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 connection between simulation relations and feedback transformations in nonlinear control systems abstract the recent introduction of simulation and bisimulation relations in the study of nonlinear control systems provides a broad potential framework for the study and classification of such systems this paper reviews the definitions of simulation and bisimulation relations and develops connections between them and the well established notions of feedback transformations and feedback equivalences

initial conditions and moment restrictions in dynamic panel data models estimation of the dynamic error components model is considered using two alternative linear estimators that are designed to improve the properties of the standard first differenced gmm estimator both estimators require restrictions on the initial conditions process asymptotic efficiency comparisons and monte carlo simulations for the simple ar 1 model demonstrate the dramatic improvement in performance of the proposed estimators compared to the usual first differenced gmm estimator and compared to non linear gmm the importance of these results is illustrated in an application to the estimation of a labour demand model using company panel data

on the periodic trajectories of boolean control networks abstract in this note we first characterize the periodic trajectories or equivalently the limit cycles of a boolean network and their global attractiveness we then investigate under which conditions all the trajectories of a boolean control network may be forced to converge to the same periodic trajectory if every trajectory can be driven to such a periodic trajectory this is possible by means of a feedback control law

fixed effects dynamic panel models a factor analytical method we consider the estimation of dynamic panel data models in the presence of incidental parameters in both dimensions individual fixed effects and time fixed effects as well as incidental parameters in the variances we adopt the factor analytical approach by estimating the sample variance of individual effects rather than the effects themselves in the presence of cross sectional heteroskedasticity the factor method estimates the average of the cross sectional variances instead of the individual variances the method thereby eliminates the incidental parameter problem in the means and in the variances over the cross sectional dimension we further show that estimating the time effects and heteroskedasticities in the time dimension does not lead to the incidental parameter bias even when t and n are comparable moreover efficient and robust estimation is obtained by jointly estimating heteroskedasticities

on the calculation of potential integrals for linear source distributions on triangular domains present analytical formulas for the singular field contributions of linear source distributions on triangular domains the formulas can be used for near field calculations of electric and magnetic source currents especially for the calculation of method of moments mom matrix elements due to the solution of surface integral equations for mom self coupling terms involving the scalar green function of free space the authors present expressions comprising analytical solutions of both the source integrals and the testing integrals

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

nearly hypersingular integrals by double arctan transformation in higher order geometry modeling in order to directly utilize the dyadic green s functions in surface integral equations sies a novel double arctan transformation for nearly hypersingular integrals is proposed in this communication this new transformation is flexible and applicable to nearly hypersingular integrals in the forms of hat r hat r r 3 hat r r 3 and 1 r 3 over the curved surfaces by a fully numerical method with the help of the sigmoidal transformation to improve the stability of this new singularly handling method there results an efficient solution for the third order near singularity problems in sies moreover the proposed method is also effective for the lower orders of the nearly singular integral kernels with typical testing cases the performance of this method is fairly evaluated and its validity and stability is well demonstrated

shrinkage tuning parameter selection with a diverging number of parameters contemporary statistical research frequently deals with problems involving a diverging number of parameters for those problems various shrinkage methods e g the lasso and smoothly clipped absolute deviation are found to be particularly useful for variable selection nevertheless the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters with a fixed predictor dimension wang and co worker have demonstrated that the tuning parameters selected by a bayesian information criterion type criterion can identify the true model consistently in this work similar results are further extended to the situation with a diverging number of parameters for both unpenalized and penalized estimators consequently our theoretical results further enlarge not only the scope of applicability of the traditional bayesian information criterion type criteria but also that of those shrinkage estimation methods

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

estimating a spatial autoregressive model with an endogenous spatial weight matrix the spatial autoregressive sar model is a standard tool for analyzing data with spatial correlation conventional estimation methods rely on the key assumption that the spatial weight matrix is strictly exogenous which would likely be violated in some empirical applications where spatial weights are determined by economic factors this paper presents model specification and estimation of the sar model with an endogenous spatial weight matrix we provide three estimation methods two stage instrumental variable 2siv method quasi maximum likelihood estimation qmle approach and generalized method of moments gmm we establish the consistency and asymptotic normality of these estimators and investigate their finite sample properties by a monte carlo study

minimum time control of boolean networks boolean networks bns are discrete time dynamical systems with boolean state variables bns have recently been attracting considerable interest as computational models for biological systems and in particular gene regulating networks boolean control networks bcns are boolean networks with boolean inputs we consider the problem of steering a bcn from a given state to a desired state in minimal time using the algebraic state space representation assr of bcns we derive several necessary conditions stated in the form of maximum principles mps for a control to be time optimal in the assr every state and input vector is a canonical vector using this special structure yields an explicit state feedback formula for all time optimal controls to demonstrate the theoretical results we develop a bcn model for the genetic switch controlling the lambda phage development upon infection of a bacteria our results suggest that this biological switch is designed in a way that guarantees minimal time respon

controllability and observability of boolean control networks the controllability and observability of boolean control networks are investigated after a brief review on converting a logic dynamics to a discrete time linear dynamics with a transition matrix some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix based on the discrete time dynamics the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely then the problem of observability is also solved by giving necessary and sufficient conditions

the time series and cross section asymptotics of dynamic panel data estimators in this paper we derive the asymptotic properties of within groups wg gmm and liml estimators for an autoregressive model with random effects when both t and n tend to infinity gmm and liml are consistent and asymptotically equivalent to the wg estimator when t n 0 the fixed t results for gmm and liml remain valid but wg although consistent has an asymptotic bias in its asymptotic distribution when t n tends to a positive constant the wg gmm and liml estimators exhibit negative asymptotic biases of order 1 t 1 n and 1 2n t respectively in addition the crude gmm estimator that neglects the autocorrelation in first differenced errors is inconsistent as t n c 0 despite being consistent for fixed t finally we discuss the properties of a random effects pseudo mle with unrestricted initial conditions when both t and n tend to infinity

fixed effects dynamic spatial panel data models and impulse response analysis abstract real data often have complicated correlations over cross section and time such correlations are of particular interests in empirical studies this paper considers using high order spatial lags and high order time lags to model complicated correlations over cross section and time we propose to use the quasi maximum likelihood qml method to estimate the model we establish the asymptotic theory of the quasi maximum likelihood estimator qmle including the consistency and limiting distribution under large n and large t setup where n denotes the number of individuals and t the number of time periods we investigate the problem of estimating impulse response functions and the associated 1 confidence intervals average direct indirect and total impacts are defined along the same spirits of lesage and pace 2009 under the dynamic spatial panel data setup the estimation and inferential theory for the three impacts are studied model selection issue is also considered monte carlo simulations confirm our theoretical results and show that the qmle after bias correction has good finite sample performance

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

optimal control of boolean control networks in this paper we address the optimal control problem for boolean control networks bcns we first consider the problem of finding the input sequences that minimize a given cost function over a finite time horizon the problem solution is obtained by means of a recursive algorithm that represents the analogue for bcns of the difference riccati equation for linear systems we prove that a significant number of optimal control problems for bcns can be easily reframed into the present setup in particular the cost function can be adjusted so as to include penalties on the switchings provided that we augment the size of the bcn state variable in the second part of the paper we address the infinite horizon optimal control problem and we provide necessary and sufficient conditions for the problem solvability the solution is obtained as the limit of the solution over the finite horizon 0 t and it is always achieved in a finite number of steps finally the average cost problem over the infinite horizon investigated in optimal control of logical control networks y zhao ieee trans autom control vol 56 no 8 pp 1766 1776 aug 2011 is addressed by making use of the results obtained in the previous sections

improved double arctan transformation for the stable evaluation of nearly hypersingular integrals in sie the evaluation of singular or near singular integrals is one of the key techniques in the integral equation method based on the previously proposed double arctan transformation dat for the nearly hypersingular integrals in curved surface modeling this work presents new transformation methods to improve the accuracy and stability of dat for the following two situations i e the field point is 1 extremely close to the source surface and 2 extremely close to the boundary of the source surface the original dat fails in these two situations and hence limits its applications the reasons that cause such an instability are studied two additional transformations are introduced to make the dat stable for these two cases for situation i the exponential transformation et is adopted to optimize the distribution of the gaussian quadrature points for situation ii the shape function transformation sft is further proposed to remove the nearly angular singularity we denote the newly developed dat with et and sft as the improved dat idat in this communication the typical testing cases are provided to validate the proposed method

nonconcave penalized likelihood with a diverging number of parameters a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by fan and li to simultaneously estimate parameters and select important variables they demonstrated that this class of procedures has an oracle property when the number of parameters is finite however in most model selection problems the number of parameters should be large and grow with the sample size in this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to as the sample size increases under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators furthermore the consistency of the sandwich formula of the covariance matrix is demonstrated nonconcave penalized likelihood ratio statistics are discussed and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions the asymptotic results are augmented by a simulation study and the newly developed methodology is illustrated by an analysis of a court case on the sexual discrimination of salary

radial angular singularity cancellation transformations derived by variable separation the variable separation method is utilized to construct new radial angular r n coordinate transformation schemes for the singularity cancellation technique derived from the concept of achieving an ideal jacobian of the transformations and with different parameter settings in the variable separation method a new augmented radial angular r 1 transformation new radial angular r 2 and radial angular r 2 cosh transformations as well as a new radial angular r 3 an augmented radial angular r 3 and an arcsinh r 3 transformation are introduced the proposed r 2 and r 3 transformations are efficient and applicable to all types of near singular kernels occurring in the method of moments mom solution of electromagnetic surface integral equations whereas the r 1 transformation is only suitable for the first order singular integrals the newly proposed transformation schemes are verified and they are also applied to deformed triangles where good performances are still achieved

simulation relations and controllability properties of linear and nonlinear control systems we examine to what extent nonlinear input disturbance systems that are connected by a simulation relation share certain controllability properties we derive several results that fit within the paradigm that if there is a simulation relation of a system a by a system b and if system a has a specified controllability property then system b has that same property as expected one can only turn the paradigm into actual theorems by imposing appropriate assumptions on the systems and or the simulation relation we prove three such results the first result we obtain deals with the property of complete controllability where we impose minimal assumptions on the input disturbance systems but require that the simulation relation be the graph of a smooth surjection between the systems state spaces that satisfies a certain compactness condition the second result deals with a somewhat weaker notion of controllability modulo the kernel of a linear mapping where it is assumed that system b is almost l

bisimulations of boolean control networks a framework for analyzing bisimulation relations of boolean control networks bcns is set up in this paper bisimulation relations are natural objectives in control systems theory a bisimulation relation between a pair of control systems defines a relation on their state spaces or state sets explaining how a trajectory or transition of one system can be paired with a trajectory or transition of the other system and vice versa the paper first formalizes the notion of bi simulation in bcns and presents detailed results characterizing bi simulation relations for bcns then as an application of the notion of bisimulation it considers the propagation of the fundamental properties of macro controllability and stabilizability through a bisimulation relation it thereby suggests the possibility that certain control properties of a bcn can be inferred by analyzing a potentially simpler bcn the analysis developed in this paper is based on the semitensor product approach which gives algorithms that have e

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

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

efficient gmm estimation of spatial dynamic panel data models with fixed effects abstract in this paper we derive the asymptotic properties of gmm estimators for the spatial dynamic panel data model with fixed effects when n is large and t can be large but small relative to n the gmm estimation methods are designed with the fixed individual and time effects eliminated from the model and are computationally tractable even under circumstances where the ml approach would be either infeasible or computationally complicated the ml approach would be infeasible if the spatial weights matrix is not row normalized while the time effects are eliminated and would be computationally intractable if there are multiple spatial weights matrices in the model also consistency of the mle would require t to be large and not small relative to n if the fixed effects are jointly estimated with other parameters of interest the gmm approach can overcome all these difficulties we use exogenous and predetermined variables as instruments for linear moments along with several levels of their neighboring variables and additional quadratic moments we stack up the data and construct the best linear and quadratic moment conditions an alternative approach is to use separate moment conditions for each period which gives rise to many moments estimation we show that these gmm estimators are n t consistent asymptotically normal and can be relatively efficient we compare these approaches on their finite sample performance by monte carlo

disturbance decoupling control design for switched boolean control networks abstract this paper investigates a kind of disturbance decoupling problems ddps for switched boolean control networks bcns that is the disturbance independent output decoupling problem via the semi tensor product of matrices by converting the dynamics of switched bcns into an algebraic form and using the redundant variable separation technique all possible state feedback controllers are designed for the disturbance independent output decoupling problem then based on the obtained state feedback disturbance decoupling controllers and the system s output equation a constructive procedure is proposed to design all possible output feedback disturbance decoupling controllers the study of two illustrative examples shows that the new results obtained in this paper are effective in designing disturbance decoupling controllers for switched bcns

simulation and bisimulation of nonlinear control systems with admissible classes of inputs and disturbances motivated by analogous concepts in theoretical computer science the concepts of simulation and bisimulation relations have recently been introduced in the study of the geometric theory of nonlinear control systems simulation relations generalize such notions as trajectory propagation and trajectory lifting while bisimulation relations generalize such notions as system equivalence and state space reduction this paper explores previously obtained necessary and sufficient conditions for the existence of bi simulation relations and determines to what extent those relations can be maintained if inputs and disturbances are restricted to specified admissible classes we show how the results obtained here for general simulation relations extend prior results obtained for trajectory propagation and trajectory lifting also addressed briefly are some sufficient conditions for simulation relations to hold semiglobally in time

high dimensional covariance matrix estimation in approximate factor models the variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems classical methods of estimating the covariance matrices are based on the strict factor models assuming independent idiosyncratic components this assumption however is restrictive in practical applications by assuming sparse error covariance matrix we allow the presence of the cross sectional correlation even after taking out common factors and it enables us to combine the merits of both methods we estimate the sparse covariance using the adaptive thresholding technique as in cai and liu j amer statist assoc 106 2011 672 684 taking into account the fact that direct observations of the idiosyncratic components are unavailable the impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied

singularity subtraction technique for high order polynomial vector basis functions on planar triangles in this paper a singularity subtraction technique is developed for computing the impedance matrix elements of various electromagnetic surface integral equation formulations with the galerkin method and high order basis functions analytical closed form formulas for computing surface integrals with r r sup n n spl ges 3 singularities times polynomial nodal shape functions of arbitrary order on a planar triangle are presented

numerical evaluation of singular and near singular potential integrals a simple and efficient numerical procedure using a singularity cancellation scheme is presented for evaluating singular and near singular potential integrals with 1 r singularities the procedure not only has several advantages over singularity subtraction methods but also improves on some aspects of other singularity cancellation methods such as polar and duffy transformations a theoretical analysis is presented for triangles quadrilaterals tetrahedrons bricks and prisms and numerical results are presented for triangles and prisms

kalman decomposition for boolean control networks the kalman decomposition problem for boolean control networks bcns is solved completely a necessary and sufficient condition described by vertex partitions of digraphs is proposed for the kalman decomposition and an algorithm is designed to compute the logical coordinate transformation that results in the kalman decomposition finally two examples are presented one example illustrates the procedure of realizing the kalman decomposition the other one reveals that not all the bcns can be transformed into the kalman decomposition form this is an essential property different from that of the traditional linear control systems

invertibility and nonsingularity of boolean control networks invertibility is an interesting and classical control theoretic problem however there has been no result for the invertibility of boolean control networks bcns so far we first adopt the theory of symbolic dynamics to characterize it first it is shown that a bcn generates a continuous mapping from the space of input trajectories to the space of output trajectories based on it the concepts of nonsingularity and invertibility of bcns are first defined as the injectivity and bijectivity of the mapping respectively second combined symbolic dynamics with the semi tensor product stp of matrices an equivalent test criterion for invertibility is given easily computable algorithms to construct the inverse bcn for an invertible bcn are presented and it is proved that invertibility remains invariant under coordinate transformations third an equivalent test criterion for nonsingularity is given via defining a novel directed graph that is called weighted pair graph lastly as an application of invertibility to systems biology we prove that the bcn model proposed in faure et al 2006 is not invertible i e we prove that arbitrarily controlling mammalian cell cycles is unfeasible at the theoretical level

theory and methods of panel data models with interactive effects this paper considers the maximum likelihood estimation of the panel data models with interactive effects motivated in economics and other social sciences a notable feature of the model is that the explanatory variables are correlated with the unobserved effects the usual within group estimator is inconsistent existing methods for consistent estimation are either designed for panel data with short time periods or are less efficient the maximum likelihood estimator has desirable properties and is easy to implement as illustrated by the monte carlo simulations this paper develops the inferential theory for the maximum likelihood estimator including consistency rate of convergence and the limiting distributions we further extend the model to include time invariant regressors and common regressors cross section invariant the regression coefficients for the time invariant regressors are time varying and the coefficients for the common regressors are cross sectionally varying

numerical integration scheme for the near singular green function gradient on general triangles a new near singularity cancellation transformation quadrature scheme for triangle domains is presented it is tailored to the green function gradient kernel static and dynamic multiplied with higher order weighting functions on curvilinear triangles the transformation is analytically invertible attention is paid to ensuring accuracy in both tangential and normal components such integrals must be routinely evaluated in modern method of moments mom implementations the scheme follows the standard three subtriangle splitting approach of which the benefits are single parameter accuracy control a geometry independent total number of quadrature points and implementation simplicity extensive numerical results show superior efficiency and reliability to existing three subdomain schemes consistent dependable error convergence is demonstrated with very low variation in accuracy for fixed quadrature order and singularity height the scheme is suitable for practical use by mom developers

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

estimation of dynamic models with error components abstract observations on n cross section units at t time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit different assumptions about the initial conditions are a initial state fixed b initial state random c the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed and d the unobserved individual effect independent of the unobserved dynamic process with initial value random asymptotic properties of the maximum likelihood and covariance estimators are obtained when t and when n the relationship between the pseudo and conditional maximum likelihood estimators is clarified a simple consistent estimator that is independent of the initial conditions and the way in which t or n is also suggested

quasi maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and t are large this paper investigates the asymptotic properties of quasi maximum likelihood estimators for spatial dynamic panel data with xed eects when both the number of individuals n and the number of time periods t are large we consider the case where t is asymptotically large relative to n the case where t is asymptotically proportional to n and the case where n is asymptotically large relative to t in the case where t is asymptotically large relative to n the estimators are p nt consistent and asymptotically normal with the limit distribution centered around 0 when n is asymptotically proportional to t the estimators are p nt consistent and asymptotically normal but the limit distribution is not centered around 0 and when n is large relative to t the estimators are consistent with rate t and have a degenerate limit distribution the estimators of the xed eects are p t consistent and asymptotically normal we also propose a bias correction for our estimators we show that when t grows faster than n 1 3 the correction will asymptotically eliminate the bias and yield a centered con dence interval

inference on higher order spatial autoregressive models with increasingly many parameters this paper develops consistency and asymptotic normality of parameter estimates for a higher order spatial autoregressive model whose order and number of regressors are allowed to approach infinity slowly with sample size both least squares and instrumental variables estimates are examined and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied besides allowing the number of parameters to increase with the data this has the advantage of accommodating some asymptotic regimes that are suggested by certain spatial settings several of which are discussed a small empirical example is also included and a monte carlo study analyses various implications of the theory in finite samples

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

a projection height independent adaptive radial angular r 2 transformation for singular integrals a new radial angular r 2 adaptive singularity cancellation transformation is proposed this new transformation is flexible and applicable to singular integrals over triangular domains when the height tends to zero and the observation point is in the plane of the source domain the transformation remains stable and approaches the corresponding transformation within the source plane usually the green s function and its gradient appear in the integral kernels leading to first order and second order singularities the newly derived transformation formula provides an efficient solution for second order singular coupling integral kernels and the formula is in particular more efficient than alternative schemes for singular vector integral kernels however it is also effective for the lower order singular integral kernels in electromagnetic boundary integral equation formulations the proposed transformation is efficient for all types of singular integrals

adaptive singularity cancellation for efficient treatment of near singular and near hypersingular integrals in surface integral equation formulations a proposed singularity cancellation technique for fully numerical evaluation of method of moments integrals in surface integral equation solutions produces reasonably accurate results with few quadrature points for singular and hypersingular integrals however for near singular and near hypersingular integrals time consuming computations need to be repeatedly performed over unnecessary regions outside the actual integration domain for a more efficient treatment of these integrals an adaptive singularity cancellation technique is proposed as such the source triangular domain is subdivided in a way that all sample points remain inside the desired integration domain and unnecessary computations are avoided second the accuracy of results in existing singularity cancellation transformations is greatly affected by variations in height of observation point above the plane of source domain this drawback has been removed in the adaptive singularity cancellation transformations additionally an optimum selection criterion for the distribution of quadrature samples is presented the criterion enables run time selection of optimum number of samples in different directions by consideration of the instantaneous geometry of the transformed integration domain

on bias inconsistency and efficiency of various estimators in dynamic panel data models abstract when a model for panel data includes lagged dependent explanatory variables then the habitual estimation procedures are asymptotically valid only when the number of observations in the time dimension t gets large usually however such datasets have substantial sample size in the cross section dimension n whereas t is often a single digit number results on the asymptotic bias n in this situation have been published a decade ago but hence far analytic small sample assessments of the actual bias have not been presented here we derive a formula for the bias of the least squares dummy variable lsdv estimator which has a o n 1 t 3 2 approximation error in a simulation study this is found to be remarkably accurate due to the small variance of the lsdv estimator which is usually much smaller than the variance of consistent generalized method of moments estimators a very efficient procedure results when we remove the bias from the lsdv estimator the simulations contain results for a particular operational corrected lsdv estimation procedure which in many situations proves to be much more efficient than various instrumental variable type estimators

a family of augmented duffy transformations for near singularity cancellation quadrature a new family of systematically constructed near singularity cancellation transformations is presented yielding quadrature rules for integrating near singular kernels over triangular surfaces this family results from a structured augmentation of the well known duffy transformation the benefits of near singularity cancellation quadrature are that no analytical integral evaluations are required and applicability in higher order basis function and curvilinear settings six specific transformations are constructed for near singularities of orders one two and three two of these transformations are found to be equivalent to existing ones the performance of the new schemes is thoroughly assessed and compared with that of existing schemes results for the gradient of the scalar green function are also presented for simplicity static kernel results are shown the new schemes are competitive with and in some cases superior to the existing schemes considered