leverage local influence and curvature in nonlinear regression summary the connections between measures of leverage statistical curvature and the local influence of a mean shift perturbation are explored in nonlinear regression models the circumstances under which the jacobian leverage reduces to a commonly used linear approximation are found to be connected to the effective residual curvature of the nonlinear model the local influence of a mean shift perturbation in the model function is seen to be closely related to the jacobian leverage

backlund transformations for nonlinear sigma models with values in riemannian symmetric spaces this work deals with backlund transformations for the principal sl n sigma model together with all reduced models with values in riemannian symmetric spaces first the dressing method of zakharov mikhailov and shabat is shown for the case of a meromorphic dressing matrix to be equivalent to a backlund transformation for an associated linearly extended system comparison of this multi backlund transformation with the composition of ordinary ones leads to a new proof of the permutability theorem a new method of solution for such multi backlund transformations mbt is developed by the introduction of a soliton correlation matrix which satisfies a riccati system equivalent to the mbt using the geometric structure of this system a linearization is achieved leading to a nonlinear superposition formula expressing the solution explicitly in terms of solutions of a single backlund transformation through purely linear algebraic relations a systematic study of all reductions of the system by involutive automorphisms is made thereby defining the multi backlund transformations and their solution for all riemannian symmetric spaces

perturbation selection and influence measures in local influence analysis cook s j roy statist soc ser b 48 1986 133 169 local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model however no rigorous approach has been developed to address two fundamental issues the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative the aim of this paper is to develop a differential geometrical framework of a perturbation model called the perturbation manifold and utilize associated metric tensor and affine curvatures to resolve these issues we will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model moreover we will introduce new influence measures that are applicable to objective functions at any point examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations

local influence analysis of nonlinear structural equation models by regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete data log likelihood function in the em algorithm we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model the basic building blocks of local influence analysis are computed via observations of the latent variables generated by the metropolis hastings algorithm while the diagnostic measures are obtained via the conformal normal curvature seven perturbation schemes including some perturbation schemes on latent vectors are investigated the proposed procedure is illustrated by a simulation study and a real example

perturbation selection and local influence analysis for nonlinear structural equation model local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs one of its important issues is related to the appropriate choice of a perturbation vector in this paper we develop a general method to select an appropriate perturbation vector and a second order local influence measure to address this issue in the context of latent variable models an application to nonlinear structural equation models is considered six perturbation schemes are investigated including three schemes under which simultaneous perturbations are made on components of latent vectors to assess the influence of these components and pinpoint the influential ones the proposed procedure is illustrated by artificial examples and a simulation study as well as a real example

missing data methods for generalized linear models a comparative review missing data is a major issue in many applied problems especially in the biomedical sciences we review four common approaches for inference in generalized linear models glms with missing covariate data maximum likelihood ml multiple imputation mi fully bayesian fb and weighted estimating equations wees there is considerable interest in how these four methodologies are related the properties of each approach the advantages and disadvantages of each methodology and computational implementation we examine data that are missing at random and nonignorable missing for ml we focus on techniques using the em algorithm and in particular discuss the em by the method of weights and related procedures as discussed by ibrahim for mi we examine the techniques developed by rubin for fb we review approaches considered by ibrahim et al for wee we focus on the techniques developed by robins et al we use a real dataset and a detailed simulation study to compare the four methods

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

perturbation and scaled cook s distance cook s cook 1977 distance is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross sectional data however for many complex data structures e g longitudinal data no rigorous approach has been developed to address a fundamental issue deleting subsets with different numbers of observations introduces different degrees of perturbation to the current model fitted to the data and the magnitude of cook s distance is associated with the degree of the perturbation the aim of this paper is to address this issue in general parametric models with complex data structures we propose a new quantity for measuring the degree of the perturbation introduced by deleting a subset we use stochastic ordering to quantify the stochastic relationship between the degree of the perturbation and the magnitude of cook s distance we develop several scaled cook s distances to resolve the comparison of cook s distance for different subset deletions theoretical and numerical examples are examined to highlight the broad spectrum of applications of these scaled cook s distances in a formal influence analysis

quadratic pseudopotentials for gl n c principal sigma models abstract matrix pseudopotentials for the gl n c principal sigma model in two dimensional minkowski space are derived through the method of closed differential ideals the structure of the pseudopotential equations is chosen to contain only quadratic nonlinearities of the matrix riccati type a set of further constraints is deduced which leads to inner backlund transformations depending on two complex parameters through a geometrical interpretation of such matrix riccati equations and the associated constraints a linearization procedure is derived and the equations are reduced to those of zakharov mikhailov and shabat 7 10 an inductive procedure is applied to explicitly solve an iterated sequence of such backlund transformations through a purely algebraic transformation of solutions to the first step the resulting nonlinear superposition formula is used to demonstrate a permutability theorem and to analyse the appearance of singularities fr nous deduisons les pseudo potentiels matriciels pour le modele sigma principal a valeurs dans gl n c defini sur l espace de minkowski bi dimensionnel en utilisant la methode des ideaux differentiels fermes on restreint la structure des equations des pseudopotentiels de facon a ce que n apparaissent que des non linearites quadratiques du type riccati matriciel nous deduisons un ensemble de contraintes supplementaires menant a des transformations de backlund internes dependantes de deux parametres complexes gr ce a l interpretation geometrique de ces equations de riccati matricielles et des contraintes associees nous deduisons un procede de linearisation et les equations se reduisent a celles de zakharov mikhailov et shabat 7 10 un procede inductif est utilise pour resoudre explicitement une succession de transformations de backlund par une transformation purement algebrique des solutions de la premiere etape la formule de superposition non lineaire qui en resulte permet de demontrer un theoreme de permutabilite et d analyser l apparition de singularites

superposition principles for matrix riccati equations a superposition rule is obtained for the matrix riccati equation mre w a wb cw wdw where w t a t b t c t and d t are real n n matrices expressing the general solution in terms of five known solutions for all n 2 the symplectic mre w wt a at d dt c bt is treated separately and a superposition rule is derived involving only four known solutions for the unitary and gl n r subcases with d a and c bt or d a and c bt respectively superposition rules are obtained involving only two solutions the derivation of these results is based upon an interpretation of the mre in terms of the action of the groups sl 2n r sp 2n r u n and gl n r on the grassman manifold gn r2n

a note on local influence based on normal curvature summary object functions other than the likelihood displacement such as a parameter estimate or a test statistic can also be used in local influence analysis the normal curvatures of these object functions have been studied in situations where the slopes were non zero in these situations we show that the normal curvature is not scale invariant and thus ambiguous conclusions will be drawn comments on the application of the general normal curvature formula are presented

local influence for incomplete data models this paper proposes a method to assess the local influence in a minor perturbation of a statistical model with incomplete data the idea is to utilize cook s approach to the conditional expectation of the complete data log likelihood function in the em algorithm it is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local influence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods an application to the generalized linear mixed model is investigated some illustrative artificial and real examples are presented

case deletion diagnostics for linear mixed models based on the q function the conditional expectation of the logarithm of the joint likelihood between responses and random effects we propose a case deletion approach to identify influential subjects and influential observations in linear mixed models the models considered here are very broad in the sense that any covariance structures can be specified in the covariance matrices of the random effects and random errors analytically explicit forms of diagnostic measures for the fixed effects and variance components are provided comparisons with existing methods including likelihood based case deletion and local influence methods are made numerical results including real data analysis and simulation studies are presented for both illustration and comparison this article has supplementary material online

finite difference time dispersion transforms for wave propagation the finite difference fd wave equation is widely implemented in seismic imaging for oil exploration but the numerical dispersion due to discretization of time and space derivatives can introduce severe numerical errors we have investigated time dispersion which might distort the phase and introduce severe artifacts to the data and images especially for long time propagation we first studied precisely how the time dispersion was produced and then we developed an efficient approach the time dispersion transforms to cope with time dispersion errors in wave propagation the proposed forward time dispersion transform can predict or simulate the time dispersion errors and it can be applied to remove time dispersion errors in reverse time migration the inverse time dispersion transform can be used to eliminate time dispersion errors from synthetic data after modeling the proposed method is general and works for low and high order time fd schemes by using this method large time steps were allowed in wave propagation thus we can remove the time dispersion errors at a negligible numerical cost and the efficiency is not affected to test the effectiveness and robustness of the proposed time dispersion transforms we used isotropic and anisotropic examples as well as modeling and imaging examples

isospectral hamiltonian flows in finite and infinite dimensions the approach to isospectral hamiltonian flow introduced in part i is further developed to include integration of flows with singular spectral curves the flow on finite dimensional ad invariant poisson submanifolds of the dual widetilde gl r of the positive part of the loop algebra widetilde gl r is obtained through a generalization of the standard method of linearization on the jacobi variety of the invariant spectral curves these curves are embedded in the total space of a line bundlet p1 c allowing an explicit analysis of singularities arising from the structure of the image of a moment map tilde j r m n r times m n r to widetilde gl r from the space of rank r deformations of a fixedn n matrixa it is shown how the linear flow of line bundles e t to tilde s over a suitably desingularized curve tilde s may be used to determine both the flow of matricial polynomialsl and the hamiltonian flow in the spacemn r mn r in terms of functions the resulting flows are proved to be completely integrable the reductions to subalgebras developed in part i are shown to correspond to invariance of the spectral curves and line bundles e t to tilde s under certain linear or anti linear involutions the integration of two examples from part i is given to illustrate the method the rosochatius system and the cnls coupled non linear schrodinger equation

conformal normal curvature and assessment of local influence in 1986 r d cook proposed differential geometry to assess local influence of minor perturbations of statistical models we construct a conformally invariant curvature the conformal normal curvature for the same purpose this curvature provides a measure of local influence ranging from 0 to 1 with objective bench marks to judge largeness we study various approaches to using the conformal normal curvature and the relationships between these approaches

bayesian sensitivity analysis with the fisher rao metric we propose a geometric framework to assess sensitivity of bayesian procedures to modelling assumptions based on the nonparametric fisher rao metric while the framework is general the focus of this article is on assessing local and global robustness in bayesian procedures with respect to perturbations of the likelihood and prior and on the identification of influential observations the approach is based on a square root representation of densities which enables analytical computation of geodesic paths and distances facilitating the definition of naturally calibrated local and global discrepancy measures an important feature of our approach is the definition of a geometric contamination class of sampling distributions and priors via intrinsic analysis on the space of probability density functions we demonstrate the applicability of our framework to generalized mixed effects models and to directional and shape data

quasideterminant multisoliton solutions of a supersymmetric chiral field model in two dimensions the darboux transformation of a supersymmetric principal chiral field model in two dimensions is studied we obtain exact superfield multisoliton solutions of the model by means of iterated darboux transformation and express them in terms of quasideterminants

bayesian influence analysis a geometric approach in this paper we develop a general framework of bayesian influence analysis for assessing various perturbation schemes to the data the prior and the sampling distribution for a class of statistical models we introduce a perturbation model to characterize these various perturbation schemes we develop a geometric framework called the bayesian perturbation manifold and use its associated geometric quantities including the metric tensor and geodesic to characterize the intrinsic structure of the perturbation model we develop intrinsic influence measures and local influence measures based on the bayesian perturbation manifold to quantify the effect of various perturbations to statistical models theoretical and numerical examples are examined to highlight the broad spectrum of applications of this local influence method in a formal bayesian analysis

influence diagnostics and outlier tests for semiparametric mixed models summary semiparametric mixed models are useful in biometric and econometric applications especially for longitudinal data maximum penalized likelihood estimators mples have been shown to work well by zhang and co workers for both linear coefficients and nonparametric functions this paper considers the role of influence diagnostics in the mple by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component we focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the mple algorithm we also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers the influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example

local influence to detect influential data structures for generalized linear mixed models biometrics 2001 dec 57 4 1166 72 related articles books linkout local influence to detect influential data structures for generalized linear mixed models ouwens mj tan fe berger mp department of methodology and statistics maastricht university the netherlands mario ouwens stat unimaas nl this article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects for these models it is shown that the subject oriented influence measure is a special case of the proposed observation oriented influence measure a two step diagnostic procedure is proposed the first step is to search for influential subjects a search for influential observations is proposed as the second step an illustration of a two treatment multiple period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects

forward modeling by a fourier method a fourier or pseudospectral forward modeling algorithm for solving the two dimensional acoustic wave equation is presented the method utilizes a spatial numerical grid to calculate spatial derivatives by the fast fourier transform time derivatives which appear in the wave equation are calculated by second order differcncing the scheme requires fewer grid points than finite diffcrcnce methods to achieve the same accuracy it is therefore believed that the fourier method will prove more efficient than finitedifference methods especially when dealing with threedimensional models the fourier forward modeling method was tested against two problems a single layer problem with a known analytic solution and a wedge problem which was also tested by physical modeling the numerical results agreed with both the analytic and physical model results furthermore the numerical model facilitates the explanation of certain events on the time section of the physical model which otherwise could not easily be taken into account

description of surfaces associated with grassmannian sigma models on minkowski space we construct and investigate smooth orientable surfaces in su n algebras the structural equations of surfaces associated with grassmannian sigma models on minkowski space are studied using moving frames adapted to the surfaces the first and second fundamental forms of these surfaces as well as the relations between them as expressed in the gauss weingarten and gauss codazzi ricci equations are found the scalar curvature and the mean curvature vector expressed in terms of a solution of grassmanian sigma model are obtained

superposition formulas for nonlinear superequations nonlinear superequations for which the general solution can be expressed algebraically in terms of a finite number of particular solutions are obtained they are based on the orthosymplectic supergroup osp m 2n and its action on a homogeneous superspace superposition formulas are discussed for the cases m 1 n arbitrary and m 2 n 1 for osp 2 2 the number of particular solutions needed to reconstruct the general solution depends on the dimension of the underlying grassmann algebra whereas for osp 1 2n it does not

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

analysis of infant growth curves using multivariate adaptive splines summary in this paper we study the effect of cocaine use by a pregnant woman on the growth of her infant after birth using a data set from a retrospective study we found that cocaine use was a marginally significant contributor to the infant growth as measured by bodyweight prom a statistical point of view the data represent a common though complex structure that has received little attention in the statistical literature to analyze these data we adopt and further enhance an approach developed recently called masal multivariate adaptive splines for the analysis of longitudinal data in addition to the fitting of growth curves we demonstrate particularly how to explore and estimate the underlying covariance structures for the longitudinal data that were collected from a rather irregular schedule

algebraic construction of the darboux matrix revisited we present algebraic construction of darboux matrices for 1 1 dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case we discuss different approaches to the darboux backlund transformation based on different dependences of the darboux matrix polynomial sum of partial fractions or the transfer matrix form we derive symmetric n soliton formulae in the general case the matrix spectral parameter and dressing actions in loop groups are also discussed we describe reductions to twisted loop groups unitary reductions the matrix lax pair for the kdv equation and reductions of chiral models harmonic maps to su n and to grassmann spaces we show that in the kdv case the nilpotent darboux matrix generates the binary darboux transformation the paper is intended as a review of known results usually presented in a novel context but some new results are included as well e g general compact formulae for n soliton surfaces and linear and bilinear constraints on the nonisospectral lax pair matrices which are preserved by darboux transformations

regression transformation diagnostics using local influence abstract following box and cox 1964 the use of transformations in regression analysis is now common recently there has been emphasis on diagnostic methods for transformation much of which has involved deletion of data cases summaries were given by cook and weisberg 1982 and atkinson 1985 this article obtains diagnostics for the estimated regression parameter of the box cox transformation of the response variable in the linear model instead of deleting cases the more general notions of perturbing assumptions of the model or components of the data are employed as in the local influence approach of cook 1986 the diagnostics then arise from local changes to the transformation parameter estimate caused by small perturbations the case direction in which small perturbations have the greatest effect is the main diagnostic quantity an appeal of the approach is that it allows simultaneous perturbations affecting all data cases not just one at a time deletions it can thus point to groups of in

superposition of solutions to backlund transformations for the su n principal σ model we show that the backlund transformations for the su n principal model may be linearized using a geometrical interpretation of these equations involving the minimal orbit of su n n in the grassmann manifold gn c2n linearization puts the equations in zakharov mikhailov shabat zms form using this form of the equations we prove inductively a nonlinear superposition law and a permutability theorem for iterated backlund transformations analogous to known results in the theory of the sine gordon and kdv equations from the superposition law we get an explicit form for multisoliton solutions to the model

transformation model diagnostics we apply the local influence method of lawrance to assess the effect of the case weights perturbation on the transformation power estimator in the box cox regression model we show that this method is the same as the local influence method proposed by cook furthermore the difference in local influence diagnostics between the case weights perturbation and the constant variances perturbation is examined and the relationship between the localinfluence diagnostic and the deletion diagnostic is studied an example is presented to illustrate local influence diagnostics

isospectral hamiltonian flows in finite and infinite dimensions i generalized moser systems and moment maps into loop algebras a moment map jr jia gl r is constructed from the poisson manifold j a of rank r perturbations of a fixed n xn matrix a to the dual r f e positive part of the formal loop algebra i r g r c 1 the adler kostant symes theorem is used to give hamiltonians which generate commutative isospectral flows on g r the pull back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in j a the latter may be identified with flows on finite dimensional coadjoint orbits in g and linearized on the jacobi variety of an invariant spectral curve xr which generically is an r sheeted riemann surface reductions of j a are derived corresponding to subalgebras of gl r c and sl r c determined as the fixed point set of automorphism groupes generated by involutions i e jdl the classical algebras as well as reductions to twisted subalgebras of s r c the theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of pde s

darboux transformation and exact multisolitons of cpn nonlinear sigma model abstract exact multisolitons of c p n sigma model are obtained by using darboux transformation in terms of quasideterminant darboux matrix the multisoliton solutions are shown to be expressed in terms of quasideterminants of gelfand and retakh 1991 10 the method of quasideterminant darboux matrix has been shown to be related with the dressing method that has already been used to compute iteratively exact multisolitons of the c p n sigma model by means of nonlinear superposition principle of backlund transformations explicit expressions of one two and three soliton solutions of c p 1 model have been computed by using properties of quasideterminants

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

a diagnostic procedure based on local influence cook s 1986 normal curvature measure is useful for sensitivity analysis of model assumptions in statistical models however there is no rigorous approach based on the normal curvature for addressing two fundamental issues to assess the extent of discrepancy between an assumed model and the underlying model from which the data are generated and to identify suspicious data points for which the discrepancy is most evident our purpose is to establish a theoretically sound procedure for resolving these issues for case weight perturbation under the framework of independent distributions we show that the local influence measure cook s distance and likelihood distance are asymptotically equivalent a diagnostic procedure based on local influence is proposed for evaluating model misspecification and for detecting influential points simultaneously we analyse two real datasets

extending the stability limit of explicit scheme with spatial filtering for solving wave equations abstract the explicit finite difference scheme is widely used for solving the wave equation however its time step is strictly constrained by the courant friedrichs lewy cfl stability limit we apply spatial filtering to reduce the high wavenumber noise caused by using a larger time step beyond the cfl stability limit we further incorporate the forward and inverse time dispersion transforms to reduce the time dispersion error this method allows us to use a time step larger than the maximum time step allowed by the cfl stability limit

sensitivity analysis for nonrandom dropout a local influence approach diggle and kenward 1994 applied statistics 43 49 93 proposed a selection model for continuous longitudinal data subject to nonrandom dropout it has provoked a large debate about the role for such models the original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests since then the view has emerged that these models should ideally be made part of a sensitivity analysis this paper presents a formal and flexible approach to such a sensitivity assessment based on local influence cook 1986 journal of the royal statistical society series b 48 133 169 the influence of perturbing a missing at random dropout model in the direction of nonrandom dropout is explored the method is applied to data from a randomized experiment on the inhibition of testosterone production in rats

second order approach to local influence to examine global and local influence and their relations for regression models we study the perturbation formed surface of a variable such as the maximum likelihood estimate of a parameter by evaluating the second derivative or curvature of the surface the corresponding slope of this surface is related to the curvature of the likelihood displacement surface of cook examples show that this approach with the aid of plots is helpful not only to discover influential cases including those hidden in an individual global sense but also to understand the nature of influence

invariants and likelihood ratio statistics because the likelihood ratio statistic is invariant under reparameterization it is possible to make a large sample expansion of the statistic itself and of its expectation in terms of invariants in particular the bartlett adjustment factor can be expressed in terms of invariant combinations of cumulants of the first two log likelihood derivatives such expansions are given first for a scalar parameter and then for vector parameters geometrical interpretation is given where possible and some special cases discussed

explicit forms of backlund transformations for the grassmannian and cp n 1 sigma models a fairly wide class of classical solutions of the euclidean two dimensional grassmannian and cpn 1 sigma models has been constructed explicitly and elementarily by the present author starting from these classical solutions we derive the explicit forms of the backlund transformations following harnad et al properties of the backlund transformations for the grassmannian models are discussed in particular a simple interpretation of the backlund transformations for the cpn 1 model is obtained generalization of these results to the noncompact grassmannian sigma models is straightforward

the application of high order differencing to the scalar wave equation the second order central difference is often used to approximate the derivatives of the wave equation it is demonstrated that gains in computational efficiency can be made by using high order approximations for these derivatives a one dimensional model is used to illustrate the relative accuracy of o t2 x2 o t2 x4 o t4 x4 ando t4 x10 central difference schemes for comparison o t2 ando t4 pseudospectral schemes are used as an additional measure of performance the results indicate that o t4 x10 differencing can achieve similar accuracy as the o t4 spectral scheme for practical illustration a two dimensional form of the o t4 x10 algorithm is used to compute the exploding reflector response of a salt dome model and compared with a fine grid o t2 x4 result transmissive sponge like boundary conditions are also examined and shown to be effective

classical nonlinear σ models on grassmann manifolds of compact or noncompact type grassmannian models are reexamined in the light of a new geometrical result namely the cartan immersion of a riemannian symmetric space g h into its isometry group g is not always a diffeomorphism onto the set m introduced by eichenherr and forger nucl phys b 164 528 1980 this is the case in particular for grassmann manifolds of all types their set m is shown to be disconnected and its structure is completely analyzed as a consequence a new constraint must be introduced in the backlund transformation bt method proposed by harnad saint aubin and shnider commun math phys 92 329 1984 it is shown however to always be satisfied for grassmann manifolds of compact type i e g compact but the problem remains open in most other cases on the other hand the bt method is extended to the euclidean regime

local influence for generalized linear models with missing covariates in the analysis of missing data sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions in this article we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data we examine two types of perturbation schemes the single case and global perturbation schemes for perturbing various assumptions in this setting we show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation we also develop several local influence measures to identify influential points and test model misspecification simulation studies are conducted to evaluate our methods and real datasets are analyzed to illustrate the use of our local influence measures

third order symplectic integration method with inverse time dispersion transform for long term simulation the symplectic integration method is popular in high accuracy numerical simulations when discretizing temporal derivatives however it still suffers from time dispersion error when the temporal interval is coarse especially for long term simulations and large scale models we employ the inverse time dispersion transform itdt to the third order symplectic integration method to reduce the time dispersion error first we adopt the pseudospectral algorithm for the spatial discretization and the third order symplectic integration method for the temporal discretization then we apply the itdt to eliminate time dispersion error from the synthetic data as a post processing method the itdt can be easily cascaded in traditional numerical simulations we implement the itdt in one typical exiting third order symplectic scheme and compare its performances with the performances of the conventional second order scheme and the rapid expansion method theoretical analyses and numerical experiments show that the itdt can significantly reduce the time dispersion error especially for long travel times the implementation of the itdt requires some additional computations on correcting the time dispersion error but it allows us to use the maximum temporal interval under stability conditions thus its final computational efficiency would be higher than that of the traditional symplectic integration method for long term simulations with the aid of the itdt we can obtain much more accurate simulation results but with a lower computational cost we use the inverse time dispersion transform to the 3rd order symplectic integration it can greatly reduce the time dispersion error especially for long travel times it is superior to the conventional 2nd and high order finite difference methods it allows the maximum temporal interval under stability conditions thus is efficient we can obtain more accurate simulation results but with a lower computational cost

high dimensional influence measure influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations for high dimensional data it is particularly so as the increased dimensionality and complexity may amplify both the chance of an observation being influential and its potential impact on the analysis in this article we propose a novel high dimensional influence measure for regressions with the number of predictors far exceeding the sample size our proposal can be viewed as a high dimensional counterpart to the classical cook s distance however whereas the cook s distance quantifies the individual observation s influence on the least squares regression coefficient estimate our new diagnosis measure captures the influence on the marginal correlations which in turn exerts serious influence on downstream analysis including coefficient estimation variable selection and screening moreover we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure

multiple influential point detection in high dimensional regression spaces influence diagnosis should be routinely conducted when one aims to construct a regression model despite its importance the problem of influence quantification is severely under investigated in a high dimensional setting mainly due to the difficulty of establishing a coherent theoretical framework and the lack of easily implementable procedures although some progress has been made in recent years existing approaches are ineffective in detecting multiple influential points especially due to the notorious masking and swamping effects to address this challenge we propose a new group deletion procedure referred to as mip by introducing two novel quantities named max and min statistics these two statistics have complimentary properties in that the max statistic is effective for overcoming the masking effect while the min statistic is useful for overcoming the swamping effect combining their strengths we further propose an efficient algorithm that can detect influential points with prespecified guarantees for wider applications we focus on developing the new proposal for the multiple response regression model encompassing the univariate response linear model as a special case the proposed influential point detection procedure is simple to implement efficient to run and enjoys attractive theoretical properties its effectiveness is verified empirically via extensive simulation study and data analysis

solutions of euclidean σ models on noncompact grassmann manifolds a method for constructing explicit solutions of classical two dimensional euclidean models on grassmann manifolds of noncompact type and their supersymmetric extensions is presented it generalizes the holomorphic method developed by din zakrzewski and sasaki in the compact case by taking properly into account the geometry of indefinite metric spaces the solutions obtained are local in the sense that they may become singular on certain curves in the plane and the signature of the solution may change across such a curve