a composite likelihood approach to binary spatial data abstract conventional geostatistics addresses the problem of estimation and prediction for continuous observations but in many practical applications in public health environmental remediation or ecological research the most commonly available data are in the form of counts e g number of cases or indicator variables denoting above or below threshold values also in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest such as a contaminant this article proposes a computationally simple method for estimation and prediction using binary or indicator data in space the proposed method is based on pairwise likelihood contributions and the large sample properties of the estimators are obtained in a straightforward manner we illustrate the methodology through application to indicator data related to gypsy moth defoliation in massachusetts

inconsistent estimation and asymptotically equal interpolations in model based geostatistics it is shown that in model based geostatistics not all parameters in the matern class can be estimated consistently if data are observed in an increasing density in a fixed domain regardless of the estimation methods used nevertheless one quantity can be estimated consistently by the maximum likelihood method and this quantity is more important to spatial interpolation the results are established by using the properties of equivalence and orthogonality of probability measures some sufficient conditions are provided for both gaussian and non gaussian equivalent measures and necessary conditions are provided for gaussian equivalent measures two simulation studies are presented that show that the fixed domain asymptotic properties can explain some finite sample behavior of both interpolation and estimation when the sample size is moderately large

finite sample adjustments in estimating equations and covariance estimators for intracluster correlations bias corrected covariance estimators are introduced in the context of an estimating equations approach for intracluster correlations among binary outcomes simulation study results show that the bias corrected covariance estimators perform better than uncorrected sandwich estimators in terms of bias and coverage probabilities additionally introduction of a matrix based bias correction into the estimating equations considerably improves point and interval estimation for the intracluster correlations the methods are illustrated using data from a nested cross sectional cluster trial on reducing underage drinking

group inverse for the block matrices with an invertible subblock let m abcd a is square be a square block matrix with an invertible subblock over a skew field k in this paper we give the necessary and sufficient conditions for the existence as well as the expressions of the group inverse for m under some conditions

working correlation structure misspecification estimation and covariate design implications for generalised estimating equations performance the method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations we investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods the asymptotic relative efficiency depends on three features of the analysis namely i the discrepancy between the working correlation structure and the unobservable true correlation structure ii the method by which the correlation parameters are estimated and iii the design by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes analytical and numerical studies of realistic data analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a gaussian estimation pseudolikelihood procedure is used with an ar 1 structure

generalized inverses over integral domains ii group inverses and drazin inverses this is a continuation of an earlier paper by the authors on generalized inverses over integral domains the main results consist of necessary and sufficient conditions for the existence of a group inverse a new formula for a group inverse when it exists and necessary and sufficient conditions for the existence of a drazin inverse we show that a square matrix a of rank r over an integral domain r has a group inverse if and only if the sum of all r r principal minors of a is an invertible element of r we also show that the group inverse of a when it exists is a polynomial in a with coefficients from r

on the generalized drazin inverse in banach algebras in terms of the generalized schur complement we present new results on existence and representation of the generalized drazin inverse for elements in banach algebras involving the generalized schur complement they extend cases studied in the literature where the generalized schur complement is assumed to be nonsingular or zero or group invertible the results are applied to obtain formulas for cases of special interest

further results on the representation of the drazin inverse of a 2 2 block matrix abstract the aim of this paper is to establish an explicit representation of the drazin inverse of a 2 2 block matrix m a b c d where a and d are square matrices in terms of the drazin inverses of a and d first we give a formula for the drazin inverse of m with the blocks satisfying the conditions bc 0 bdc 0 and bd 2 0 further we derive representations of the drazin inverse of m under less restrictive conditions than those found in the current literature

additive results for the generalized drazin inverse in a banach algebra abstract in this paper we investigate additive properties of the generalized drazin inverse in a banach algebra we find some new conditions under which the generalized drazin inverse of the sum a b could be explicitly expressed in terms of a a d b b d also some recent results of castro and koliha new additive results for the g drazin inverse proc roy soc edinburgh sect a 134 2004 1085 1097 are extended

coupling fluid flow with porous media flow the transport of substances back and forth between surface water and groundwater is a very serious problem we study herein the mathematical model of this setting consisting of the stokes equations in the fluid region coupled with the darcy equations in the porous medium coupled across the interface by the beavers joseph saffman conditions we prove existence of weak solutions and give a complete analysis of a finite element scheme which allows a simulation of the coupled problem to be uncoupled into steps involving porous media and fluid flow subproblems this is important because there are many legacy codes available which have been optimized for uncoupled porous media and fluid flow

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

estimating equations for removal data analysis we consider the problem of estimating a population size from successive catches taken during a removal experiment and propose two estimating functions approaches the traditional quasi likelihood tql approach for dependent observations and the conditional quasi likelihood cql approach using the conditional mean and conditional variance of the catch given previous catches asymptotic covariance of the estimates and the relationship between the two methods are derived simulation results and application to the catch data from smallmouth bass show that the proposed estimating functions perform better than other existing methods especially in the presence of overdispersion

more results on generalized drazin inverse of block matrices in banach algebras abstract in a banach algebra a let x a b c d a relative to the idempotent p a where a p a p is generalized drazin invertible under assumptions that the generalized schur complement s d c a d b 1 p a 1 p and the element c a b 1 p a 1 p are generalized drazin invertible we establish some formulae for the generalized drazin inverse of x in terms of a matrix in the generalized banachiewicz schur form and its powers we develop necessary and sufficient conditions for the existence and the expressions for the group inverse of a block matrix in banach algebras the provided results extend earlier works given in the literature

some block matrices with signed drazin inverses abstract the sign pattern of a real matrix m is the 0 1 1 matrix obtained from m by replacing each entry by its sign let q m be the set of real matrices with the same sign pattern as m for any m q m if the drazin inverses of m and m have the same sign pattern then m is said to have signed drazin inverse in this paper we give a complete characterization for a class of anti triangular matrices with signed drazin inverse and present a complete characterization for sign symmetric bipartite matrices with signed drazin inverse

a representation for the drazin inverse of block matrices with a singular generalized schur complement abstract consider a 2 2 block complex square matrix m a b c d where a and d are square matrices suppose that i aa d b o and c i aa d o where a d is the drazin inverse of a the representations of the drazin inverse m d have been studied in the case where the generalized schur complement s a ca d b is either zero or nonsingular in this paper we develop a representation under certain conditions for m d when s is singular and group invertible moreover this formula includes the case where s o or nonsingular a numerical example is given to illustrate the result

meta analytical synthesis of regression coefficients under different categorization scheme of continuous covariates recently the number of clinical prediction models sharing the same regression task has increased in the medical literature however evidence synthesis methodologies that use the results of these regression models have not been sufficiently studied particularly in meta analysis settings where only regression coefficients are available one of the difficulties lies in the differences between the categorization schemes of continuous covariates across different studies in general categorization methods using cutoff values are study specific across available models even if they focus on the same covariates of interest differences in the categorization of covariates could lead to serious bias in the estimated regression coefficients and thus in subsequent syntheses to tackle this issue we developed synthesis methods for linear regression models with different categorization schemes of covariates a 2 step approach to aggregate the regression coefficient estimates is proposed the first step is to estimate the joint distribution of covariates by introducing a latent sampling distribution which uses one set of individual participant data to estimate the marginal distribution of covariates with categorization the second step is to use a nonlinear mixed effects model with correction terms for the bias due to categorization to estimate the overall regression coefficients especially in terms of precision numerical simulations show that our approach outperforms conventional methods which only use studies with common covariates or ignore the differences between categorization schemes the method developed in this study is also applied to a series of who epidemiologic studies on white blood cell counts

perturbation of the drazin inverse for matrices with equal eigenprojections at zero abstract let a denote the eigenprojection of a matrix a corresponding to the eigenvalue 0 we characterize matrices b such that b a and derive from the results 1 error bounds for the drazin inverse of a perturbation 2 improvement of error bounds given recently by wei 10 wei and wang 11 and castro gonzalez et al 4 and 3 a new characterization of ep matrices

the perturbation theory for the drazin inverse and its applications abstract let a and e be n n matrices and b a e denote the drazin inverse of a by ad we give an upper bound for the relative error b d a d a d under certain circumstances an error bound for the solution for the singular equations ax b b r a is also considered

on the drazin inverse of the sum of two operators and its application to operator matrices abstract given two bounded linear operators f g on a banach space x such that g 2 f g f 2 0 we derive an explicit expression for the drazin inverse of f g for this purpose firstly we obtain a formula for the resolvent of an auxiliary operator matrix in the form m f i g f g from the provided representation of f g d several special cases are considered in particular we recover the case g f 0 studied by hartwig et al r e hartwig g wang y wei some additive results on drazin inverse linear algebra appl 322 2001 207 217 for matrices and by djordjevic and wei d s djordjevic y wei additive results for the generalized drazin inverse j aust math soc 73 1 2002 115 126 for operators finally we apply our results to obtain representations for the drazin inverse of operator matrices in the form m a b c d which are extensions of some cases given in the literature

several expressions for the generalized drazin inverse of a block matrix in a banach algebra we present some new representations for the generalized drazin inverse of a block matrix with generalized schur complement being generalized drazin invertible in a banach algebra under conditions weaker than those used in recent papers on the subject

a note on the representation for the drazin inverse of 2 2 block matrices abstract in this note we consider representations of the drazin inverse of 2 2 block matrices under conditions weaker than those used in recent papers on the subject in particular in d s djordjevic p s stanimirovic on the generalized drazin inverse and generalized resolvent czechoslovak math j 51 126 2001 617 634 r hartwig x li y wei representations for the drazin inverse of 2 2 block matrix siam j matrix anal appl 27 2006 757 771

drazin inverse of partitioned matrices in terms of banachiewicz schur forms abstract let m a b c d be a partitioned matrix where a and d are square matrices denote the drazin inverse of a by a d the purpose of this paper is twofold firstly we develop conditions under which the drazin inverse of m having generalized schur complement s d ca d b group invertible can be expressed in terms of a matrix in the banachiewicz schur form and its powers secondly we deal with partitioned matrices satisfying rank m rank a d rank s d and give conditions under which the group inverse of m exists and a formula for its computation

an approach to the analysis of repeated measurements summary a linear model for repeated measurements is proposed in which the correlation structure within each time sequence of measurements includes parameters for measurement error variation between experimental units and serial correlation within units an approach to data analysis is presented which involves preliminary analysis by ordinary least squares use of the empirical semi variogram of residuals to suggest a suitable correlation structure and formal inference using likelihood based methods applications to two biological data sets are described

analytical and numerical study of a coupled cardiovascular drug delivery model a two dimensional coupled model of drug delivery in the cardiovascular tissue using biodegradable drug eluting stents is developed qualitative behavior stability analysis as well as simulations of the model have been presented numerical results computed with an implicit explicit finite element method show a complete agreement with the expected physical behavior

a latent process regression model for spatially correlated count data summary this paper proposes a regression model for spatially correlated count data that generalizes the work spatially correlated count data arise in a variety of settings frequently it is of interest to make marginal inferences about spatial trends and effects of explanatory variables on spatially correlated counts an example application described in this paper involves an examination of the distribution of neuronal cells in a laboratory culture well our motivation for examining the distribution of cells was due to the implications of the distribution for the choice of an efficient sampling method to estimate total cell count total neuronal cell counts in a culture well are ordinarily estimated using data from multiple sampled subregions viewed under the microscope or with the aid of an image analysis system because counting all cells in a culture well is prohibitively time consuming as routine practice these sampling methods typically involve recording from multiple randomly selected fields the area of the field and number of cells visible in the field a cell per unit area density is estimated from the data and the total cell count estimate for the well is obtained by multiplication by the total well area these methods implicitly assume that cells are distributed completely at random throughout the well experience would suggest that there could be trends in neuron density and clustering tendencies for example neurons can tend to a higher density in the center of a well due to a slight vortex that occurs when the cultures are moved before the neurons have attached themselves to the substratum neurons also may distribute in higher density around the edges of a culture well due to a meniscus and slightly greater depth of medium at the edge of a well spatial clustering may result if neural cell bodies migrate along the cell body s neuritic processes or if the tissue culture tray is

block representations of the generalized drazin inverse abstract under specific conditions we develop new formulae for the generalized drazin inverse of a block matrix in banach algebras also we present necessary and sufficient conditions for the existence and the expression of the group inverse of a block matrix

the group inverse of a triangular matrix block conditions are given for the group inverse of a triangular matrix over a field to exist these involve the zero nonzero schur complement applications are given to idempotent matrices

a note on the representations for the drazin inverse of 2 2 block matrices abstract in 1979 campbell and meyer proposed the problem of finding a formula for the drazin inverse of a 2 2 matrix m a b c d in terms of its various blocks where the blocks a and d are required to be square matrices special cases of the problems have been studied in particular a representation of the drazin inverse of m denoted by md has recently been obtained under the assumptions that c i aad b o and a i aad b o together with the condition that the generalized schur complement d cadb be either nonsingular or zero we derive an alternative representation for md under the same assumptions but with the condition on the schur complement in the hypothesis replaced by the condition that r caa d n b n d where r and n are the range and null space of a matrix

a regression modeling approach for describing patterns of hiv genetic variation we introduce a novel approach for describing patterns of hiv genetic variation using regression modeling techniques parameters are defined for describing genetic variation within and between viral populations by generalizing simpson s index of diversity regression models are specified for these variation parameters and the generalized estimating equation framework is used for estimating both the regression parameters and their corresponding variances conditions are described under which the usual asymptotic approximations to the distribution of the estimators are met this approach provides a formal statistical framework for testing hypotheses regarding the changing patterns of hiv genetic variation over time within an infected patient the application of these methods for testing biologically relevant hypotheses concerning hiv genetic variation is demonstrated in an example using sequence data from a subset of patients from the multicenter aids cohort study

spatial modeling of regional variables abstract in this article accumulated sudden infant death syndrome sids data from 1974 1978 and 1979 1984 for the counties of north carolina are analyzed after a spatial exploratory data analysis markov random field models are fit to the data the spatial trend is meant to capture the large scale variation in the data and the variance and spatial dependence are meant to capture the small scale variation the trend could be a function of other explanatory variables or could simply be modeled as a function of spatial location both models are fit and compared the results give an excellent illustration of a phenomenon already well known in time series that autocorrelation in data can be due to an undiscovered explanatory variable indeed for 1974 1978 we confirm a dependence of sids rate on proportion of nonwhite babies born along with insignificant spatial correlation without this regressor variable however the spatial correlation is significant in 1979 1984 perhaps due to reporting bias o

on group inverse of singular toeplitz matrices in this paper we show that the group inverse of a real singular toeplitz matrix can be represented as the sum of products of lower and upper triangular toeplitz matrices such a matrix representation generalizes gohberg semencul formula in the literature

representations of the drazin inverse for a class of block matrices abstract in this paper we give a formula for the drazin inverse of a block matrix f i i e 0 where e is square and i is the identity matrix further we get representations of the drazin inverse for matrices of the form m a b c 0 where a is square under some conditions expressed in terms of the individual blocks

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

the representation and approximation of the drazin inverse of a linear operator in hilbert space we present a unified representation theorem for the drazin inverse of linear operators in hilbert space and a general error bound five specific expressions computational procedures and their error bounds for the drazin inverse are uniformly derived from the unified representation theorem

new additive results for the g drazin inverse the paper studies additive properties of the generalized drazin inverse g drazin inverse in a banach algebra and finds an explicit expression for the g drazin inverse of the sum a b in terms of a and b and their g drazin inverses under fairly mild conditions on a and b

some generalized inverses of partition matrix and quotient identity of generalized schur complement abstract in this paper we first define some generalized schur complements then we study the representation of m p inverse m 1 group inverse m 1 g and drazin m 1 d for the partitioned matrix m 1 a b c d based on this we give three kind quotient identities of generalized schur complement about the partitioned matrix k a b e c d f g h l and develops the results in paper m redivo zaglia pseudo schur complement and their applications appl num math 50 2004 511 519 k jbilou a messaoudi k taba some schur complement identities and applications to matrix exatrapolation methods linear algebra appl 392 2004 195 210 in the end of the paper we give the application of these generalized schur complement in solution of linear equation and give numerical example to show our results

some additive results on drazin inverse some additive perturbation results for drazin inverses are given in particular a formula is given for the drazin inverse of a sum of two matrices when one of the products of these matrices vanishes some special applications of this are also considered

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

representation for the generalized drazin inverse of block matrices in banach algebras abstract several representations of the generalized drazin inverse of a block matrix with a group invertible generalized schur complement in banach algebra are presented

power and sample size requirements for gee analyses of cluster randomized crossover trials the cluster randomized crossover design has been proposed to improve efficiency over the traditional parallel cluster randomized design which often involves a limited number of clusters in recent years the cluster randomized crossover design has been increasingly used to evaluate the effectiveness of health care policy or programs and the interest often lies in quantifying the population averaged intervention effect in this paper we consider the two treatment two period crossover design and develop sample size procedures for continuous and binary outcomes corresponding to a population averaged model estimated by generalized estimating equations accounting for both within period and interperiod correlations in particular we show that the required sample size depends on the correlation parameters through an eigenvalue of the within cluster correlation matrix for continuous outcomes and through two distinct eigenvalues of the correlation matrix for binary outcomes we demonstrate that the empirical power corresponds well with the predicted power by the proposed formulae for as few as eight clusters when outcomes are analyzed using the matrix adjusted estimating equations for the correlation parameters concurrently with a suitable bias corrected sandwich variance estimator

performance of analytical methods for overdispersed counts in cluster randomized trials sample size degree of clustering and imbalance many different methods have been proposed for the analysis of cluster randomized trials crts over the last 30 years however the evaluation of methods on overdispersed count data has been based mostly on the comparison of results using empiric data i e when the true model parameters are not known in this study we assess via simulation the performance of five methods for the analysis of counts in situations similar to real community intervention trials we used the negative binomial distribution to simulate overdispersed counts of crts with two study arms allowing the period of time under observation to vary among individuals we assessed different sample sizes degrees of clustering and degrees of cluster size imbalance the compared methods are i the two sample t test of cluster level rates ii generalized estimating equations gee with empirical covariance estimators iii gee with model based covariance estimators iv generalized linear mixed models glmm and v bayesian hierarchical models bayes hm variation in sample size and clustering led to differences between the methods in terms of coverage significance power and random effects estimation glmm and bayes hm performed better in general with bayes hm producing less dispersed results for random effects estimates although upward biased when clustering was low gee showed higher power but anticonservative coverage and elevated type i error rates imbalance affected the overall performance of the cluster level t test and the gee s coverage in small samples important effects arising from accounting for overdispersion are illustrated through the analysis of a community intervention trial on solar water disinfection in rural bolivia

the representation and characterization of drazin inverses of operators on a hilbert space in this note the representation and characterization of drazin inverses of operators on a hilbert space are established

on the drazin inverse of block matrices and generalized schur complement in this paper we give an additive result for the drazin inverse with its applications we obtain representations for the drazin inverse of a 2x2 complex block matrix having generalized schur complement s d ca db equal to zero or nonsingular several situations are analyzed and recent results are generalized r e hartwig x li y wei representations for the drazin inverse of a 2x2 block matrix siam j matrix anal appl 27 3 2006 757 771

formulae for the generalized drazin inverse of a block matrix in terms of banachiewicz schur forms abstract we introduce new expressions for the generalized drazin inverse of a block matrix with the generalized schur complement being generalized drazin invertible in a banach algebra under some conditions we generalized some recent results for drazin inverse and group inverse of complex matrices

expression of the drazin and mp inverse of partitioned matrix and quotient identity of generalized schur complement in this paper we give representations of the drazin and mp inverse of a 2x2 block matrix and quotient identities for the generalized schur complement of a partitioned 3x3 matrix under conditions different than those used in recent papers on the subject we present numerical examples to illustrate our results

empirical bayes estimates of cancer mortality rates using spatial models we give results of empirical bayes eb estimation of mortality rates designed to smooth observed smr when random fluctuation of the observed deaths is important we have specially studied the case where the prior distributions of the eb method have a spatial structure the need for spatial modelling of cancer mortality rates in france is first shown with testing autocorrelation and fitting autoregressive spatial models conditional car or simultaneous sar a positive autocorrelation of the rates is shown for most cancer sites studied as expected eb estimates of mortality rates for common tumours are similar to smrs for rare tumours the eb method identifies the extreme rates more clearly than smrs by smoothing the smrs with large variances car or sar models are adequate prior distributions for autocorrelated rates and produce quite similar rate estimates

using second order generalized estimating equations to model heterogeneous intraclass correlation in cluster randomized trials in cluster randomized trials it is commonly assumed that the magnitude of the correlation among subjects within a cluster is constant across clusters however the correlation may in fact be heterogeneous and depend on cluster characteristics accurate modeling of the correlation has the potential to improve inference we use second order generalized estimating equations to model heterogeneous correlation in cluster randomized trials using simulation studies we show that accurate modeling of heterogeneous correlation can improve inference when the correlation is high or varies by cluster size we apply the methods to a cluster randomized trial of an intervention to promote breast cancer screening

some results on the generalized drazin inverse of operator matrices the generalized drazin inverse m d of a 2 2 operator matrix is considered where a x and d y are generalized drazin invertible expressions for the generalized drazin inverse m d of operator matrix m in terms of the individual blocks a b c d a d and d d are derived under some conditions

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

solvability of certain quadratic operator equations and representations of drazin inverses abstract let e be a banach space b e be the set of bounded linear operators on e and i be the identity operator on e in this paper the solvability of the quadratic operator equations ax x 2 b and xa i xbx is studied where a b e is invertible and b b e is nilpotent it is proved that the first quadratic operator equation is solvable if furthermore ab ba or e c n for n 2 3 and b 2 0 a counterexample is given such that the second quadratic operator equation is unsolvable as an application in the general setting of bounded linear operators on banach spaces a new expression of the drazin inverse a b i 0 d is given under the condition that a b b e are drazin invertible and ab ba

on the problem of permissible covariance and variogram models the covariance and variogram models ordinary or generalized are important statistical tools used in various estimation and simulation techniques which have been recently applied to diverse hydrologic problems for example the efficacy of kriging a method for interpolating filtering or averaging spatial phenomena depends to a large extent on the covariance or variogram model chosen the aim of this article is to provide the users of these techniques with convenient criteria that may help them to judge whether a function which arises in a particular problem and is not included among the known covariance or variogram models is permissible as such a model this is done by investigating the properties of the candidate model in both the space and frequency domains in the present article this investigation covers stationary random functions as well as intrinsic random functions i e nonstationary functions for which increments of some order are stationary then based on the theoretical results obtained a procedure is outlined and successfully applied to a number of candidate models in order to give to this procedure a more practical context we employ stereological equations that essentially transfer the investigations to one dimensional space together with approximations in terms of polygonal functions and fourier bessel series expansions there are many benefits and applications of such a procedure polygonal models can be fit arbitrarily closely to the data also the approximation of a particular model in the frequency domain by a fourier bessel series expansion can be very effective this is shown by theory and by example

estimating equations for spatially correlated data in multi dimensional space summary we use the quasilikelihood concept to propose an estimating equation for spatial data with correlation across the study region in a multi dimensional space with appropriate mixing con ditions we develop a central limit theorem for a random field under various lp metrics the consistency and asymptotic normality of quasilikelihood estimators can then be derived we also conduct simulations to evaluate the performance of the proposed estimating equation and a dataset from east lansing woods is used to illustrate the method

mathematical model for degradation and drug release from an intravitreal biodegradable implant abstract in this paper we study from a mathematical point of view the drug release and the degradation process in the context of biodegradable intravitreal implants in particular two different clinical situations are considered non vitrectomized and vitrectomized eyes in the former case we assume that the vitreous humor is replaced by a saline solution or a silicone oil in intravitreal space the intravitreal liquid enters the implant by non fickian diffusion causing the degradation of the poly lactic co glycolic acid based implant then drug in the implant dissolves and diffuses out of the polymeric matrix the transport of drug in the vitreous chamber and retina is modeled by fickian diffusion and convection generated by the flow of the vitreous humor in order to numerically solve the system of partial differential equations that define the model we propose an implicit explicit finite element method that allows for the decoupling of the solution reducing the computational cost of the simulations several numerical experiments showing the effectiveness of the proposed numerical schemes are also included the proposed mathematical model may be useful to optimize patient specific treatments in clinical practice

new additive results for the generalized drazin inverse in this paper we investigate additive properties of generalized drazin inverse of two drazin invertible linear operators in banach spaces under the commutative condition of pq qp we give explicit representations of the generalized drazin inverse p q d in term of p pd q and qd we consider some applications of our results to the perturbation of the drazin inverse and analyze a number of special cases

representations for the drazin inverse of 2 2 block operator matrix with singular schur complement abstract in this paper we present formulae for the drazin inverse of 2 2 block operator matrix with generalized schur complement being drazin invertible moreover necessary and sufficient conditions for the existence as well as the expressions for the group inverse are obtained

correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria the method of generalized estimating equations gee is popular in the biostatistics literature for analyzing longitudinal binary and count data it assumes a generalized linear model for the outcome variable and a working correlation among repeated measurements in this paper we introduce a viable competitor the weighted scores method for generalized linear model margins we weight the univariate score equations using a working discretized multivariate normal model that is a proper multivariate model because the weighted scores method is a parametric method based on likelihood we propose composite likelihood information criteria as an intermediate step for model selection the same criteria can be used for both correlation structure and variable selection simulations studies and the application example show that our method outperforms other existing model selection methods in gee from the example it can be seen that our methods not only improve on gee in terms of interpretability and efficiency but also can change the inferential conclusions with respect to gee copyright 2016 john wiley sons ltd

a note on the drazin inverses with banachiewicz schur forms let h be a hilbert space m the closed subspace of h with orthocomplement m according to the orthogonal decomposition email protected m every operator email protected b h can be written in a block form m abcd in this note we give necessary and sufficient conditions for a partitioned operator matrix m to have the drazin inverse with banachiewicz schur form in addition this paper investigates the relations among the drazin inverse the moore penrose inverse and the group inverse when they can be expressed in the banachiewicz schur forms

a generalized estimating equations approach for spatially correlated binary data applications to the analysis of neuroimaging data this paper proposes a generalized estimating equations approach for the analysis of spatially correlated binary data when there are large numbers of spatially correlated observations on a moderate number of subjects this approach is useful when the scientific focus is on modeling the marginal mean structure proper modeling of the spatial correlation structure is shown to provide large efficiency gains along with precise standard error estimates for inference on mean structure parameters generalized estimating equations for estimating the parameters of both the mean and spatial correlation structure are proposed the use of semivariogram models for parameterizing the correlation structure is discussed and estimation of the sample semivariogram is proposed as a technique for choosing parametric models and starting values for generalized estimating equations estimation the methodology is illustrated with neuroimaging data collected as part of the national institute of neurological disorders and stroke ninds stroke data bank a simulation study demonstrates the importance of accurate modeling of the spatial correlation structure in data with large numbers of spatially correlated observations such as those found in neuroimaging studies

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

formulas for the drazin inverse of special block matrices properties of the drazin inverse of the matrix f iie0 with e square are investigated based on this approach it is obtained an explicit formula for the drazin inverse of matrices of the form a ip tquv t where u v p and q are nxk the representation for a d is given in terms of kxk matrices involving the individual blocks under some conditions some special cases are also analyzed

semiparametric time varying coefficient model for matched case crossover studies in matched case crossover studies it is generally accepted that the covariates on which a case and associated controls are matched cannot exert a confounding effect on independent predictors included in the conditional logistic regression model this is because any stratum effect is removed by the conditioning on the fixed number of sets of the case and controls in the stratum hence the conditional logistic regression model is not able to detect any effects associated with the matching covariates by stratum however some matching covariates such as time often play an important role as an effect modification leading to incorrect statistical estimation and prediction therefore we propose three approaches to evaluate effect modification by time the first is a parametric approach the second is a semiparametric penalized approach and the third is a semiparametric bayesian approach our parametric approach is a two stage method which uses conditional logistic regression in the first stage and then estimates polynomial regression in the second stage our semiparametric penalized and bayesian approaches are one stage approaches developed by using regression splines our semiparametric one stage approach allows us to not only detect the parametric relationship between the predictor and binary outcomes but also evaluate nonparametric relationships between the predictor and time we demonstrate the advantage of our semiparametric one stage approaches using both a simulation study and an epidemiological example of a 1 4 bi directional case crossover study of childhood aseptic meningitis with drinking water turbidity we also provide statistical inference for the semiparametric bayesian approach using bayes factors copyright 2016 john wiley sons ltd

the drazin inverses of products and differences of orthogonal projections in this note the drazin inverses of products and differences of orthogonal projections on a hilbert space are established

expressions for the g drazin inverse of additive perturbed elements in a banach algebra abstract we study additive properties of the g drazin inverse in a banach algebra a in our development we derive a representation of the resolvent of a 2 2 matrix with entries in a which is then used to find explicit expressions for the g drazin inverse of the sum a b under new conditions on a b a as an application of our results we obtain a representation for the drazin inverse of a 2 2 complex block matrix in terms of the individual blocks under certain conditions

representations for the drazin inverse of the sum p q r s and its applications abstract let p q r and s be complex square matrices and m p q r s a quadruple p q r s is called a pseudo block decomposition of m if pq qp 0 ps sq qr rp 0 and r d s d 0 where r d and s d are the drazin inverses of r and s respectively we investigate the problem of finding formulae for the drazin inverse of m the explicit representations for the drazin inverses of m and p q r are developed under some assumptions as its application some representations are presented for 2 2 block matrices a b 0 c and a b d c where the blocks a and c are square matrices several results of this paper extend the well known representation for the drazin inverse of a b 0 c given by hartwig and shoaf meyer and rose in 1977 an illustrative example is given to verify our new representations

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

representations for the drazin inverses of 2 2 block matrices abstract let m denote a 2 2 block complex matrix a b c d where a and d are square matrices not necessarily with the same orders in this paper explicit representations for the drazin inverse of m are presented under the condition that bd i c 0 for i 0 1 n 1 where n is the order of d

analyzing spatially distributed binary data using independent block estimating equations summary we estimate the relation between binary responses and corresponding covariate vectors both observed over a large spatial lattice we assume a hierarchical generalized linear model with probit link function partition the lattice into blocks and adopt the working assumption of independence between the blocks to obtain an easily solved estimating equation standard errors are obtained using the sandwich estimator together with window subsampling sherman 1996 journal of the royal statistical society series b 58 509 523 we apply this to a large data set describing long term vegetation growth together with two other approximate likelihood approaches pairwise composite likelihood cl and estimation under a working assumption of independence the independence and cl methods give similar point estimates and standard errors while the independent block approach gives considerably smaller standard errors as well as more easily interpretable point estimates we present numerical evidence suggesting this increased efficiency may hold more generally

unbiased estimating equations from working correlation models for irregularly timed repeated measures the method of generalized estimating equations gees has been criticized recently for a failure to protect against misspecification of working correlation models which in some cases leads to loss of efficiency or infeasibility of solutions however the feasibility and efficiency of gee methods can be enhanced considerably by using flexible families of working correlation models we propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance gee the supplementary estimating equations are obtained by differentiation of the cholesky decomposition of the working correlation or as score equations for decoupled gaussian pseudolikelihood the estimating equations are solved with computational effort equivalent to that required for a first order gee full details and analytic expressions are developed for a generalized markovian model that was evaluated through simulation large sample sandwich standard errors for working correlation parameter estimates are derived and shown to have good performance the proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children

analysis of binary spatial data by quasi likelihood estimating equations the goal of this paper is to describe the application of quasi likelihood estimating equations for spatially correlated binary data in this paper a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest with mild assumptions on the correlations the leonov shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses the consistency and asymptotic normality for quasi likelihood estimates can then be derived by modeling spatial correlation with a variogram we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well known example based on data from lansing woods the comparison of generalized estimating equations and the proposed approach is also discussed

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

a note on the drazin inverse of an anti triangular matrix abstract in this paper we give formulae for the generalized drazin inverse m d of an anti triangular matrix m under some conditions moreover some particular cases of these results are also considered

on the perturbation of the group generalized inverse for a class of bounded operators in banach spaces abstract given a bounded operator a on a banach space x with drazin inverse a d and index r we study the class of group invertible bounded operators b such that i a d b a is invertible and r b n a r 0 we show that they can be written with respect to the decomposition x r a r n a r as a matrix operator b b 1 b 12 b 21 b 21 b 1 1 b 12 where b 1 and b 1 2 b 12 b 21 are invertible several characterizations of the perturbed operators are established extending matrix results we analyze the perturbation of the drazin inverse and we provide explicit upper bounds of b a d and b b a d a we obtain a result on the continuity of the group inverse for operators on banach spaces

a comparison of several approaches for choosing between working correlation structures in generalized estimating equation analysis of longitudinal binary data the method of generalized estimating equations gee models the association between the repeated observations on a subject with a patterned correlation matrix correct specification of the underlying structure is a potentially beneficial goal in terms of improving efficiency and enhancing scientific understanding we consider two sets of criteria that have previously been suggested respectively for selecting an appropriate working correlation structure and for ruling out a particular structure s in the gee analysis of longitudinal studies with binary outcomes the first selection criterion chooses the structure for which the model based and the sandwich based estimator of the covariance matrix of the regression parameter estimator are closest while the second selection criterion chooses the structure that minimizes the weighted error sum of squares the rule out criterion deselects structures for which the estimated correlation parameter violates standard constraints for binary data that depend on the marginal means in addition we remove structures from consideration if their estimated parameter values yield an estimated correlation structure that is not positive definite we investigate the performance of the two sets of criteria using both simulated and real data in the context of a longitudinal trial that compares two treatments for major depressive episode practical recommendations are also given on using these criteria to aid in the efficient selection of a working correlation structure in gee analysis of longitudinal binary data