canonical bases of invariant polynomials for the irreducible reflection groups of types e6 e7 and e8 abstract given a rank n irreducible finite reflection group w the w invariant polynomial functions defined in r n can be written as polynomials of n algebraically independent homogeneous polynomial functions p 1 x p n x called basic invariant polynomials their degrees are well known and typical of the given group w the polynomial p 1 x has the lowest degree equal to 2 it has been proved that it is possible to choose all the other n 1 basic invariant polynomials in such a way that they satisfy a certain system of differential equations including the laplace equations p a x 0 a 2 n and so are harmonic functions bases of this kind are called canonical explicit formulas for canonical bases of invariant polynomials have been found for all irreducible finite reflection groups except for those of types e 6 e 7 and e 8 those for the groups of types e 6 e 7 and e 8 are determined in this article

entropic lattice boltzmann representations required to recover navier stokes flows there are two disparate formulations of the entropic lattice boltzmann scheme one of these theories revolves around the analog of the discrete boltzmann h function of standard extensive statistical mechanics while the other revolves around the nonextensive tsallis entropy it is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in tsallis like forms however with the imposition of the pressure tensor moment constraint as is fundamentally necessary for the recovery of the navier stokes equations it is proved that the entropy function must be of the discrete boltzmann form three dimensional simulations are performed which illustrate some of the differences between standard lattice boltzmann and entropic lattice boltzmann schemes as well as the role played by the number of phase space velocities used in the discretization

advances in multi domain lattice boltzmann grid refinement grid refinement has been addressed by different authors in the lattice boltzmann method community the information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view while a decimation is performed when going from the fine to the coarse grid a reconstruction must performed to pass form the coarse to the fine grid in this context we introduce a decimation technique for the copy from the fine to the coarse grid based on a filtering operation we show this operation to be extremely important because a simple copy of the information is not sufficient to guarantee the stability of the numerical scheme at high reynolds numbers then we demonstrate that to reconstruct the information a local cubic interpolation scheme is mandatory in order to get a precision compatible with the order of accuracy of the lattice boltzmann method these two fundamental extra steps are validated on two classical 2d benchmarks the 2d circular cylinder and the 2d dipole wall collision the latter is especially challenging from the numerical point of view since we allow strong gradients to cross the refinement interfaces at a relatively high reynolds number of 5000 a very good agreement is found between the single grid and the refined grid cases the proposed grid refinement strategy has been implemented in the parallel open source library palabos

robust fitting of the binomial model we consider the problem of robust inference for the binomial m pi model the discreteness of the data and the fact that the parameter and sample spaces are bounded mean that standard robustness theory gives surprising results for example the maximum likelihood estimator mle is quite robust it cannot be improved on for m 1 but can be for m 1 we discuss four other classes of estimators m estimators minimum disparity estimators optimal mgp estimators and a new class of estimators which we call e estimators we show that e estimators have a non standard asymptotic theory which challenges the accepted relationship between robustness concepts and thereby provided new perspectives on these concepts

on conservation at grid interfaces this paper considers the solution of hyperbolic systems of conservation laws on discontinuous grids in particular we consider what happens to conservation at grid interfaces a procedure is presented to derive conservative difference approximations at the grid interfaces for two dimensional grids which overlap in an arbitrary configuration the same procedures are applied to compute interface formulas for grids which are refined in space and or time and for continuous grids where a switch in the scheme causes the discontinuity

grid refinement for lattice bgk models lattice boltzmann models proposed at the end of the 1980s as the noise free version of lattice gas models are based on gas kinetic representation of fluid flow their recent modifications the lattice bgk models provide especially simple effective and stable algorithms for the solution of hydrodynamical problems a local second order grid refinement scheme for the lattice bgk model is proposed in this work the refinement scheme and a boundary fitting scheme for complicated geometries are applied to simulate a benchmark problem of flow past a cylinder in a channel with small and moderate reynolds numbers

assessing influence on regression coefficients in generalized linear models summary suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case we apply the local influence method of cook 1986 to assess the effect of small perturbations of the data including the vector of responses case weights explanatory variables and the components of one case the resulting diagnostics allow one to check for different kinds of influence and may give insight into its workings two examples illustrate some of the diagnostics

assessing robustness of generalised estimating equations and quadratic inference functions in the presence of data contamination or outliers some empirical studies have indicated that the two methods of generalised estimating equations and quadratic inference functions appear to have rather different robustness behaviour this paper presents a theoretical investigation from the perspective of the influence function to identify the causes for the difference we show that quadratic inference functions lead to bounded influence functions and the corresponding m estimator has a redescending property but the generalised estimating equation approach does not we also illustrate that unlike generalised estimating equations quadratic inference functions can still provide consistent estimators even if part of the data is contaminated we conclude that the quadratic inference function is a preferable method to the generalised estimating equation as far as robustness is concerned this conclusion is supported by simulations and real data examples

binary regression models for contaminated data on etudie la nature des observations aberrantes dans le contexte des donnees de regression binaires on propose un modele simple qui permet qu un petit nombre de reponses binaires soit mal enregistre

generalized additive models some applications abstract generalized additive models have the form x fj x j where might be the regression function in a multiple regression or the logistic transformation of the posterior probability pr y 1 x in a logistic regression in fact these models generalize the whole family of generalized linear models x x where x g x is some transformation of the regression function we use the local scoring algorithm to estimate the functions fj xj nonparametrically using a scatterplot smoother as a building block we demonstrate the models in two different analyses a nonparametric analysis of covariance and a logistic regression the procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in a standard linear analysis a variety of inferential tools have been developed to aid the analyst in assessing the relevance and significance of the estimated functions these include confidence curves degrees of freedom estimates and approximat

deletion diagnostics for generalised estimating equations summary deletion diagnostics are proposed for generalised estimating equations the diagnostics consider leverage and residuals to measure the influence of a subset of observations on the estimated regression parameters and on the estimated values of the linear predictor computational formulae are provided which correspond to the influence of a single observation and of an entire cluster of correlated observations additionally diagnostics are given which approximate the effect of deletion of an arbitrary subset of observations under a model with general covariance structure and arbitrary link function extending proposition 3 of christensen pearson johnson 1992 the proposed measures are applied to medical data

a canonical system of basic invariants of a finite reflection group abstract a canonical system of basic invariants is a system of invariants satisfying a set of differential equations the properties of a canonical system are related to the mean value property for polytopes in this article we naturally identify the vector space spanned by a canonical system of basic invariants with an invariant space determined by a fundamental antiinvariant from this identification we obtain explicit formulas of canonical systems of basic invariants the construction of the formulas does not depend on the classification of finite irreducible reflection groups

a generalized linear model for analysing receiver operating characteristic curves we present a continuation ratio model for analysing ordinal categorical data and we apply the model to the problem of estimating receiver operating characteristic roc curves we apply the methods to post prandial capillary blood glucose measurements as a criterion for a potential screening test for diabetes mellitus one can obtain point estimates of sensitivity and specificity and their associated standard errors at any value along the observed range of post prandial capillary blood glucose measurements also in comparison to the models for rocs described by tosteson and begg roc curves based on the continuation ratio model have the desired features that allow rocs to be concave but not necessarily symmetric

theory and applications of an alternative lattice boltzmann grid refinement algorithm this contribution proposes an alternative lattice boltzmann grid refinement algorithm that overcomes the drawbacks that plague existing approaches we demonstrate that this algorithm is accurate and applicable for all values of the relaxation time we also show that this algorithm can significantly speed up the flow settlement process by using a hierarchy of grid levels the stationary regime can be approached up to a thousand times faster than with a single grid resolution

least median of weighted squares in logistic regression with large strata summary one aim of robust regression is to find estimators with high finite sample breakdown points although various robust estimators have been proposed in logistic regression models their breakdown points are not yet known here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point provided the estimator has to fulfill a weak condition in logistic regression models with large strata however a modification of rousseeuw s least median of squares estimator is shown to have a finite sample breakdown point of approximately 2

efficient bounded influence regression estimation abstract the least squares estimator for in the classical linear regression model is strongly efficient under certain conditions however in the presence of heavy tailed errors and or anomalous data the least squares efficiency can be markedly reduced in this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first order condition for strong efficiency subject to the constraint we then show that the estimator is asymptotically normal the article concludes with an outline of an algorithm for computing a bounded influence regression estimator and with an example comparing least squares robust regression as developed by huber and the estimator proposed in this article

influence functions for iteratively defined statistics summary hampel s influence function and its finite sample counterparts are the basis for a number of diagnostic statistics these diagnostics can be expensive to compute in the natural way when the estimation calculations are iterative as they frequently are when maximum likelihood or robust methods are used we show how the influence function can be calculated in these situations by implicit differentiation of the fixed point equation satisfied by the limit of the iterative procesb we consider in particular the cases of newton s method and iteratively reweighted least squares where interesting analytic results are available as an application we consider the generalization of pregibon s 1981 logistic regression diagnostics to cover generalized linear models with noncanonical link functions such as probit regression

consistency of deviance based m estimators summary in a general estimation problem the deviance function generates statistics that are similar to squared standardized residuals a deviance based m estimator dbme is defined as an adaptively weighted maximum likelihood estimator where the weights depend upon the deviances in both a single parameter and a regression setting we give some general conditions under which a dmbe is consistent for a suitable weighting scheme these conditions are satisfied in many continuous cramer rao regular families and in related linear or nonlinear regression cases the conditions fail and the estimator is inconsistent in most discrete families

weighted likelihood equations with bootstrap root search abstract we discuss a method of weighting likelihood equations with the aim of obtaining fully efficient and robust estimators we discuss the case of continuous probability models using unimodal weighting functions these weighting functions downweight observations that are inconsistent with the assumed model at the true model therefore the proposed estimating equations behave like the ordinary likelihood equations we investigate the number of solutions of the estimating equations via a bootstrap root search the estimators obtained are consistent and asymptotically normal and have desirable robustness properties an extensive simulation study and real data examples illustrate the operating characteristics of the proposed methodology

residuals in generalized linear models abstract generalized linear models are regression type models for data not normally distributed appropriately fitted by maximum likelihood rather than least squares typical examples are models for binomial or poisson data with a linear regression model for a given ordinarily nonlinear function of the expected values of the observations use of such models has become very common in recent years and there is a clear need to study the issue of appropriate residuals to be used for diagnostic purposes several definitions of residuals are possible for generalized linear models the statistical package glim baker and nelder 1978 routinely prints out residuals where v is the function relating the variance to the mean of y and is the maximum likelihood estimate of the ith mean as fitted to the regression model these residuals are the signed square roots of the contributions to the pearson goodness of fit statistic another choice of residual is the signed square root of the contribution to the devia

robust inference for generalized linear models by starting from a natural class of robust estimators for generalized linear models based on the notion of quasi likelihood we define robust deviances that can be used for stepwise model selection as in the classical framework we derive the asymptotic distribution of tests based on robust deviances and we investigate the stability of their asymptotic level under contamination the binomial and poisson models are treated in detail two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures

basic invariants of finite reflection groups abstract any finite reflection group g admits a distinguished basis of g invariants canonically attached to a certain system of invariant differential equations we determine it explicitly for groups of types a b d and i in a systematic way

on the use of nonparametric regression for model checking summary the use of nonparametric regression is explored to check the fit of a parametric regression model the principal aim is to check the validity of the regression curve rather than necessarily to detect outliers a pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model the types of data considered include discrete response variables where standard diagnostic techniques are often not appropriate and first order autoregressive series several numerical examples are given nonparametric regression can be used in an informal graphical way to assess the relationship between a response and an explanatory variable in this paper we aim to develop more formal methods of assessing the assumptions of a parametric model in particular when regression diagnostics of the type developed for normal linear models are not readily available the principal aim is to check the validity of the systematic part of the model by comparing a nonparametric estimate of the regression curve with a parametric one such a comparison may also identify outliers although the distinction between outliers and model inadequacy is not always easy two techniques are used to assess the fit of a parametric model in 2 confidence bands are constructed around the fitted regression curve by simulation a comparison of these with the nonparametric curve gives an indication of the nature of any departures from the model in 3 a pseudo likelihood ratio test is developed this provides a quantitative global assessment of fit in applying these ideas special emphasis is given to discrete data and notably logistic regression because of the difficulty in applying standard residual based model checking techniques to this type of response variable a poisson regression example is discussed in 4 however the underlying ideas have wider applications autoregressive time series of order 1 are discussed in 6 sections 5 and 7 discuss general issues we first discuss the context of binary regression with a single covariate and the difficulties caused by the discreteness of the response variable the observed data are assumed to be of the form xi yi ni where xi is a covariate value and yi has a binomial

robust logistic discrimination summary logistic discrimination is a well established method for allocating observations to one of two or more populations in this paper we show how the logistic model can be adapted to make it robust against outlying observations from the populations the new model is successfully tested using simulated data against ordinary logistic discrimination and also against logistic discrimination where parameters are fitted using resistant methods the model is then used on data collected from the teeth of rats logistic discrimination is a partially parametric method for discrimination applicable in many situations and under several sampling schemes notable references to the method are day kerridge 1967 anderson 1972 1979 1982 and anderson blair 1982 the appeal of the logistic method for discrimination is that only the ratio of likelihoods has to be modelled and not the full distributional form of the underlying variables press wilson 1978 and byth mclachlan 1980 show that in many circumstances logistic discrimination is preferable to the usual linear discrimination based on either normal populations with equal covariance matrices or fisher s linear discriminant for the two group case suppose x is a vector of observations h1 and h2 are the two groups and a a parameter vector then the log likelihood ratio is modelled as

optimally bounded score functions for generalized linear models with applications to logistic regression summary we study optimally bounded score functions for estimating regression parameters in a generalized linear model our work extends results obtained by krasker welsch 1982 for the linear model and provides a simple proof of krasker welsch s first order condition for strong optimality the application of these results to logistic regression is studied in some detail with an example given comparing the bounded influence estimator with maximum likelihood where h q and c are known functions and 0 is a vector of regression parameters models of this type include logistic and probit regression poisson regression linear regression with known variance and certain models for lifetime data our motivation for seeking robust estimators is the same as that in the linear model maximum likelihood estimation is sometimes sensitive to outlying data for logistic regression pregibon 1981 1982 has documented the nonrobustness of the maximum likelihood estimator and expounded the benefits of diagnostics as well as robust or resistant fitting procedures see also johnson 1985 much of the work on robust estimation concerns finding estimators which sacrifice little efficiency at the assumed model while providing protection against outliers and model violations we follow this course finding bounded influence estimators minimizing certain functionals of the asymptotic covariance matrix related work includes that of hampel 1978 krasker 1980 and krasker welsch 1982 when fitting models to data two important issues are identification of outliers and influential cases and accommodation of these observations frequently when influential cases are present the fitted model is not representative of the bulk of the data to rectify this one can simply delete influential cases and refit via standard methods but this

robust inference with binary data in this paper robustness properties of the maximum likelihood estimator mle and several robust estimators for the logistic regression model when the responses are binary are analysed it is found that the mle and the classical rao s score test can be misleading in the presence of model misspecification which in the context of logistic regression means either misclassification s errors in the responses or extreme data points in the design space a general framework for robust estimation and testing is presented and a robust estimator as well as a robust testing procedure are presented it is shown that they are less influenced by model misspecifications than their classical counterparts they are finally applied to the analysis of binary data from a study on breastfeeding

confidence bands for logistic regression with restricted predictor variables confidence bands are constructed for the logistic response function when there is an interval restriction on each of the predictor variables the construction involves application of a general fitting procedure using scheffe s s method described by casella and strawderman 1980 journal of the american statistical association 75 862 868 specific details are given for the case of one predictor variable along with details for a fixed width alternative to the s method bands in the one predictor case monte carlo results suggest that both bands are conservative for small sample sizes such as n 25 by n 200 the s method s coverage probabilities are seen to attain their nominal levels while the fixed width bands remain conservative the procedures are exemplified with data from a genetic toxicology experiment

an analysis of density dependent viability selection abstract generalized linear modeling techniques and resistant fitting methods were used to analyze the results of two experiments to test for density dependent viability selection on chromosomal variants in drosophila pseudoobscura fruit flies in the framework of the generalized linear model a series of nested hypotheses were fitted by the maximum likelihood method the hypotheses describe how the viabilities of two genotypes relative to a third varied with density and other factors an additional analysis of the absolute viabilities of the three genotypes was also performed by the maximum likelihood method estimates were computed by the em algorithm resistant methods of fitting were then performed for the best fitting relative viability models the analyses confirm that the relative viability of one genotype increased linearly with density with slope and intercept viability differences between genotypes can thus be explained by variation in density

data analytic methods for matched case control studies the recent introduction of complex multivariate statistical models in matched case control studies is a mixed blessing their use can lead to a better understanding of the way in which many variables contribute to the risk of disease on the other hand these powerful methods can obscure salient features in the data that might have been detected by other less sophisticated methods this shortcoming is due to a lack of support methodology for the routine use of these models satisfactory computation of estimated relative risks and their standard errors is not sufficient justification for the fitted model goodness of fit must be examined if inferences are to be trusted this paper is concerned with the analysis of matched case control studies with logistic models analogies of these models to linear regression models are emphasized in particular basic concepts such as analysis of variance multiple correlation coefficient one degree of freedom tests and residual analysis are discussed the fairly new field of regression diagnostics is also introduced all procedures are illustrated on a study of bladder cancer in males

on the finite difference based lattice boltzmann method in curvilinear coordinates the lattice boltzmann method is a microscopic based approach for solving the fluid flow problems at the macroscopic scales the presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility to circumvent such difficulties a finite difference based lattice boltzmann method fdlbm in curvilinear coordinates is explored using body fitted coordinates with non uniform grids several test cases including the impulsively started cylindrical couette flow steady state cylindrical couette flow steady flow over flat plates and steady flow over a circular cylinder are used to examine various issues related to the fdlbm the effect of boundary conditions for the distribution functions on the solution the merits between second order central difference and upwind schemes for advection terms and the effect of the reynolds number are investigated favorable results are obtained using fdlbm in curvilinear coordinates indicating that the method is potentially capable of solving finite reynolds number flow problems in complex geometries

the lattice boltzmann equation a new tool for computational fluid dynamics abstract we present a series of applications which demonstrate that the lattice boltzmann equation is an adequate computational tool to address problems spanning a wide spectrum of fluid regimes ranging from laminar to fully turbulent flows in two and three dimensions

robust analysis of generalized linear mixed models the method of maximum likelihood ml is widely used for analyzing generalized linear mixed models glmm s a full maximum likelihood analysis requires numerical integration techniques for calculation of the log likelihood and to avoid the computational problems involving irreducibly high dimensional integrals several maximum likelihood algorithms have been proposed in the literature to estimate the model parameters by approximating the log likelihood function although these likelihood algorithms are useful for fitting the glmm s efficiently under strict model assumptions they can be highly influenced by the presence of unusual data points in this article the author develops a technique for finding robust maximum likelihood rml estimates of the model parameters in glmm s which appears to be useful in downweighting the influential data points when estimating the parameters the asymptotic properties of the robust estimators are investigated under some regularity conditions small simulations are

interpolation methods and the accuracy of lattice boltzmann mesh refinement a lattice boltzmann model to solve the equivalent of the navier stokes equations on adaptively refined grids is presented a method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite volume representations this new approach relies on a space time interpolation and solving constrained least squares problems to ensure conservation the effectiveness of this method at maintaining the second order accuracy of lattice boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies these results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation examples highlighting the mesh adaptivity of this method are also provided

conditionally unbiased bounded influence estimation in general regression models with applications to generalized linear models abstract in this article robust estimation in generalized linear models for the dependence of a response y on an explanatory variable x is studied a subclass of the class of m estimators is defined by imposing the restriction that the score function must be conditionally unbiased given x within this class of conditionally fisher consistent estimators optimal bounded influence estimators of regression parameters are identified and their asymptotic properties are studied the estimators studied in this article and the efficient bounded influence estimators studied by stefanski carroll and ruppert 1986 depend on an auxiliary centering constant and nuisance matrix the centering constant can be given explicitly for the conditionally fisher consistent estimators and thus they are easier to compute than the estimators studied by stefanski et al 1986 in addition estimation of the nuisance matrix has no effect on the asymptotic distribution of the conditionally fisher consistent estimators the sam

an overview of the variables selection methods for the minimum sum of absolute errors regression the minimum sum of absolute errors regression is a robust alternative to the least squares regression whenever the errors follow a distribution for which the sample median is a more efficient estimator of location parameter than the sample mean the errors follow a long tailed distribution there are outliers in the values of the response variable in the data or the absolute error loss function is more appropriate than the quadratic loss function often an initial model may contain a large number of variables however in many situations it is neither necessary nor important to include all the variables in the model the methods for variable selection for the minimum sum of absolute errors regression are not as well documented and known as for the least squares regression our objective is to present an overview of the procedures to fit models with fewer variables and some criteria for selecting a model

least absolute deviations fits for generalized linear models reference stap article 1992 004view record in web of science record created on 2006 04 04 modified on 2016 08 08

interpolated boundary condition for lattice boltzmann simulations of flows in narrow gaps several different interpolation schemes have been proposed for improving the accuracy of lattice boltzmann simulations in the vicinity of a solid boundary however these methods require at least two or three fluid nodes between nearby solid surfaces a condition that may not be fulfilled in dense suspensions or porous media for example here we propose an interpolation of the equilibrium distribution which leads to a velocity field that is both second order accurate in space and independent of viscosity the equilibrium interpolation rule infers population densities on the boundary itself to reduce the span of nodes needed for interpolation it requires a minimum of one grid spacing between the nodes by contrast the linear interpolation rule requires two fluid nodes in the gap and leads to a viscosity dependent slip velocity while the multireflection rule is viscosity independent but requires a minimum of three fluid nodes

multireflection boundary conditions for lattice boltzmann models we present a general framework for several previously introduced boundary conditions for lattice boltzmann models such as the bounce back rule and the linear and quadratic interpolations the objectives are twofold first to give theoretical tools to study the existing link type boundary conditions and their corresponding accuracy second to design boundary conditions for general flows which are third order kinetic accurate using these new boundary conditions couette and poiseuille flows are exact solutions of the lattice boltzmann models for a reynolds number mathrm re 0 stokes limit for arbitrary inclination with the lattice directions numerical comparisons are given for stokes flows in periodic arrays of spheres and cylinders linear periodic array of cylinders between moving plates and for navier stokes flows in periodic arrays of cylinders for mathrm re l200 these results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce back reflection up to an order of magnitude on the hydrodynamics fields further improvement is achieved with the new multireflection boundary conditions reaching a level of accuracy close to the quasianalytical reference solutions even for rather modest grid resolutions and few points in the narrowest channels more important the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions finally the good stability of these schemes is highlighted by some simulations of moving obstacles a cylinder between flat walls and a sphere in a cylinder

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

regression models for choice based samples with misclassification in the response variable abstract in this paper we provide a general framework to deal with the presence of misclassification in the response variable in choice based samples the contaminated data sampling distribution is written as a function of the error free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values we propose an extension of imbens econometrica 60 1992 1187 efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error the performance of both the estimators and the test is investigated in a monte carlo simulation study which shows very encouraging results

robust regression for clustered data with application to binary responses summary generalized estimating equations gee can be highly influenced by the presence of unusual data points a generalization of the gee procedure which yields parameter estimates and fitted values that are resistant to influential data is introduced resistant generalized estimating equations regee include weights in the estimating equations to downweight influential observations or clusters influential observations are downweighted according to their leverage or residual in an example of correlated binary regression applied to 137 urinary incontinent elderly patients from 38 medical practices

resistant fits for some commonly used logistic models with medical application logistic regression type models are used in many applications some examples include the classical dose response experiment prospective and retrospective studies of disease incidence with and without matching and the analysis of ordinal data in most instances the model is fitted by the method of maximum likelihood which like least squares is sensitive to atypical observations an alternative to maximum likelihood is proposed and illustrated by examples

a robust confidence interval for location robust estimation procedures have been the subject of a large number of comparative studies less attention has been paid to confidence intervals and tests based on these procedures and to cases in which the underlying distribution is nonsymmetric this article investigates the properties of just one interval m estimator of location the estimator is quite easy to compute and the associated point estimator of location has proven to be quite efficient in comparative studies the results indicate that in most cases including some skewed distributions the confidence coefficient of the estimator holds quite close to its specified value

on the covariance between parameter estimates in models of twin data we study the covariance between estimates of additive genetic variance and either dominance genetic variance or common environmental variance in likelihood based twin analyses the central tools used in these investigations are the asymptotic covariances of variance component estimates which we present for several commonly used twin models we first illustrate the use of the asymptotic covariance terms for determining the optimal ratio of monozygotic to dizygotic group sample sizes for a twin study we then focus attention on the asymptotic correlations between estimates of additive genetic variance and either dominance genetic variance or common environmental variance and their use in understanding when parameters are efficiently estimable from twin data the results of this investigation are confirmed by simulation studies and highlight inherent limitations of the twin model in the sense that having only twin data limits the ability to detect individual variance components finally remarks on possible alternative statistical methods are given and results are presented to illustrate the improvements in efficiency that are possible with additional family data in particular the results provide insight into the limitations of inference from twin data

on robustness in the logistic regression model summary we investigate robustness in the logistic regression model copas has studied two forms of robust estimator a robust resistant estimate of pregibon and an estimate based on a misclassification model he concluded that robust resistant estimates are much more biased in small samples than the usual logistic estimate is and recommends a bias corrected version of the misclassification estimate we show that there are other versions of robust resistant estimates which have bias often approximately the same as and sometimes even less than the logistic estimate these estimates belong to the mallows class in addition the corrected misclassification estimate is inconsistent at the logistic model we develop a simple consistent modification the modified estimate is a member of the mallows class but unlike most robust estimates it has an interpretable tuning constant the results are illustrated on data sets featuring different kinds of outliers

finite volume scheme for the lattice boltzmann method on unstructured meshes department of mathematics and statistics bowling green state university bowling green ohio 43403 received 9 september 1998 a nite volume scheme for the lattice boltzmann method is developed for unstructured triangular meshes intwo dimensions the accuracy of this new scheme is demonstrated by comparing the numerical results with theexact solutions to the navier stokes equations for taylor vortex ow shear ow between two parallel plates shear ow between two rotating cylinders and poiseuille ow the agreement between the numerical andanalytical results is very good for each of these tests s1063 651x 99 07804 6 pacs number s 47 10 1g 47 11 1j 05 20 ddi introduction

grid refinement in lattice boltzmann methods based on volumetric formulation abstract we describe a general algorithmic concept for grid refinement in the lattice boltzmann method unlike most of the previously known approaches the present one is based on volumetric formulation so that conservation laws are exactly guaranteed