable results of monte carlo experiments for finite sample properties of the estimators are reported finally the mess 1 1 is applied to belgium s outward fdi data and we observe that the dominant motivation of belgium s outward fdi lies in finding cheaper factor inputs

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

rapid and accurate computation of the distance function using grids we present two fast and simple algorithms for approximating the distance function for given isolated points on uniform grids the algorithms are then generalized to compute the distance to piecewise linear objects by incorporating the geometry of huygens principle in the reverse order with the classical viscosity solution theory for the eikonal equation u 1 the algorithms become almost purely algebraic and yield very accurate approximations the generalized closest point formulation used in the second algorithm provides a framework for further extension to compute the distance accurately to smooth geometric objects on different grid geometries without the construction of the voronoi diagrams this method provides a fast and simple translator of data commonly given in computational geometry to the volumetric representation used in level set methods

a simple level set method for solving stefan problems a simple level set method for solving stefan problems is presented this method can be applied to problems involving dendritic solidification our method consists of an implicit finite difference scheme for solving the heat equation and a level set approach for capturing the front between solid and liquid phases of a pure substance our method is accurate with respect to some exact solutions of the stefan problem results indicate that this method can handle topology changes and complicated interfacial shapes and that it can numerically simulate many of the physical features of dendritic solidification

exact and higher order properties of the mle in spatial autoregressive models with applications to inference abstract the quasi maximum likelihood estimator for the autoregressive parameter in a spatial autoregression usually cannot be written explicitly in terms of the data a rigorous analysis of the first order asymptotic properties of the estimator under some assumptions on the evolution of the spatial design matrix is available in lee 2004 but very little is known about its exact or higher order properties in this paper we first show that the exact cumulative distribution function of the estimator can under mild assumptions be written in terms of that of a particular quadratic form simple examples are used to illustrate important exact properties of the estimator that follow from this representation in general models a complete exact analysis is not possible but a higher order saddlepoint approximation is made available by the main result we use this approximation to construct confidence intervals for the autoregressive parameter coverage properties of the proposed confidence intervals are studied by monte carlo simulation and are found to be excellent in a variety of circumstances

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

tree methods for moving interfaces fast adaptive numerical methods for solving moving interface problems are presented the methods combine a level set approach with frequent redistancing and semi lagrangian time stepping schemes which are explicit yet unconditionally stable a quadtree mesh is used to concentrate computational effort on the interface so the methods move an interface withndegrees of freedom ino nlogn work per time step efficiency is increased by taking large time steps even for parabolic curvature flows the methods compute accurate viscosity solutions to a wide variety of difficult moving interface problems involving merging anisotropy faceting and curvature

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

estimation of fixed effects panel regression models with separable and nonseparable space time filters abstract this paper considers a quasi maximum likelihood estimation for a linear panel data model with time and individual fixed effects where the disturbances have dynamic and spatial correlations which might be spatially stable or unstable we first consider both separable and nonseparable space time filters for the stable model the separable space time filter is subject to a parametric restriction which results in relative computational simplicity in contrast to the spatial econometrics literature we expose economic restrictions imposed by the separable space time filter model and explore computational tractability of the nonseparable filter model throughout this paper the effect of initial observations is taken into account which results in an exact likelihood function for estimation this is important when the span of time periods is short we then investigate spatial unstable cases where we propose to apply a spatial differencing to all variables in the regression equation as a data transformation which may eliminate unstable or explosive spatial components in order to achieve a robust estimator for estimates of the parameters in both the regression part and the disturbance process they are n t consistent and asymptotically centered normal regardless of whether t is large or not and whether the process is stable or not

shape based mutual segmentation we present a novel variational approach for simultaneous segmentation of two images of the same object taken from different viewpoints due to noise clutter and occlusions neither of the images contains sufficient information for correct object background partitioning the evolving object contour in each image provides a dynamic prior for the segmentation of the other object view we call this process mutual segmentation the foundation of the proposed method is a unified level set framework for region and edge based segmentation associated with a shape similarity term the suggested shape term incorporates the semantic knowledge gained in the segmentation process of the image pair accounting for excess or deficient parts in the estimated object shape transformations including planar projectivities between the object views are accommodated by a registration process held concurrently with the segmentation the proposed segmentation algorithm is demonstrated on a variety of image pairs the homography between each of the image pairs is estimated and its accuracy is evaluated

a general method for third order bias and variance corrections on a nonlinear estimator motivated by a recent study of bao and ullah 2007a on finite sample properties of mle in the pure sar spatial autoregressive model a general method for third order bias and variance corrections on a nonlinear estimator is proposed based on stochastic expansion and bootstrap working with concentrated estimating equation simplifies greatly the high order expansions for bias and variance a simple bootstrap procedure overcomes a major difficulty in analytically evaluating expectations of various quantities in the expansions the method is then studied in detail using a more general sar model with its effectiveness in correcting bias and improving inference fully demonstrated by extensive monte carlo experiments compared with the analytical approach the proposed approach is much simpler and has a much wider applicability the validity of the bootstrap procedure is formally established the proposed method is then extended to the case of more than one nonlinear estimator

computing multivalued physical observables for the semiclassical limit of the schrodinger equation we develop a level set method for the computation of multivalued physical observables density velocity etc for the semiclassical limit of the schrodinger equation this method uses an eulerian formulation and applies directly to arbitrary number of space dimensions the main idea is to evolve the density near an n dimensional manifold that is identified as the common zeros of n level set functions in phase space these level set functions are generated from solving the liouville equation with initial data chosen to embed the phase gradient simultaneously we track a new quantity f by solving again the liouville equation near the obtained zero level set but with initial density as initial data the multivalued density and higher moments are thus resolved by integrating f along the n dimensional manifold in the phase directions we show that this is equivalent to using the wigner approach but decomposing the velocity from the density each of which evolves by the same liouville equation the main advantages of this approach in contrast to the standard kinetic equation approach using the liouville equation with a dirac measure initial data include 1 the liouville equations are solved with l initial data and a singular integral involving the email protected function is evaluated only in the post processing step thus avoiding oscillations and excessive numerical smearing 2 a local level set method can be utilized to significantly reduce the computation in the phase space these advantages allow us to compute for the first time all physical observables for multidimensional problems in an eulerian framework

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

a fast semi lagrangian contouring method for moving interfaces abstract general moving interface problems are solved by a new approach evaluating an explicit semi lagrangian advection formula with efficient geometric algorithms and extracting the moving interface with a fast new contouring technique the new approach decouples spatial and temporal resolutions and grid free adaptive refinement of the interface increases accuracy dramatically a modular implementation with a fast new intrinsic geometry module computes highly accurate solutions to geometric moving interface problems involving merging anisotropy and faceting with a high order embedded geometry module it solves second order problems involving curvature dynamic topology and nonlocal interactions

estimation of simultaneous systems of spatially interrelated cross sectional equations in this paper we consider a simultaneous system of spatially interrelated cross sectional equations our speci cation incorporates spatial lags in the endogenous and exogenous variables in modelling the disturbance process we allow for both spatial correlation as well as correlation across equations the data set is taken to be a single cross section of observations the model may be viewed as an extension of the widely used single equation cli3 ord model we suggest computationally simple limited and full information instrumental variable estimators for the parameters of the system and give formal large sample results

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

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

a topology preserving level set method for shape optimization the classical level set method which represents the boundary of the unknown geometry as the zero level set of a function has been shown to be very effective in solving shape optimization problems the present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints we propose a logarithmic barrier penalty which acts to enforce the constraints leading to an approximate solution to shape design problems

inference with dependent data using cluster covariance estimators this paper presents a novel way to conduct inference using dependent data in time series spatial and panel data applications our method involves constructing t and wald statistics utilizing a cluster covariance matrix estimator cce we then use an approximation that takes the number of clusters groups as xed and the number of observations per group to be large and calcu late limiting distributions of the t and wald statistics this approximation is analogous to xed b asymptotics of kiefer and vogelsang 2002 2005 kv for heteroskedasticity and autocorrelation consistent inference but in our case yields standard t and f distributions where the number of groups essentially plays the role of sample size we provide simulation evidence that demonstrates our procedure outperforms conventional inference procedures and performs comparably to kv

partial maximum likelihood estimation of spatial probit models this paper analyzes spatial probit models for cross sectional dependent data in a binary choice context observations are divided by pairwise groups and bivariate normal distributions are specified within each group partial maximum likelihood estimators are introduced and they are shown to be consistent and asymptotically normal under some regularity conditions consistent covariance matrix estimators are also provided estimates of average partial effects can also be obtained once we characterize the conditional distribution of the latent error finally a simulation study shows the advantages of our new estimation procedure in this setting our proposed partial maximum likelihood estimators are shown to be more efficient than the generalized method of moments counterparts

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

sharp interface cartesian grid method i an easily implemented technique for 3d moving boundary computations a cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three dimensional immersed boundaries the embedded boundaries are represented using level sets and treated in a sharp manner without the use of source terms to represent boundary effects the narrow band distance function field in the level set boundary representation facilitates implementation of the finite difference flow solver the resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second order accuracy the accuracy of the finite difference scheme is established and shown to be comparable to finite volume schemes that are considerably more difficult to implement moving boundaries are handled naturally the pressure solver is accelerated using an algebraic multigrid technique adapted to be effective in the presence of moving embedded boundaries benchmarking of the method is performed against available numerical as well as experimental results

identification and qml estimation of multivariate and simultaneous equations spatial autoregressive models abstract this paper investigates a simultaneous equations spatial autoregressive model which incorporates simultaneity effects own variable spatial lags and cross variable spatial lags as explanatory variables and allows for correlation between disturbances across equations in exposition we also discuss a multivariate spatial autoregressive model that can be treated as a reduced form of the simultaneous equations model we study parameter spaces parameter identification asymptotic properties of the quasi maximum likelihood estimation and computational issues monte carlo experiments illustrate the advantages of the qml broader applicability and efficiency compared to instrumental variables based estimation methods in the existing literature

unified m estimation of fixed effects spatial dynamic models with short panels abstract it is well known that quasi maximum likelihood qml estimation of dynamic panel data dpd models with short panels depends on the assumptions on the initial values and a wrong treatment of them will result in inconsistency and serious bias the same issues apply to spatial dpd sdpd models with short panels in this paper a unified m estimation method is proposed for estimating the fixed effects sdpd models containing three major types of spatial effects namely spatial lag spatial error and space time lag the method is free from the specification of the distribution of the initial observations and robust against nonnormality of the errors consistency and asymptotic normality of the proposed m estimator are established a martingale difference representation of the underlying estimating functions is developed which leads to an initial condition free estimate of the variance of the m estimators monte carlo results show that the proposed methods have excellent finite sample performance

gmm estimation of social interaction models with centrality this paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous contextual correlated and group fixed effects when the network structure in a group is captured by a graph in which the degrees of nodes are not all equal the different positions of group members as measured by the bonacich 1987 centrality provide additional information for identification and estimation in this case the bonacich centrality measure for each group can be used as an instrument for the endogenous social effect but the number of such instruments grows with the number of groups we consider the 2sls and gmm estimation for the model the proposed estimators are asymptotically efficient respectively within the class of iv estimators and the class of gmm estimators based on linear and quadratic moments when the sample size grows fast enough relative to the number of instruments

specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances this study develops a methodology of inference for a widely used cliff ord type spatial model containing spatial lags in the dependent variable exogenous variables and the disturbance terms while allowing for unknown heteroskedasticity in the innovations we first generalize the gmm estimator suggested in kelejian and prucha 1998 1999 for the spatial autoregressive parameter in the disturbance process we also define iv estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the gmm estimator much of the theory is kept general to cover a wide range of settings

an efficient gmm estimator of spatial autoregressive models in this paper we consider gmm estimation of the regression and mrsar models with sar disturbances we derive the best gmm estimator within the class of gmm estimators based on linear and quadratic moment conditions the best gmm estimator has the merit of computational simplicity and asymptotic efficiency it is asymptotically as efficient as the ml estimator under normality and asymptotically more efficient than the gaussian qml estimator otherwise monte carlo studies show that with moderate sized samples the best gmm estimator has its biggest advantage when the disturbances are asymmetrically distributed when the diagonal elements of the spatial weights matrix have enough variation incorporating kurtosis of the disturbances in the moment functions will also be helpful

a fast modular semi lagrangian method for moving interfaces a fast modular numerical method for solving general moving interface problems is presented it simplifies code development by providing a black box solver which moves a given interface one step with given normal velocity the method combines an efficiently redistanced level set approach a problem independent velocity extension and a second order semi lagrangian time stepping scheme which reduces numerical error by exact evaluation of the signed distance function adaptive quadtree meshes are used to concentrate computational effort on the interface so the method moves an n element interface in o n log n work per time step efficiency is increased by taking large time steps even for parabolic curvature flows numerical results show that the method computes accurate viscosity solutions to a wide variety of difficult geometric moving interface problems involving merging anisotropy faceting nonlocality and curvature

gmm and 2sls estimation of mixed regressive spatial autoregressive models the gmm method and the classical 2sls method are considered for the estimation of mixed regressive spatial autoregressive models these methods have computational advantage over the conventional maximum likelihood method the proposed gmm estimators are shown to be consistent and asymptotically normal within certain classes of gmm estimators best ones are derived the proposed gmm estimators improve upon the 2sls estimators and are applicable even if all regressors are irrelevant a best gmm estimator may have the same limiting distribution as the ml estimator with normal disturbances

testing for serial correlation spatial autocorrelation and random effects using panel data abstract this paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time in addition the model allows for heterogeneity across the spatial units using random effects the paper then derives several lagrange multiplier tests for this panel data regression model including a joint test for serial correlation spatial autocorrelation and random effects these tests draw upon two strands of earlier work the first is the lm tests for the spatial error correlation model discussed in anselin and bera 1998 spatial dependence in linear regression models with an introduction to spatial econometrics in ullah a giles d e a eds handbook of applied economic statistics marcel dekker new york and in the panel data context by baltagi et al 2003 testing panel data regression models with spatial error correlation journal of econometrics 117 123 150 the second is the lm tests for the error component panel data model with serial correlation derived by baltagi and li 1995 testing ar 1 against ma 1 disturbances in an error component model journal of econometrics 68 133 151 hence the joint lm test derived in this paper encompasses those derived in both strands of earlier works in fact in the context of our general model the earlier lm tests become marginal lm tests that ignore either serial correlation over time or spatial error correlation the paper then derives conditional lm and lr tests that do not ignore these correlations and contrast them with their marginal lm and lr counterparts the small sample performance of these tests is investigated using monte carlo experiments as expected ignoring any correlation when it is significant can lead to misleading inference

a numerical method for finding positive solution of diffusive logistic equation with constant yield harvesting abstract we consider a reaction diffusion equation u x au x bu x 2 ch x 0 with dirichlet boundary condition by using a numerical method based on sub super solution we will show the existence of positive solution

locally corrected semi lagrangian methods for stokes flow with moving elastic interfaces we present a new method for computing two dimensional stokes flow with moving interfaces that respond elastically to stretching the interface is moved by semi lagrangian contouring a distance function is introduced on a tree of cells near the interface transported by a semi lagrangian time step and then used to contour the new interface the velocity field in a periodic box is calculated as a potential integral resulting from interfacial and body forces using a technique based on ewald summation with analytically derived local corrections the interfacial stretching is found from a surprisingly natural formula a test problem with an exact solution is constructed and used to verify the speed accuracy and robustness of the approach

on the reinitialization procedure in a narrow band locally refined level set method for interfacial flows a local level set algorithm for simulating interfacial flows described by the two dimensional incompressible navier stokes equations is presented the governing equations are solved using a finite difference discretization on a cartesian grid and a second order approximate projection method the level set transport and reinitialization equations are solved in a narrow band around the interface using an adaptive refined grid which is reconstructed every time step and refined using a simple uniform cell splitting operation within the band instabilities at the border of the narrow band are avoided by smoothing the level set function in the outer part of the band the influence of different pde based reinitialization strategies on the accuracy of the results is investigated the ability of the proposed method to accurately compute interfacial flows is discussed using different tests namely the advection of a circle of fluid in two different time reversed vortex flows the advection of zalesak s rotating disk the propagation of small amplitude gravity and capillary waves at the interface between two superposed viscous fluids in deep water and a classical test of rayleigh taylor instability with and without surface tension effects the interface location error and area loss for some of the results obtained are compared with those of a recent particle level set method copyright 2005 john wiley sons ltd

fast tree based redistancing for level set computations level set methods for moving interface problems require efficient techniques for transforming an interface to a globally defined function whose zero set is the interface such as the signed distance to the interface this paper presents efficient algorithms for this redistancing problem the algorithms use quadtrees and triangulation to compute global approximate signed distance functions a quadtree mesh is built to resolve the interface and the vertex distances are evaluated exactly with a robust search strategy to provide both continuous and discontinuous interpolants given a polygonal interface with n elements our algorithms run in o n space and o n log n time two dimensional numerical results show they are highly efficient in practice

lawson s triangulation is nearly optimal for controlling error bounds one way of evaluating a triangulation method is to study how well it controls error bounds and stability in computations lawson s method which maximizes the smallest angle over all triangulations controls error bounds for linear interpolates as well as for certain derivative estimates in particular no other triangulation improves these bounds by more than a factor of 2 although lawson s triangulation method does not minimize the largest edge over all triangulations it nearly does this edge is no longer than 2 sqrt 3 times the longest edge in any other triangulation thus lawson s triangulation method controls error bounds in polynomial interpolation schemes

computation of three dimensional dendrites with finite elements starting from an initial seed crystal inside an undercooled liquid the solid phase begins to grow rapidly and develops unstable growth patterns some growth directions are preferred because of anisotropic parameters in the physical model this results in the development of dendrites the physical model includes the heat equation for both the liquid and solid phases the gibbs thomson law couples velocity and curvature of the interface and the temperature we describe a numerical method that enables us to compute dendritic growth of crystals in two and three space dimensions the method consists of two coupled finite element algorithms the first one solves the heat equation the other operates on a discretization of the free boundary and computes the evolution of this moving interface the two methods work with totally independent grids by using timedependent locally refined and coarsened adaptive meshes in both methods we are able to reach a spatial resolution necessary to compute dendritic growth in two and three space dimensions

a hybrid level set volume constraint method for incompressible two phase flow a second order hybrid level set volume constraint method hlsvc for numerically simulating deforming boundaries is presented we combine the hlsvc interface advection algorithm with a two phase flow solver in order to numerically capture deforming bubbles and drops whose actual volume s fluctuate about fixed target volume s three novel developments are described 1 a new method for enforcing a volume constraint in which the number of bubbles and drops can change due to merging or splitting 2 a new second order semi lagrangian narrow band level set reinitialization algorithm and 3 validation of a two phase flow numerical method by comparison with linear stability analysis results for a co flowing liquid jet in gas the new interface capturing method is tested on benchmark problems in which the velocity is prescribed passive advection of interfaces and in which the velocity is determined by the incompressible navier stokes equations for two phase flow the error in interface position when using the hybrid level set volume constraint method is reported for many benchmark problems in polar coordinates cylindrical coordinates and on an adaptive grid in which one criteria of adaptivity is the magnitude of the interface curvature

on the asymptotic distribution of the moran i test statistic with applications by far the most popular test for spatial correlation is the one based on moran s 1950 i test statistic despite this the available results in the literature concerning the large sample distribution of this statistic are limited and have been derived under assumptions that do not cover many applications of interest in this paper we 3rst give a general result concerning the large sample distribution of moran i type test statistics we then apply this result to derive the large sample distribution of the moran i test statistic for a variety of important models in order to establishth ese results we also give a new central limit theorem for linear quadratic forms 2001 elsevier science s a all rights reserved jel classi cation c12 c21

optimal point location in a monotone subdivision point location often known in graphics as hit detection is one of the fundamental problems of computational geometry in a point location query we want to identify which of a given collection of geometric objects contains a particular point let mathcal s denote a subdivision of the euclidean plane into monotone regions by a straight line graph of m edges in this paper we exhibit a substantial refinement of the technique of lee and preparata siam j comput 6 1977 pp 594 606 for locating a point in mathcal s based on separating chains the new data structure called a layered dag can be built in o m time uses o m storage and makes possible point location in o log m time unlike previous structures that attain these optimal bounds the layered dag can be implemented in a simple and practical way and is extensible to subdivisions with edges more general than straight line segments