empirical correction to the likelihood ratio statistic for structural equation modeling with many variables survey data typically contain many variables structural equation modeling sem is commonly used in analyzing such data the most widely used statistic for evaluating the adequacy of a sem model is t ml a slight modification to the likelihood ratio statistic under normality assumption t ml approximately follows a chi square distribution when the number of observations n is large and the number of items or variables p is small however in practice p can be rather large while n is always limited due to not having enough participants even with a relatively large n empirical results show that t ml rejects the correct model too often when p is not too small various corrections to t ml have been proposed but they are mostly heuristic following the principle of the bartlett correction this paper proposes an empirical approach to correct t ml so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi square distribution results show that empirically corrected statistics follow the nominal chi square distribution much more closely than previously proposed corrections to t ml and they control type i errors reasonably well whenever n max 50 2p the formulations of the empirically corrected statistics are further used to predict type i errors of t ml as reported in the literature and they perform well

application of the perfectly matched layer pml absorbing boundary condition to elastic wave propagation a method is presented for application of the perfectly matched layer pml absorbing boundary condition abc to the p sv velocity stress finite difference method the pml consists of a nonphysical material containing both passive loss and dependent sources that provides active absorption of fields it has been used in electromagnetic applications where it has provided excellent results for a wide range of angles and frequencies in this work numerical simulations are used to compare the pml and an optimal second order elastic abc peng and toksoz j acoust soc am 95 733 745 1994 reflection factors are used to compare angular performance for continuous wave illumination snapshots of potentials are used to compare performance for broadband illumination these comparisons clearly demonstrate the superiority of the pml formulation within the pml there is a 60 increase in the number of unknowns per grid cell relative to the velocity stress formulation however the high quality of the pml abc allows the use of a smaller grid which can result in a lower overall computational cost

a novel multigrid based preconditioner for heterogeneous helmholtz problems an iterative solution method in the form of a preconditioner for a krylov subspace method is presented for the helmholtz equation the preconditioner is based on a helmholtz type differential operator with a complex term a multigrid iteration is used for approximately inverting the preconditioner the choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with fourier analysis multigrid analysis results are verified by numerical experiments high wavenumber helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner

a dispersion minimizing compact finite difference scheme for the 2d helmholtz equation in this paper we present a dispersion minimizing compact finite difference scheme for solving the 2d helmholtz equation which is a fourth order scheme the error between the numerical wavenumber and the exact wavenumber is analyzed and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters

an optimal 9 point finite difference frequency space 2 d scalar wave extrapolator in this study a new finite difference technique is designed to reduce the number of grid points needed in frequency space domain modeling the new algorithm uses optimal nine point operators for the approximation of the laplacian and the mass acceleration terms the coefficients can be found by using the steepest descent method so that the best normalized phase curves can be obtained this method reduces the number of grid points per wavelength to 4 or less with consequent reductions of computer memory and cpu time that are factors of tens less than those involved in the conventional second order approximation formula when a band type solver is used on a scalar machine

generalized two parameter equation of growth abstract we considered the general growth equation y ay by that encompasses the well known growth equations by bertalanffy and verhulst pearl logistic as special cases the solutions of this equation for some values of and or can be found in the literature here we present the general solution for any real and and discuss its behavior we found that the generalized gompertz growth equation y ay by ln y and its solution could be considered a limiting case of the general growth equation and its solution respectively thus all three classical growth models bertalanffy logistic and gompertz are nested within the general model this nesting relationship makes it possible to compare statistically the applicability of models to data

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

the existence of optimal parameters of the generalized logistic function the estimation of optimal parameters in a mathematical model described by the generalized logistic function with saturation level a and the asymmetry coefficient is a nonlinear least squares problem in this paper we prove the existence of optimal parameters under considerably weaker conditions than those required in 1

laplace periodogram for time series analysis a new type of periodogram called the laplace periodogram is derived by replacing least squares with least absolute deviations in the harmonic regression procedure that produces the ordinary periodogram of a time series an asymptotic analysis reveals a connection between the laplace periodogram and the zero crossing spectrum this relationship provides a theoretical justification for use of the laplace periodogram as a nonparametric tool for analyzing the serial dependence of time series data superiority of the laplace periodogram in handling heavy tailed noise and nonlinear distortion is demonstrated by simulations a real data example shows its great effectiveness in analyzing heart rate variability in the presence of ectopic events and artifacts

the inverse medium problem in heterogeneous pml truncated domains using scalar probing waves abstract we discuss the inverse medium problem associated with semi infinite domains in particular we attempt to image the spatial variability of shear moduli or shear wave velocities from scant surficial measurements of an arbitrarily heterogeneous semi infinite domain s response to prescribed dynamic excitations we use a full waveform approach to drive the inversion process within a pde constrained optimization framework due to the semi infinite extent of the targeted domains we introduce perfectly matched layers pmls to arrive at finite computational domains the numerical implementation is based on a mixed finite element method that is used to resolve the ensuing state and adjoint boundary value problems both of which are pml endowed to alleviate the inherent solution multiplicity we use tikhonov and total variation tv regularization schemes in conjunction with a regularization factor continuation scheme to further improve the optimizer s chances to converge we also discuss a source frequency continuation scheme we report on two dimensional numerical experiments using synthetic data included are layered profiles and profiles involving inclined layers and inclusions we also report on our methodology s reconstruction of the highly heterogeneous marmousi benchmark velocity model

fuzzy least absolutes regression using shape preserving operations the purpose of this study is to introduce a new fuzzy regression model based on the least absolutes method the fuzzy simple and fuzzy multivariate regression models with fuzzy input fuzzy output are considered in which the coefficients of the models are themselves fuzzy the proposed method is based on a new metric on the space of lr fuzzy numbers fuzzy arithmetic operations are based on the weakest triangular norm t w which is the unique triangular norm that preserves the shape of fuzzy numbers during multiplication the results of comparative studies and numerical examples indicate that using the similarity measure criterion as well as a predictive ability index the proposed method has a better performance than the least squares method especially when the data set includes some outlier data point s

the infinitesimal jackknife with exploratory factor analysis the infinitesimal jackknife a nonparametric method for estimating standard errors has been used to obtain standard error estimates in covariance structure analysis in this article we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices both maximum likelihood estimation and ordinary least squares estimation are considered

analysis of covariance structures under elliptical distributions abstract this article examines the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions it is shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution the asymptotic covariance matrix of sample covariances has a structure that results in the retention of many of the asymptotic properties of normal theory methods if a scale adjustment is applied the likelihood ratio tests of fit have the usual asymptotic chi squared distributions difference tests retain their property of asymptotic independence and maximum likelihood estimators retain their relative asymptotic efficiency within the class of estimators based on the sample covariance matrix an adjustment to the asymptotic covariance matrix of normal theory maximum likelihood estimators for elliptical distributions is provided this adjustment is particularly simple in models for patterned covariance or co

a frequency space 2 d scalar wave extrapolator using extended 25 point finite difference operator finite difference frequency domain modeling for the generation of synthetic seismograms and crosshole tomography has been an active field of research since the 1980s the generation of synthetic seismograms with the time domain finite difference technique has achieved considerable success for waveform crosshole tomography and for wider applications in seismic reverse time migration this became possible with the rapid development of high performance computers however the space frequency x finite difference modeling technique is still beyond the capability of the modern supercomputer in terms of both cost and computer memory therefore finite difference time domain modeling is much more popular among exploration geophysicists a limitation of the space frequency domain is that the recently developed nine point scheme still requires that g the number of grid points per wavelength be 5 this value is greater than for most other numerical modeling techniques for example the pseudospectral scheme

discontinuous galerkin methods for the helmholtz equation with large wave number this paper develops and analyzes some interior penalty discontinuous galerkin ipdg methods using piecewise linear polynomials for the helmholtz equation with the first order absorbing boundary condition in two and three dimensions it is proved that the proposed discontinuous galerkin methods are stable hence well posed without any mesh constraint for each fixed wave number k optimal order with respect to h error estimate in the broken h 1 norm and suboptimal order estimate in the l 2 norm are derived without any mesh constraint the latter estimate improves to optimal order when the mesh size h is restricted to the preasymptotic regime i e k 2 h gtrsim 1 numerical experiments are also presented to gauge the theoretical result and to numerically examine the pollution effect with respect to k in the error bounds the novelties of the proposed ipdg methods include the following first the methods penalize not only the jumps of the function values across the element edges but also the jumps of the normal and tangential derivatives second the penalty parameters are taken as complex numbers of positive imaginary parts so essentially and practically no constraint is imposed on the penalty parameters since the helmholtz problem is a non hermitian and indefinite linear problem as expected the crucial and the most difficult part of the whole analysis is to establish the stability estimates i e a priori estimates for the numerical solutions to this end the cruxes of our analysis are to establish and to make use of a local version of the rellich identity for the laplacian and to mimic the stability analysis for the pde solutions given in p cummings analysis of finite element based numerical methods for acoustic waves elastic waves and fluid solid interactions in the frequency domain ph d thesis the university of tennessee knoxville tn 2001 p cummings and x feng math models methods appl sci 16 2006 pp 139 160 u hetmaniuk commun math sci 5 2007 pp 665 678

origins and uses of linear programming methods for treating l1 and l regressions corrections and comments on abstract this note comments on and corrects some of the referrals and comments of castillo et al castillo e minguez r castillo c confino a s 2008 dealing with the multiplicity of solutions of the l 1 and l regression models european journal of operational research 188 460 484 concerning the origins and uses of linear programming to estimate l 1 and l statistical regressions

normalizing transformatins and bootstrap confidence intervals this paper considers the problem of constructing approximate confidence intervals for functional parameters in the nonparametric case the approach based on transformation theory is applied to improve standard confidence intervals the accelerated bias corrected percentile interval introduced by efron relies on the existence of a normalizing transformation with bias and skewness corrections although calculation does not require explicit knowledge of its functional form we formally construct such a transformation and estimate bias and skewness correction factors for nonparametric situations the resulting interval is shown to be second order accurate to this end edgeworth expansions for the distributions of transformed statistics are derived using the von mises expansion

a multigrid based preconditioned krylov subspace method for the helmholtz equation with pml abstract in this paper we generalize the complex shifted laplacian preconditioner to the complex shifted laplacian pml preconditioner for the helmholtz equation with perfectly matched layer helmholtz pml equation the helmholtz pml equation is discretized by an optimal 9 point difference scheme and the preconditioned linear system is solved by the krylov subspace method especially by the biconjugate gradient stabilized method bi cgstab the spectral analysis of the linear system is given and a new matrix based interpolation operator is proposed for the multigrid method which is used to approximately invert the preconditioner the numerical experiments are presented to illustrate the efficiency of the preconditioned bi cgstab method with the multigrid based on the new interpolation operator also numerical results are given for comparing the performance of the new interpolation operator with that of classic bilinear interpolation operator and the one suggested in erlangga et al 2006 10

spectral analysis of the discrete helmholtz operator preconditioned with a shifted laplacian shifted laplace preconditioners have attracted considerable attention as a technique to speed up convergence of iterative solution methods for the helmholtz equation in this paper we present a comprehensive spectral analysis of the helmholtz operator preconditioned with a shifted laplacian our analysis is valid under general conditions the propagating medium can be heterogeneous and the analysis also holds for different types of damping including a radiation condition for the boundary of the computational domain by combining the results of the spectral analysis of the preconditioned helmholtz operator with an upper bound on the gmres residual norm we are able to provide an optimal value for the shift and to explain the mesh dependency of the convergence of gmres preconditioned with a shifted laplacian we illustrate our results with a seismic test problem

compact difference scheme for parabolic and schrodinger type equations with variable coefficients abstract we develop a new compact scheme for the second order pde parabolic and schrodinger type with a variable time independent coefficient it has a higher order and smaller error than classic implicit scheme the dirichlet and neumann boundary problems are considered the relative finite difference operator is almost self adjoint

adaptive finite element method for the sound wave problems in two kinds of media abstract in this paper we consider the adaptive finite element method for sound wave propagation problems in two kinds of media which are the linear anisotropic acoustic materials the cloak metamaterials and penetrable media and the nonlinear acoustic materials a posteriori error estimator based on the new flux recovery technique and a residual type posteriori error estimator are proposed based on our a posteriori error estimators the adaptive finite element algorithm is given for numerical simulations of the helmholtz equations in different media extensive numerical results demonstrate the effectiveness of the adaptive algorithm

matrix dependent prolongations and restrictions in a blackbox multigrid solver multigrid methods are studied for the solution of linear systems resulting from the 9 point discretization of a general linear second order elliptic partial differential equation in two dimensions the rate of convergence of standard multigrid methods often deteriorates when the coefficients in the differential equation are discontinuous or when dominating first order terms are present these difficulties may be overcome by choosing the prolongation and restriction operators in a special way a novel way to do this is proposed as a result a blackbox solver written in standard fortran 77 has been developed numerical experiments for several hard test problems are described and comparison is made with other algorithms the standard mg method and a method introduced by kettler a significant improvement of robustness and efficiency is found

solving helmholtz equation at high wave numbers in exterior domains this paper presents effective difference schemes for solving the helmholtz equation at high wave numbers considering the problems in the polar and spherical coordinates we show that pollution free difference schemes can be constructed for annulus and hollow sphere domains but the pollution effect cannot be avoided in the neighborhood of the origin of the coordinate using the fact that the pollution effect appears in a small neighborhood of the origin of the coordinate we propose a local mesh refinement approach so that a fine grid is applied only for a small region near the origin of the coordinate and a much larger grid size is employed in the remaining domain the most attractive feature of this approach is that the computational storage can be significantly reduced while keeping almost the same numerical accuracy moreover by applying a two level local refinement technique we can further enhance the performance of the proposed scheme numerical simulations are reported to verify the effectiveness of the proposed schemes for the helmholtz problem in exterior domains

dispersion analysis and error estimation of galerkin finite element methods for the helmholtz equation when applying numerical methods for the computation of stationary waves from the helmholtz equation one obtains numerical waves that are dispersive also in non dispersive media the numerical wave displays a phase velocity that depends on the parameter k of the helmholtz equation in dispersion analysis the phase difference between the exact and the numerical solutions is investigated in this paper the authors recent result on the phase difference for one dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic it is then shown that previous error estimates in h1 norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only on the other hand recently proven error estimates for constant resolution contain a pollution term with certain assumptions on the exact solution this term is of the order of the phase difference thus a link is established between the results of dispersion analysis and the results of numerical analysis throughout the paper the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems special attention is given to the performance of the galerkin method with a higher order of polynomial approximation p h p version

a review of bootstrap confidence intervals on passe en revue plusieurs methodes distinctes basees sur le bootstrap pour construire des intervalles de confiance

a fourth order optimal finite difference scheme for the helmholtz equation with pml abstract in this paper 17 point and 25 point finite difference fd schemes for the helmholtz equation with perfectly matched layer pml in the two dimensional domain are presented it is shown that the 17 point fd scheme is inconsistent in the presence of pml however the 25 point fd scheme is pointwise consistent an error analysis for the numerical approximation of the exact wavenumber is also presented we present the global and refined 25 point finite difference schemes based on minimizing the numerical dispersion numerical experiments are given to illustrate the improvement of the accuracy and the reduction of the numerical dispersion

discrete total lp norm approximation problem for the exponential function in this paper we consider the total l p norm p 0 approximation problem for the exponential function we give sufficient conditions which guarantee the existence of such optimal parameters

an optimal 25 point finite difference scheme for the helmholtz equation with pml in this paper we present an optimal 25 point finite difference scheme for solving the helmholtz equation with perfectly matched layer pml in two dimensional domain based on minimizing the numerical dispersion we propose the refined choice strategy for choosing optimal parameters of the 25 point finite difference scheme numerical experiments are given to illustrate the improvement of the accuracy and the reduction of the numerical dispersion

concise formulas for the standard errors of component loading estimates concise formulas for the asymptotic standard errors of component loading estimates were derived the formulas cover the cases of principal component analysis for unstandardized and standardized variables with orthogonal and oblique rotations the formulas can be used under any distributions for observed variables as long as the asymptotic covariance matrix for sample covariances correlations is available the estimated standard errors in numerical examples were shown to be equivalent to those by the methods using information matrices

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

a dispersion minimizing finite difference scheme and preconditioned solver for the 3d helmholtz equation in this paper a new 27 point finite difference method is presented for solving the 3d helmholtz equation with perfectly matched layer pml which is a second order scheme and pointwise consistent with the equation an error analysis is made between the numerical wavenumber and the exact wavenumber and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters a full coarsening multigrid based preconditioned bi cgstab method is developed for solving the linear system stemming from the helmholtz equation with pml by the finite difference scheme the shifted laplacian is extended to precondition the 3d helmholtz equation and a spectral analysis is given the discrete preconditioned system is solved by the bi cgstab method with a multigrid method used to invert the preconditioner approximately full coarsening multigrid is employed and a new matrix based prolongation operator is constructed accordingly numerical results are presented to demonstrate the efficiency of both the new 27 point finite difference scheme with refined parameters and the preconditioned bi cgstab method with the 3d full coarsening multigrid

three points method for searching the best least absolute deviations plane in this paper a new method for estimation of optimal parameters of a best least absolute deviations plane is proposed which is based on the fact that there always exists a best least absolute deviations plane passing through at least three different data points the proposed method leads to a solution in finitely many steps moreover a modification of the aforementioned method is proposed that is especially adjusted to the case of a large number of data and the need to estimate parameters in real time both methods are illustrated by numerical examples on the basis of simulated data and by one practical example from the field of robotics

a method for solving the parameter identification problem for ordinary differential equations of the second order we give a method for solving the parameter identification problem for ordinary differential equations of the second order using a noninterpolated moving least squares method the method is tested in two practical examples

high order finite difference methods for the helmholtz equation high order finite difference methods for solving the helmholtz equation are developed and analyzed in one and two dimensions on uniform grids the standard pointwise representation has a second order accurate local truncation error we also study two schemes which have a fourth order accurate local truncation error one of the high order schemes is based on generalizations of the pade approximation the second scheme is based on high order approximation to the derivative calculated from the helmholtz equation itself a symmetric high order representation is developed for a neumann boundary condition numerical results are presented on model problems approximated with the developed schemes

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

a posteriori estimation and adaptive control of the pollution error in the h version of the finite element method abstract we studied the pollution error in the h version of the finite element method and its effect on the quality of the local error indicators resp the quality of the derivatives recovered by local postprocessing in the interior of the mesh here we show that it is possible to construct a posteriori estimates of the pollution error in a patch of elements by employing the local error indicators over the entire mesh we also give an adaptive algorithm for the local control of the pollution error in a patch of elements of interest

accurate finite difference methods for time harmonic wave propagation finite difference methods for solving problems of time harmonic acoustics are developed and analyzed multi dimensional inhomogeneous problems with variable possibly discontinuous coefficients are considered accounting for the effects of employing non uniform grids a weighted average representation is less sensitive to transition in wave resolution due to variable wave numbers or non uniform grids than the standard pointwise representation further enhancement in method performance is obtained by basing the stencils on generalizations of pade approximation or generalized definitions of the derivative reducing spurious dispersion anisotropy and reflection and by improving the representation of source terms the resulting schemes have fourth order accurate local truncation error on uniform grids and third order in the non uniform case guidelines for discretization pertaining to grid orientation and resolution are presented

bootstrap technology and applications bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis although these methods depend on the availability of fast inexpensive computing they offer the potential for highly accurate methods of inference moreover they can even eliminate the need to impose a convenient statistical model that does not have a strong scientific basis in this article we review some bootstrap methods emphasizing applications through illustrations with some real data special attention is given to regression problems with dependent data and choosing tuning parameters for optimal performance

a perfectly matched layer for the helmholtz equation in a semi infinite strip the perfectly matched layer pml has become a widespread technique for preventing reflections from far field boundaries for wave propagation problems in both the time dependent and frequency domains we develop a discretization to solve the helmholtz equation in an infinite two dimensional strip we solve the interior equation using high order finite differences schemes the combined helmholtz pml problem is then analyzed for the parameters that give the best performance we show that the use of local high order methods in the physical domain coupled with a specific second order approximation in the pml yields global high order accuracy in the physical domain we discuss the impact of the parameters on the effectiveness of the pml numerical results are presented to support the analysis

dealing with the multiplicity of solutions of the l1 and l regression models abstract it is well known that the least absolute value l and the least sum of absolute deviations l1 algorithms produce estimators that are not necessarily unique in this paper it is shown how the set of all solutions of the l1 and l regression problems for moderately large sample sizes can be obtained in addition if the multiplicity of solutions wants to be avoided two new methods giving the same optimal l1 and l values but supplying unique solutions are proposed the idea consists of using two steps in the first step the optimal values of the l1 and l errors are calculated and in the second step in case of non uniqueness of solutions one of the multiple solutions is selected according to a different criterion for the l the procedure is used sequentially but removing in each iteration the data points with maximum absolute residual and adding the corresponding constraints for keeping these residuals and this process is repeated until no change in the solution is obtained in this way not only the maximum absolute residual values are minimized in the modified method but also the maximum absolute residual values of the remaining points sequentially until no further improvement is possible in the l1 case a least squares criterion is used but restricted to the l1 residual condition thus in the modified l1 method not only the l1 residual is minimized but also the sum of squared residuals subject to the l1 residual the methods are illustrated by their application to some well known examples and their performances are tested by some simulations which show that the lack of uniqueness problem cannot be corrected for some experimental designs by increasing the sample size

analysis of a parameter identification problem we consider a special parameter identification problem occurring in marketing research and give conditions on the empirical data which guarantee the existence of the solution to the problem furthermore we analyze several different approaches and methods for solving this parameter identification problem

solving parameter estimation problem in new product diffusion models in this paper we propose a new method for the parameter identification in new product diffusion models the method can be used regardless of whether the analytical solution of the differential equation describing the model is known or not this is the main advantage of our method over the known methods another advantage of this method is the simplicity of its implementation and negligible computing time the method is based on finite differences method and the moving least squares method for data smoothing

a dispersion minimizing subgridding finite difference scheme for the helmholtz equation with pml in this paper we present a dispersion minimizing subgridding finite difference scheme for solving the helmholtz equation with perfectly matched layer pml in the two dimensional domain which is a second order scheme and pointwise consistent with the equation subgrids are used to discretize the computational domain and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters for transitional nodes numerical experiments are given to illustrate that the newly proposed schemes can produce highly accurate seismic modeling results with enhanced efficiency compared to uniform grids

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

a unified approach to exploratory factor analysis with missing data nonnormal data and in the presence of outliers factor analysis is regularly used for analyzing survey data missing data data with outliers and consequently nonnormal data are very common for data obtained through questionnaires based on covariance matrix estimates for such nonstandard samples a unified approach for factor analysis is developed by generalizing the approach of maximum likelihood under constraints statistical properties of the estimates for factor loadings and error variances are obtained a rescaled bartlett corrected statistic is proposed for evaluating the number of factors equivariance and invariance of parameter estimates and their standard errors for canonical varimax and normalized varimax rotations are discussed numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures

estimation of parameters of the shifted gompertz distribution using least squares maximum likelihood and moments methods nonlinear least squares procedures for estimating the parameters of the shifted gompertz distribution are proposed simulation studies are carried out to compare weighted and unweighted least squares methods the maximum likelihood method and method of moments this work concludes that least squares methods via weighting factors to estimate the parameters of this probability distribution give a better performance than unweighted least squares methods showing the importance of weighting factors besides results of this simulation study show that a good performance is obtained using the maximum likelihood method and the estimators obtained with more bias are those of the method of moments

normalizing transformations of some statistics in multivariate analysis summary a general procedure for finding normalizing transformations is applied to various statistics in multivariate analysis it is shown that fisher s z transformation for a sample correlation coefficient in a normal sample and wilson hilferty s approximation for a chi squared variate can be derived by the same line of approach

dispersion and pollution of the fem solution for the helmholtz equation in one two and three dimensions for high wave numbers the helmholtz equation suffers the so called pollution effect this effect is directly related to the dispersion a method to measure the dispersion on any numerical method related to the classical galerkin fem is presented this method does not require to compute the numerical solution of the problem and is extremely fast numerical results on the classical galerkin fem p method is compared to modified methods presented in the literature a study of the influence of the topology triangles is also carried out the efficiency of the different methods is compared the numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well the most effective modified method is the qsfem 1 2 but it is also very complicated in the general setting the residual free bubble 3 4 is effective in one dimension but not in higher dimensions the least square method 1 5 approach lowers the dispersion but relatively little the results for triangular meshes show that the best topology is the criss cross pattern copyright 1999 john wiley sons ltd

application of the bootstrap methods in factor analysis a monte carlo experiment is conducted to investigate the performance of the bootstrap methods in normal theory maximum likelihood factor analysis both when the distributional assumption is satisfied and unsatisfied the parameters and their functions of interest include unrotated loadings analytically rotated loadings and unique variances the results reveal that a bootstrap bias estimation performs sometimes poorly for factor loadings and nonstandardized unique variances b bootstrap variance estimation performs well even when the distributional assumption is violated c bootstrap confidence intervals based on the studentized statistics are recommended d if structural hypothesis about the population covariance matrix is taken into account then the bootstrap distribution of the normal theory likelihood ratio test statistic is close to the corresponding sampling distribution with slightly heavier right tail

a dispersion minimizing finite difference scheme for the helmholtz equation based on point weighting abstract in this paper we develop a new dispersion minimizing finite difference scheme for the helmholtz equation with perfectly matched layer pml in two dimensional domain which is a second order 9 point scheme to discretize the second derivative operator we employ a linear combination of a point and its neighboring grid points to replace each of the five points in the traditional central difference scheme based on minimizing the numerical dispersion the combination weights are determined by minimizing the numerical dispersion with a flexible selection strategy the new scheme is simple rotation free and pointwise consistent with the equation which is different from the classical rotated 9 point difference scheme obtained by combining the cartesian coordinate system and the rotated system moreover it is a robust scheme even if the step sizes of different directions are not equal convergence analysis and dispersion analysis are given several numerical examples are presented to illustrate the numerical convergence and effectiveness of the new scheme

on nonlinear weighted least squares estimation of bass diffusion model the bass model is one of the most well known and widely used models of first purchase demand estimation of its parameters has been approached in the literature by various techniques the focus of this paper is on a nonlinear weighted least squares fitting approach as a main result two theorems on the existence of the least squares estimate are obtained one of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate some numerical experiments are given to illustrate the efficiency of our approach

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

on statistical data analysis based on the l1 norm and related methods an introduction to statistical data analysis l 1 norm based y dodge the place of the l 1 norm in robust estimation p j huber i historical development the historical development of the l 1 and l estimation procedures r w farebrother bounded influence inference in regression a review e ronchetti ii computational algorithms and computer packages algorithms for unconstrained l 1 linear regression j e gentle s c narula v a sposito the reduced gradient algorithm m r osborne the l 1 estimate as limiting case of an l p or huber estimate h ekblom a review of computational methods for solving the nonlinear l 1 norm estimation problem r gonin a h money fitting data through homotopy methods j p schellhorn blinwdr a fortran program for robust and bounded influence regression r dutter solving bounded influence regression problems with robsys a marazzi xplore a computing environment for exploratory regression w hardle iii estimation characterization properties and selection of variables l 1 distances in statistical inference comparison of topological functional and statistical properties i vajda the role played by l 1 in data analysis b fichet l 1 embeddings of a data structure i d g le calve assessing the accuracy of the sample median estimated standard errors vs interpolated confidence intervals s j sheather the median of a finite measure on a banach space j h b kemperman variable selection in linear model based on trimmed least squares estimator j antoch numerical techniques for finding estimates which minimize the upper bound of the absolute deviation a gaivoronski asymptotic properties of restricted l 1 estimates of regression j dupacova adaptive combination of least squares and least absolute deviations estimators y dodge j jureckova iv statistical inference procedures a comparison of asymptotic testing methods for l 1 regression r koenker least absolute errors analysis of variance j w mckean r m schrader small sample properties of least absolute errors analysis of variance r m schrader j w mckean bootstrap and inference procedures for l 1 regression g stangenhaus invariant tests in bivariate models and the l 1 criterion b m brown t p hettmansperger using regression fractiles to identify outliers s portnoy various discrepancy measures in model testing two competing regression models v v fedorov v nonparametric analysis kernel estimates of the sparsity function a h welsh what does optimal bandwidth selection mean for nonparametric regression estimation j s marron density estimation from dependent sample l gyorfi vi cluster analysis clustering by means of medoids l kaufman p j rousseeuw l 1 in fuzzy clustering e trauwaert using the l 1 norm within cluster analysis h spath vii applications an application of l 1 to astronomy p j rousseeuw