asymptotics of r md and lad estimators in linear regression models with long range dependent errors this paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are gaussian or a function of gaussian random variables that are strictly stationary and long range dependent this result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with long range dependent errors the latter result in turn yields the asymptotic distribution of the jaeckel 1972 rank estimators the paper also studies the least absolute deviation and a class of certain minimum distance estimators of regression parameters and the kernel type density estimators of the marginal error density when the errors are long range dependent

z2 graded identities of the grassmann algebra in positive characteristic let f be an infinite field of characteristic p 2 and let e be the grassmann algebra generated by an infinite dimensional vector space v over f in this paper we describe the t2 ideal of the z2 graded polynomial identities of the grassmann algebra e for any z2 grading such that v is homogeneous in the grading in particular we give a description of the t2 ideal of the graded identities of e in the case there is a finite number of homogeneous elements of the linear basis of e belonging to one of the homogenous components of e

group gradings on the jordan algebra of upper triangular matrices abstract let g be an arbitrary group and let k be a field of characteristic different from 2 we classify the g gradings on the jordan algebra uj n of upper triangular matrices of order n over k it turns out that there are up to a graded isomorphism two families of gradings the elementary gradings analogous to the ones in the associative case and the so called mirror type mt gradings moreover we prove that the g gradings on uj n are uniquely determined up to a graded isomorphism by the graded identities they satisfy

on estimation of a regression model with long memory stationary errors we consider estimation of a regression model with long memory stationary errors first we estimate the regression parameters by the least squares estimator lse and next those describing the correlation structure of the error terms by using the residuals obtained from the lse certain regularity conditions introduced to develop the asymptotic theory no longer hold in this model in this situation we derive asymptotic properties of the preceding estimation procedure

asymptotic properties of the lse in a regression model with long memory stationary errors we consider asymptotic properties of the least squares estimator lse in a regression model with long memory stationary errors first we derive a necessary and sufficient condition that the lse be asymptotically efficient relative to the best linear unbiased estimator blue then we derive the asymptotic distribution of the lse under a condition on the higher order cumulants of the white noise process of the errors

elementary gradings on the lie algebra utn the algebras utn k utn k of the upper triangular matrices over a field k are of significant importance in the theory of algebras with polynomial identities group gradings on algebras appear in various areas and provide an indispensable tool in the study of the algebraic and combinatorial properties of the algebras in question in this paper we consider the lie algebra utn k utn k of all upper triangular matrices of order n we study the group gradings on this algebra it turns out that the gradings on the lie algebra utn k utn k are much more intricate than those in the associative case in this paper we describe the elementary gradings on the lie algebra utn k utn k finally we study the canonical grading on utn k utn k by the cyclic group znzn of order n we produce a finite basis of the graded polynomial identities satisfied by this grading

finite volume method with lattice boltzmann flux scheme for incompressible porous media flow at the representative elementary volume scale based on the darcy brinkman forchheimer equation a finite volume computational model with lattice boltzmann flux scheme is proposed for incompressible porous media flow in this paper the fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice boltzmann equation for porous media flow the time scaled midpoint integration rule is adopted to discretize the governing equation which makes the time step become limited by the courant friedricks lewy condition the force term which evaluates the effect of the porous medium is added to the discretized governing equation directly the numerical simulations of the steady poiseuille flow the unsteady womersley flow the circular couette flow and the lid driven flow are carried out to verify the present computational model the obtained results show good agreement with the analytical finite difference and or previously published solutions

wavelet generalized least squares a new blu estimator of linear regression models with 1 f errors long memory noise is common to many areas of signal processing and can seriously confound estimation of linear regression model parameters and their standard errors classical autoregressive moving average arma methods can adequately address the problem of linear time invariant short memory errors but may be inefficient and or insufficient to secure type 1 error control in the context of fractal or scale invariant noise with a more slowly decaying autocorrelation function here we introduce a novel method called wavelet generalized least squares wls which is to a good approximation the best linear unbiased blu estimator of regression model parameters in the context of long memory errors the method also provides maximum likelihood ml estimates of the hurst exponent which can be readily translated to the fractal dimension or spectral exponent characterizing the correlational structure of the errors and the error variance the algorithm exploits the whitening or kar

lattice boltzmann flux scheme for the convection diffusion equation and its applications in this work a lattice boltzmann flux scheme for the convection diffusion equation cde is proposed in this scheme the fluxes across the cell interface are calculated by using the local solution of the multiple relaxation time lattice boltzmann equation for cde the present method is suitable for simulating both isotopic and anisotropic diffusion processes meanwhile through applying the midpoint time integration technique the present method relaxes the time step constraint in the original lattice boltzmann flux scheme four convection diffusion problems are simulated to validate the present scheme the obtained results agree well with the analytical or previous published solutions

low and high order accurate boundary conditions the present contribution focuses on the accuracy of reflection type boundary conditions in the stokesbrinkmandarcy modeling of porous flows solved with the lattice boltzmann method lbm which we operate with the two relaxation time trt collision and the brinkman force based scheme bf called bf trt scheme in parallel we compare it with the stokesbrinkmandarcy linear finite element method fem where the dirichlet boundary conditions are enforced on grid vertices in bulk both bf trt and fem share the same defect in their discretization a correction to the modeled brinkman equation appears given by the discrete laplacian of the velocity proportional resistance force this correction modifies the effective brinkman viscosity playing a crucial role in the triggering of spurious oscillations in the bulk solution while the exact form of this defect is available in lattice aligned straight or diagonal flows in arbitrary flow lattice orientations its approximation is constructed at boundaries we verify that such a brinkman viscosity correction has an even more harmful impact already at the first order it shifts the location of the no slip wall condition supported by traditional lbm boundary schemes such as the bounce back rule for that reason this work develops a new class of boundary schemes to prescribe the dirichlet velocity condition at an arbitrary wall boundary node distance and that supports a higher order accuracy in the accommodation of the trt brinkman solutions for their modeling we consider the standard bf scheme and its improved version called ibf this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows our framework extends the one and two point families of linear and parabolic link wise boundary schemes respectively called b li and b mli which avoid the interference of the brinkman viscosity correction in their closure relations the performance of lbm and fem is thoroughly evaluated in three benchmark tests which are run throughout three distinctive permeability regimes the first configuration is a horizontal porous channel studied with a symbolic approach where we construct the exact solutions of fem and bf ibf with different boundary schemes the second problem refers to an inclined porous channel flow which brings in as new challenge the formation of spurious boundary layers in lbm that is numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low accurate boundary scheme the third problem considers a porous flow past a periodic square array of solid cylinders which intensifies the previous two tests with the simulation of a more complex flow pattern the ensemble of numerical tests provides guidelines on the effect of grid resolution and the trt free collision parameter over the accuracy and the quality of the velocity field spanning from stokes to darcy permeability regimes it is shown that with the use of the high order accurate boundary schemes the simple uniform mesh based trt lbm formulation can even surpass the accuracy of fem employing hardworking body fitted meshes

contrasts under long range correlations the background of the paper is the empirical observation from a variety of subject areas that long range correlations appear to be much more frequent than has been previously assumed this includes high quality measurement series which are commonly treated as prototypes of i i d observations evidence is briefly cited in the paper it has already been shown elsewhere that long range dependence leads to results that can be qualitatively different from those obtained under short range dependence and in particular that long range dependence has drastic effects on the naive statistical treatment of absolute constants the natural question arising from this also of relevance for statistical practice is how the long range dependence affects the statistics for contrasts the main answer given in this paper is twofold

uniform moment bounds of fisher s information with applications to time series in this paper a uniform over some parameter space moment bound for the inverse of fisher s information matrix is established this result is then applied to develop moment bounds for the normalized least squares estimate in nonlinear stochastic regression models the usefulness of these results is illustrated using time series models in particular an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving average models is obtained this asymptotic expression provides a solid theoretical foundation for some model selection criteria

group gradings on the lie algebra of upper triangular matrices abstract the algebras u t n of the n n upper triangular matrices over a field k are of significant importance in the theory of algebras with polynomial identities group gradings on algebras appear in various areas and provide an indispensable tool in the study of the algebraic and combinatorial properties of the algebras in question we classify the group gradings on the lie algebra u t n it was proved by valenti and zaicev in 2007 that every group grading on the associative algebra u t n is isomorphic to an elementary grading the elementary gradings on u t n are also well understood see 6 it follows from our results that there are nonelementary gradings on u t n thus the gradings on the lie algebra u t n are much more intricate than those in the associative case

on z2 graded identities of ut2 e and their growth abstract let f be an infinite field of characteristic different from two and e be the infinite dimensional grassmann algebra over f we consider the upper triangular matrix algebra ut 2 e with entries in e endowed with the z 2 grading inherited by the natural z 2 grading of e and we study its ideal of z 2 graded polynomial identities t z 2 ideal and its relatively free algebra in particular we show that the set of z 2 graded polynomial identities of ut 2 e does not depend on the characteristic of the field moreover we compute the z 2 graded hilbert series of ut 2 e and its z 2 graded gelfand kirillov dimension

wavelet regression in random design with heteroscedastic dependent errors we investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of besov scales f b s r and for a variety of l p error measures we consider error distributions with long range dependence parameter 0 2 it is seen that there are three rate phases namely the dense sparse and long range dependence phase depending on the relative values of s p and furthermore we show that long range dependence does not come into play for shape estimation f f the theory is illustrated with some numerical examples

efficient location and regression estimation for long range dependent regression models in this paper we construct an efficient weighted least squares estimator for the mean and more generally for the regression parameters in certain gaussian long range dependent regression models including polynomial regression the form of the estimator does not depend on the whole dependence structure of the residuals but only on the local behaviour of the spectral density at zero by using an estimator of the self similarity parameter we give a fully efficient estimator furthermore we construct efficient weighted m estimators

statistical inference on regression with spatial dependence central limit theorems are developed for instrumental variables estimates of linear and semiparametric partly linear regression models for spatial data general forms of spatial dependence and heterogeneity in explanatory variables and unobservable disturbances are permitted we discuss estimation of the variance matrix including estimates that are robust to disturbance heteroscedasticity and or dependence a monte carlo study of finite sample performance is included in an empirical example the estimates and robust and non robust standard errors are computed from indian regional data following tests for spatial correlation in disturbances and nonparametric regression fitting some final comments discuss modifications and extensions

time series regression with long range dependence a central limit theorem is established for time series regression estimates which include generalized least squares in the presence of long range dependence in both errors and stochastic regressors the setting and results differ significantly from earlier work on regression withlong range dependent errors spectral singularities are permitted at any frequency when sufficiently strong spectral singularities in the error and a regressor coincide at the same frequency least squares need no longer be n 1 2 consistent where n is the sample size however we show that our class of estimates is n 1 2 consistent and asymptotically normal in the generalized least squares case we show that efficient estimation is still possible when the error autocorrelation is known only up to finitely many parameters we include a monte carlo study of finite sample performance and provide an extension to nonlinear least squares

on z2 graded polynomial identities of the grassmann algebra abstract let f be a field of characteristic zero and let e be the grassmann algebra of an infinite dimensional f vector space l in this paper we study the z 2 graded polynomial identities of e with respect to any fixed z 2 grading such that l is an homogeneous subspace we found explicit generators for the ideal t 2 e of graded polynomial identities of e and we determine its cocharacter and codimension sequences