asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

robust estimation of the variance in moment methods for extra binomial and extra poisson variation when faced with data in the form of overdispersed counts or proportions moment methods allow consistent parameter estimation when only the form of the mean and variance is specified if the variance form is misspecified these methods still yield consistent parameter estimates though with lower efficiency and the variances of the estimates will be inconsistent a variance correction is available that yields consistent variance estimates in these circumstances the asymptotic and small sample efficiencies of this correction are calculated and its performance under variance misspecification is studied a group randomized breast self examination prevention study that is now underway serves as a focal point for the study of these properties the use of the variance correction in modelling is illustrated on a teratology data set

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

estimation of the negative binomial parameter κ by maximum quasi likelihood we investigate estimation of the parameter k of the negative binomial distribution for small samples using a method of moments estimate mme and a maximum quasi likelihood estimate mqle previous work is reviewed the importance of indirect estimation of k through its reciprocal a and of allowance for negative estimates of k or a are discussed samples of size 50 are simulated 10 000 times for each of several parameter combinations to examine the properties of the estimates samples of sizes 10 20 30 and 50 are simulated 1 000 times to investigate the effect of sample size both estimators perform reasonably well except when the mean is small and the sample size does not exceed 20 three examples are given one of a designed experiment for which the mqle is especially suited confidence limits are derived for the mqle further work along these lines is required for adequate assessment of the usual maximum likelihood estimate

positive linear maps and spreads of matrices ii abstract it is shown how positive linear maps can be used to obtain lower bounds for spreads of normal matrices some known results and some new ones are obtained in this way

some inequalities for central moments of matrices abstract in this paper we shall study non commutative central moment inequalities with a focus on whether the commutative bounds are tight in the non commutative case as well we prove that the answer is affirmative for the fourth central moment and several particular results are given in the general case as an application we shall present some lower estimates of the spread of hermitian and normal matrices as well

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

bounds for the spectrum of normal matrices abstract let a be a normal matrix with eigenvalues 1 2 n and let denote the smallest disc containing these eigenvalues we give some inequalities relating the center and radius of to the entries in a when applied to hermitian matrices our results give lower bounds on the spread maxij i j of a when applied to positive definite hermitian matrices they give lower bounds on the kantorovich ratio maxij i j i j

estimation bias using the beta binomial distribution in teratology kupper et al 1986 biometrics 42 85 98 considered the fitting of dose response regressions to litter proportions in teratology experiments they found that the estimators which maximise the beta binomial likelihood become biased when the intralitter correlation is incorrectly assumed to be homogeneous this paper considers the nature of this bias and its implications for the analysis of litter proportions in toxicology

characterization of birkhoff james orthogonality the birkhoff james orthogonality is a generalization of hilbert space orthogonality to banach spaces we investigate this notion of orthogonality when the banach space has more structures we start by doing so for the banach space of square matrices moving gradually to all bounded operators on any hilbert space then to an arbitrary c algebra and finally a hilbert c module

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

when are simple ls estimators enough an empirical study of ls tls and gtls a variety of least squares estimators of significantly different complexity and generality are available to solve over constrained linear systems the most theoretically general may not necessarily be the best choice in practice problem conditions may be such that simpler and faster algorithms if theoretically inferior would yield acceptable errors we investigate when this may happen using homography estimation as the reference problem we study the errors of ls tls equilibrated tls and gtls algorithms with different noise types and varying intensity and correlation levels to allow direct comparisons with algorithms from the applied mathematics and computer vision communities we consider both inhomogeneous and homogeneous systems we add noise to image co ordinates and system matrix entries in separate experiments to take into account the effect on noise properties heteroscedasticity of pre processing data transformations we find that the theoretically most general algorithms may not always be worth their higher complexity comparable results are obtained with moderate levels of noise intensity and correlation we identify such levels quantitatively for the reference problem thus suggesting when simpler algorithms can be applied with limited errors in spite of their restrictive assumptions

variance bounds with an application to norm bounds for commutators abstract murthy and sethi m n murthy v k sethi sankhya ser b 27 1965 201 210 gave a sharp upper bound on the variance of a real random variable in terms of the range of values of that variable we generalise this bound to the complex case and more importantly to the matrix case in doing so we make contact with several geometrical and matrix analytical concepts such as the numerical range and introduce the new concept of radius of a matrix we also give a new and simplified proof for a sharp upper bound on the frobenius norm of commutators recently proven by bottcher and wenzel a bottcher d wenzel the frobenius norm and the commutator linear algebra appl 429 2008 1864 1885 and point out that at the heart of this proof lies exactly the matrix version of the variance we have introduced as an immediate application of our variance bounds we obtain stronger versions of bottcher and wenzel s upper bound

some inequalities for positive linear maps it has long been known that an analogue of jensen s inequality holds for positive unital linear maps on matrix algebras provided that instead of ordinary convex functions one restricts to matrix convex functions we show that this restriction is not necessary in the case of 2 2 matrices a noncommutative analogue of the variance is studied and a basic inequality with several applications is established

estimating prevalence by group testing using generalized linear models a method is described for estimating prevalence by group testing using generalized linear models this provides a simple way of analysing such data using widely available software existing methodology to correct for overdispersion using quasi likelihoods is applied to the group testing model the methods are illustrated by an estimation of salmonella contamination in eggs and of yellow fever virus infection in a mosquito population

testing for independence in a two way table new interpretations of the chi square statistic the classical chi square test for independence in a two way contingency table often rejects the independence hypothesis at an extremely small significance level particularly when the sample size is large this paper proposes some alternative distributions to independence to help interpret the chi 2 statistic in such situations the uniform alternative in which every possible contingency table of the given dimension and sample size receives equal probability leads to the volume test as originally suggested in a regression context by h hotelling exponential family theory is used to generate a class of intermediate alternatives between independence and uniformity leading to a random effects model for contingency tables

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

a comparison of methods for testing homogeneity of proportions in teratologic studies summary we consider teratologic studies in which the aim is to compare the survival rate of animals in a treatment group to the corresponding rate in a control group the design of such studies often involves the allocation of intact litters of animals to treatment invalidating the application of standard statistical methods we review the strengths and weaknesses of several approaches for dealing with this problem including methodology recently developed for the analysis of clustered binary data a simulation study is conducted in which litter sizes are generated from a distribution having specified mean and degree of imbalance it is recommended on the basis of this study and on theoretical considerations that the choice of method should depend on whether the comparison of interest is experimental or observational for experimental comparisons involving the random assignment of litters to different treatment groups methods based on the adjustment of standard chi square statistics are recommended unless the number of litters in each group is very large

orthogonality of matrices and some distance problems abstract if a and b are matrices such that a zb a for all complex numbers z then a is said to be orthogonal to b we find necessary and sufficient conditions for this to be the case some applications and generalisations are also discussed

lower bounds for the spread of a matrix a characterization of the spread of a normal matrix is used to derive several simple lower bounds for the spread comparisons are then made with several known bounds

linear mixed models with heterogeneous within cluster variances this paper describes an extension of linear mixed models to allow for heterogeneous within cluster variances in the analysis of clustered data unbiased estimating equations based on quasilikelihood pseudolikelihood and method of moments are introduced and are shown to give consistent estimators of the regression coefficients variance components and heterogeneity parameter under regularity conditions cluster specific random effects and variances are predicted by the posterior modes the method is illustrated through an analysis of menstrual diary data and its properties are evaluated in a simulation study

positive linear maps and perturbation bounds of matrices abstract we show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices some related bounds for the spread and condition number of hermitian matrices are also discussed here

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

characterizations and lower bounds for the spread of a normal matrix abstract the spread of an n n matrix a with eigenvalues 1 n is defined by spr a max j k j k we prove that if a is normal then spr a max x ax y ay x y c n x y 1 max x ay y ax x y c n x y 1 re x y 0 max x ay y ax x y c n x y 1 x y 0 max spr z a z a 2 z c z 1 2 max x a 2 x x ax 2 x a ax x ax 2 1 2 x c n x 1 we also present several lower bounds for spr a given by these characterizations

efficiency lost by analyzing counts rather than event times in poisson and overdispersed poisson regression models abstract inference for point processes is most efficient if the event times for each individual are available sometimes the study design is such that only aggregated data are collected consisting of the number of events or recurrences for each individual over the observation period this article discusses the loss in efficiency of an analysis of the aggregated counts versus an analysis of the actual event times one particular case is exemplified that in which the purpose of the experiment or trial is to compare the effects of treatments and the loss in efficiency in the estimator of the treatment effect is computed the specific point process considered here is the nonhomogeneous poisson process with a proportional intensity model for the treatment effects random effects models are also considered with estimation via a quasi likelihood approach the quasi likelihood analysis proposed here is an extension of such techniques for the homogeneous poisson process the resulting estimating equations for

generalized variance component models for clustered categorical response variables a generalized variance component model is proposed for the analysis of a categorical response variable with extra multinomial variation categorical data obtained from research designs such as randomized multicenter clinical trials or complex sample surveys with clustering frequently exhibit extra variation resulting from intracluster correlation general correlation patterns are accounted for by utilizing a mixed effects modelling approach estimating the cluster variance components through the method of moments and modelling functions of the observed proportions through the use of estimating equations a flexible set of assumptions characterizing the underlying covariance structure for the proportions can be accommodated the importance of accounting for extra variation when performing hypothesis tests is highlighted with an application to data from a multi investigator clinical trial

a saturated model for analyzing exchangeable binary data applications to clinical and developmental toxicity studies abstract correlated binary data occur very frequently in statistical practice in many applications it is reasonable to assume that data from the same cluster are exchangeable such data are commonly encountered in cluster sample surveys teratological experiments ophthalmologic and otolaryngologic studies and other clinical trials the standard methods of analyzing these data include the use of beta binomial models and generalized estimating equations with third and fourth moments specified by working matrices the focus of these procedures is an estimation of the mean and variance parameters more information can be obtained when data are exchangeable by expressing the joint distribution of a set of exchangeable binary random variables in terms of the probability of similar response within cluster this article introduces a procedure for obtaining maximum likelihood estimates of population parameters such as the marginal means moments and correlations of orders two and higher applications are m

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12