modeling sparse longitudinal data on riemannian manifolds modern data collection often entails longitudinal repeated measurements that assume values on a riemannian manifold analyzing such longitudinal riemannian data is challenging because of both the sparsity of the observations and the nonlinear manifold constraint addressing this challenge we propose an intrinsic functional principal component analysis for longitudinal riemannian data information is pooled across subjects by estimating the mean curve with local frechet regression and smoothing the covariance structure of the linearized data on tangent spaces around the mean dimension reduction and imputation of the manifold valued trajectories are achieved by utilizing the leading principal components and applying best linear unbiased prediction we show that the proposed mean and covariance function estimates achieve state of the art convergence rates for illustration we study the development of brain connectivity in a longitudinal cohort of alzheimer s disease and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine invariant metric in a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers we show that the proposed method leads to nicely interpretable eigenfunctions and principal component scores data used in preparation of this article were obtained from the alzheimer s disease neuroimaging initiative database

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

iterations of the non classical symmetries method and conditional lie backlund symmetries iterations of the non classical symmetries method give rise to new nonlinear equations which inherit the lie point symmetry algebra of the original equation invariant solutions of these heir equations supply new solutions of the original equation we show that particular cases of such invariant solutions correspond to zhdanov s conditional lie backlund symmetries

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

conditional symmetry of a porous medium equation abstract we obtain an exhaustive description of conditional symmetries admitted by a nonlinear porous medium equation in one spatial dimension it is proved that solving the determining equations for the conditional symmetries either yields classical lie symmetries or is equivalent to solving the porous medium equation itself the second possibility is shown to be typical for an arbitrary evolution type partial differential equation in one spatial variable we show that this very property is responsible for the well known phenomenon when using non classical symmetries yield exact solutions which prove to be invariant ones

lie symmetries of nonlinear multidimensional reaction diffusion systems ii we present a complete description of the classical lie symmetries of a coupled system of partial differential equations comprising a pair of semilinear reaction diffusion equations with constant diffusivities and arbitrary nonlinearities in the reaction terms in any number of spatial dimensions part i cherniha r m and king j r 2000 j phys a math gen 33 267 82 j phys a math gen 33 7839 41 addressed the case of unequal diffusivities here we complete the analysis by treating the case of equal diffusivities in which the symmetry structure is richer still such models arise in the description of numerous physical chemical and biological systems and we also indicate the possible application in such contexts of some of the specific cases arising from the group classification specifically a variety of lie s ansatze and exact solutions of the so called reaction diffusion systems of a type that arises in mathematical biology are constructed

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

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

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

symmetry reductions and exact solutions of a class of nonlinear heat equations abstract classical and nonclassical symmetries of the nonlinear heat equation ut uxx f u are considered the method of differential grobner bases is used both to find the conditions on f u under which symmetries other than the trivial spatial and temporal translational symmetries exist and to solve the determining equations for the infinitesimals a catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of the nonlinear heat equation for cubic f u in terms of the roots of f u 0

new non lie ansatze and exact solutions of nonlinear reaction diffusion convection equations a constructive method for obtaining new exact solutions of nonlinear evolution equations is further developed the method is based on the consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high order ordinary differential equation using this method new non lie ansatze and exact solutions are obtained for two classes of diffusion equations with power and exponential nonlinearities which describe real processes in physics chemistry and biology the analysis of the found solutions and the relation of the proposed method to some approaches which have been suggested in several recently published papers are presented

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

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

on the weak symmetry groups of partial differential equations abstract we define an algorithm to characterize all weak symmetry groups of a partial differential equation new invariant solutions to the fokker planck equation are found

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

conditional lie backlund symmetry and reduction of evolution equations we suggest a generalization of the notion of invariance of a given partial differential equation with respect to a lie backlund vector field such a generalization proves to be effective and enables us to construct principally new ansatz reducing evolution type equations to several ordinary differential equations in the framework of the said generalization we obtain principally new reductions of a number of nonlinear heat conductivity equations ut uxx f u ux with poor lie symmetry and obtain their exact solutions it is shown that these solutions cannot be constructed by means of the symmetry reduction procedure

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

lie and conditional symmetries of the three component diffusive lotka volterra system lie and q conditional symmetries of the classical three component diffusive lotka volterra system in the case of one space variable are studied the group classification problems for finding lie symmetries and q conditional symmetries of the first type are completely solved notably non lie symmetries q conditional symmetry operators for a multi component nonlinear reaction diffusion system are constructed for the first time the results are compared with those derived for the two component diffusive lotka volterra system the conditional symmetry obtained for the non lie reduction of the three component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found particularly the exact solution describing different scenarios of competition between three species is constructed

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

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

functional models for time varying random objects functional data analysis provides a popular toolbox of functional models for the analysis of samples of random functions that are real valued in recent years samples of time varying object data such as time varying networks that are not in a vector space have been increasingly collected these data can be viewed as elements of a general metric space that lacks local or global linear structure and therefore common approaches that have been used with great success for the analysis of functional data such as functional principal component analysis cannot be applied we propose metric covariance a novel association measure for paired object data lying in a metric space d that we use to define a metric autocovariance function for a sample of random valued curves where generally will not have a vector space or manifold structure the proposed metric autocovariance function is non negative definite when the squared semimetric d2 is of negative type then the eigenfunctions of the linear operator with the autocovariance function as kernel can be used as building blocks for an object functional principal component analysis for valued functional data including time varying probability distributions covariance matrices and time dynamic networks analogues of functional principal components for time varying objects are obtained by applying frechet means and projections of distance functions of the random object trajectories in the directions of the eigenfunctions leading to real valued frechet scores using the notion of generalized frechet integrals we construct object functional principal components that lie in the metric space we establish asymptotic consistency of the sample based estimators for the corresponding population targets under mild metric entropy conditions on and continuity of the valued random curves these concepts are illustrated with samples of time varying probability distributions for human mortality time varying covariance matrices derived from trading patterns and time varying networks that arise from new york taxi trips

similarity reductions of the 1 3 dimensional burgers equation we consider the 1 3 dimensional burgers equation u t u x x u y y u z z uu x which has considerable interest in mathematical physics we complete the list of similarity reductions that are obtained from the lie symmetries admitted by this equation to achieve this goal we employ two and three dimensional subalgebras of the lie symmetry algebra in addition to the one dimensional subalgebras that appears in the literature we solve analytically where it is possible the reduced ordinary differential equations and hence we obtain closed form solutions for the original equation finally we derive certain non lie solutions

on a reduction and solutions of nonlinear wave equations with broken symmetry a generalised definition for invariance of partial differential equations is proposed exact solutions of the equations with broken symmetry are obtained

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

singular reduction operators in two dimensions the notion of singular reduction operators i e of singular operators of nonclassical conditional symmetry of partial differential equations in two independent variables is introduced all possible reductions of these equations to first order odes are exhaustively described as examples properties of singular reduction operators of 1 1 dimensional evolution and wave equations are studied it is shown how to favourably enhance the derivation of nonclassical symmetries for this class by an in depth prior study of the corresponding singular vector fields

symmetries and heir equations for the laminar boundary layer model iterations of the nonclassical symmetries method applied to both the prandtl equation and prandtl system give rise to new nonlinear equations which inherit the lie symmetry algebra of the original prandtl equation system invariant solutions of these heir equations supply new solutions of the original equation system

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

the analysis of a finite element method for the three species lotka volterra competition diffusion with dirichlet boundary conditions a galerkin finite element method is developed for the two dimensional three dimensional nonlinear time dependent three species lotka volterra competition diffusion equations on a bounded domain the existence and uniqueness of the solution to the numerical formulation are proved an error estimate for the numerical solution is obtained numerical computations are carried out to examine the expected orders of accuracy in the error estimates

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

a precise definition of reduction of partial differential equations we give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry classical and non classical reductions of partial differential equations using the introduced definition of reduction of differential equations we establish equivalence of the non classical conditional symmetry and direct ansatz approaches to reduction of partial differential equations as an illustration we give an example of non classical reduction of the nonlinear wave equation in 1 3 dimensions the conditional symmetry approach when applied to the equation in question yields a number of non lie reductions which are far reaching generalizations of the well known symmetry reductions of the nonlinear wave equations

extended symmetry analysis of generalized burgers equations using enhanced classification techniques we carry out the extended symmetry analysis of the class of generalized burgers equations of the form ut uux f t x uxx 0 this enhances all the previous results on symmetries of these equations and includes the description of admissible transformations lie symmetries lie and nonclassical reductions hidden symmetries conservation laws potential admissible transformations and potential symmetries the study is based on the fact that the class is normalized and its equivalence group is finite dimensional

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

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

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

non linear reaction diffusion systems with variable diffusivities lie symmetries ansatze and exact solutions abstract this work first considers the classical lie symmetry analysis of a class of systems of two quasilinear reaction diffusion equations having variable diffusivities subsequently non lie reductions to systems of first order ordinary differential equations are obtained for a subclass of these systems in particular families of exact solutions of a diffusive lotka volterra type system are constructed

on non linear partial differential equations with an infinite dimensional conditional symmetry abstract the invariance of non linear partial differential equations under a certain infinite dimensional lie algebra a n z in n spatial dimensions is studied the special case a 1 2 was introduced in j stat phys 75 1994 1023 and contains the schrodinger lie algebra sch 1 as a lie subalgebra it is shown that there is no second order equation which is invariant under the massless realizations of a n z however a large class of strongly non linear partial differential equations is found which are conditionally invariant with respect to the massless realization of a n z such that the well known monge ampere equation is the required additional condition new exact solutions are found for some representatives of this class

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

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

principal component analysis for functional data on riemannian manifolds and spheres author s dai xiongtao muller hans georg abstract functional data analysis on nonlinear manifolds has drawn recent interest we propose an intrinsic principal component analysis for smooth riemannian manifold valued functional data and study its asymptotic properties the proposed riemannian functional principal component analysis rfpca is carried out by first mapping the manifold valued data through riemannian logarithm maps to tangent spaces around the time varying fr x27 echet mean function and then performing a classical multivariate functional principal component analysis on the linear tangent spaces representations of the riemannian manifold valued functions and the eigenfunctions on the original manifold are then obtained by mapping back with exponential maps the tangent space approximation through functional principal component analysis is shown to be well behaved in terms of controlling the residual variation if the riemannian manifold has nonnegative curvature we derive uniform convergence rates for the model components including the mean function covariance function eigenfunctions and functional principal component scores and apply the proposed methodology to obtain a novel framework for the analysis of longitudinal compositional data this is achieved by mapping longitudinal compositional data to trajectories on the sphere and we illustrate this approach with longitudinal fruit fly behavior patterns the proposed riemannian functional principal component analysis is shown to be superior in terms of trajectory recovery in comparison to an unrestricted functional principal component analysis in applications that include flight trajectories as well as in simulations rfpca is also found to produce principal component scores that are better predictors for classification compared to traditional functional functional principal component scores

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

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

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

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 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

the symmetry and some exact solutions of the nonlinear many dimensional liouville d alembert and eikonal equations multiparametrical exact solutions of the many dimensional nonlinear d alembert liouville sine gordon and eikonal equations are obtained the maximally extensive local invariance groups of the equations are determined and invariants of the extended poincare group are found

group invariant solutions of differential equations we introduce the concept of a weak symmetry group of a system of partial differential equations that generalizes the nonclassical method introduced by bluman and cole for finding group invariant