the effect of two stage sampling on ordinary least squares methods abstract we look at the effect of intracluster correlation on standard procedures in linear regression the ordinary least squares estimator of the coefficient vector performs well in most cases but the usual estimator of cov and procedures based on this such as confidence intervals and hypothesis tests can be seriously misleading the size of the effect however tends to be smaller than the corresponding effect on the variance of an estimated mean in two stage sampling provided that the cluster sample sizes are approximately equal

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

between and within cluster covariate effects in the analysis of clustered data standard methods for the regression analysis of clustered data postulate models relating covariates to the response without regard to between and within cluster covariate effects implicit in these analyses is the assumption that these effects are identical example data show that this is frequently not the case and that analyses that ignore differential between and within cluster covariate effects can be misleading consideration of between and within cluster effects also helps to explain observed and theoretical differences between mixture model analyses and those based on conditional likelihood methods in particular we show that conditional likelihood methods estimate purely within cluster covariate effects whereas mixture model approaches estimate a weighted average of between and within cluster covariate effects

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

a general framework for updating belief distributions we propose a framework for general bayesian inference we argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function which is recovered as a special case modern application areas make it increasingly challenging for bayesians to attempt to model the true data generating mechanism for instance when the object of interest is low dimensional such as a mean or median it is cumbersome to have to achieve this via a complete model for the whole data distribution more importantly there are settings where the parameter of interest does not directly index a family of density functions and thus the bayesian approach to learning about such parameters is currently regarded as problematic our framework uses loss functions to connect information in the data to functionals of interest the updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions importantly the procedure coincides with bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings connections to other inference frameworks are highlighted

flexible bivariate correlated count data regression multivariate count data are common in many disciplines the variables in such data often exhibit complex positive or negative dependency structures we propose three bayesian approaches to modeling bivariate count data by simultaneously considering covariate dependent means and correlation a direct approach utilizes a bivariate negative binomial probability mass function developed in famoye 2010 journal of applied statistics the second approach fits bivariate count data indirectly using a bivariate poisson gamma mixture model the third approach is a bivariate gaussian copula model based on the results from simulation analyses the indirect and copula approaches perform better overall than the direct approach in terms of model fitting and identifying covariate dependent association the proposed approaches are applied to two rna sequencing data sets for studying breast cancer and melanoma brca us and skcm us respectively obtained through the international cancer genome consortium

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

regression analysis of overdispersed correlated count data with subject specific covariates a robust likelihood approach for the analysis of overdispersed correlated count data that takes into account cluster varying covariates is proposed we emphasise two characteristics of the proposed method that the correlation structure satisfies the constraints on the second moments and that the estimation of the correlation structure guarantees consistent estimates of the regression coefficients in addition we extend the mean specification to include within and between cluster effects the method is illustrated through the analysis of data from two studies in the first study cross sectional count data from a randomised controlled trial are analysed to evaluate the efficacy of a communication skills training programme the second study involves longitudinal count data which represent counts of damaged hand joints in patients with psoriatic arthritis motivated by this study we generalize our model to accommodate for a subpopulation of patients who are not susceptible to the development of damaged hand joints

on asymptotic normality of limiting density functions with bayesian implications walker 1969 presented a straightforward approach to asymptotic normality of posterior distributions based on independent and identically distributed i i d observations dawid 1970 extended this work by providing a weaker set of conditions to cover some distributions whose ranges depend on the parameters of interest more recently heyde and johnstone 1979 simplified walker s conditions for stochastic processes in this paper we introduce three basic normality conditions for limiting density functions in the bayesian context our approach is data determined and is nonprobabilistic in nature nevertheless the results thus obtained can be easily converted to probabilistic ones when compared with those given by other investigators it is shown that our conditions as a whole have a greater generality and flexibility than those previously assumed either by dawid or heyde and johnstone in particular for the i i d case the commonly assumed wald type uniform boundedness condition for tail behaviours is shown to be unnecessary for asymptotic normality section 3 3 the advantage of our approach is further exemplified by a simple proof of the asymptotic normality of distributions conjugate to the exponential family

inversion of spherical means and the wave equation in even dimensions we establish inversion formulas of the so called filtered back projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball we also find several formulas to recover initial data of the form f 0 or 0 g for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball provided that the initial data has support in the ball

interpreting statistical evidence by using imperfect models robust adjusted likelihood functions summary the strength of statistical evidence is measured by the likelihood ratio two key performance properties of this measure are the probability of observing strong misleading evidence and the probability of observing weak evidence for the likelihood function associated with a parametric statistical model these probabilities have a simple large sample structure when the model is correct here we examine how that structure changes when the model fails this leads to criteria for determining whether a given likelihood function is robust continuing to perform satisfactorily when the model fails and to a simple technique for adjusting both likelihoods and profile likelihoods to make them robust we prove that the expected information in the robust adjusted likelihood cannot exceed the expected information in the likelihood function from a true model we note that the robust adjusted likelihood is asymptotically fully efficient when the working model is correct and we show that in some important examples this efficiency is retained even when the working model fails in such cases the bayes posterior probability distribution based on the adjusted likelihood is robust remaining correct asymptotically even when the model for the observable random variable does not include the true distribution finally we note a link to standard frequentist methodology in large samples the adjusted likelihood functions provide robust likelihood based confidence intervals

an algorithm for system immersion into nonlinear observer form siso case the class of nonlinear systems that can be put into nonlinear observer form linear system with output injection can be broadened if we employ the system immersion we provide an immersion algorithm for siso nonlinear systems with relative degree r the proposed algorithm is an extension of the previous results and does not require the relative degree 1 assumption in addition it is seen that the immersion can always be computed via algebraic computations and simple integrations except in a very special case in which the relative degree equals the system dimension in this case only one first order differential equation appears in the algorithm

modelling heterogeneity in clustered count data with extra zeros using compound poisson random effect in medical and health studies heterogeneities in clustered count data have been traditionally modeled by positive random effects in poisson mixed models however excessive zeros often occur in clustered medical and health count data in this paper we consider a three level random effects zero inflated poisson model for health care utilization data where data are clustered by both subjects and families to accommodate zero and positive components in the count response compatibly we model the subject level random effects by a compound poisson distribution our model displays a variance components decomposition which clearly reflects the hierarchical structure of clustered data a quasi likelihood approach has been developed in the estimation of our model we illustrate the method with analysis of the health care utilization data the performance of our method is also evaluated through simulation studies

a robust adjustment of the profile likelihood under mild misspecifications of model assumptions maximum likelihood estimates often remain consistent and asymptotically normal asymptotic normality will often hold for the signed root of the likelihood ratio statistic and the score statistic as well however standard estimates of asymptotic variance are usually inconsistent this occurs when bartlett s second identity fails in the manner of mccullagh and tibshirani a variance correction may be used to adjust the profile likelihood so this identity obtains the resulting likelihood yields the robust versions of the signed root wald and score statistic suggested by kent and royall assuming model correctness asymptotic expansions for the first three cumulants of each robust statistic are derived it is seen that bias and skewness are not severely affected by using a robust statistic an invariant expression derived for the asymptotic relative efficiency of a robust method allows assessment in numerous examples considered even for moderately large sample sizes losses in efficiency are significant making the misuse of a robust variance estimate potentially costly computer algebra is used in many of the calculations reported in this paper

inference for clustered data using the independence loglikelihood we use the properties of independence estimating equations to adjust the independence loglikelihood function in the presence of clustering the proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix which is easily calculated the methodology competes favourably with established techniques based on independence estimating equations we provide some insight as to why this is so the adjustment is applied to examples relating to the modelling of wind speed in europe and annual maximum temperatures in the u k

a finiteness criterion for nonlinear input output differential systems we solve the following problem which has been dealt with in several publications when does a system have the same input output behaviour as a system depending linearly on the state variables precise definitions of this question are supplied in the text a particular case of the problem is the equivalence of a system with a bilinear one at the end we illustrate our methods and the scope of our results by a brief study of several examples

generalized estimating equations for correlated binary data using the odds ratio as a measure of association summary moment methods for analyzing repeated binary responses have been proposed by liang zeger 1986 and extended by prentice 1988 in their generalized estimating equations both liang zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses because the odds ratio has many desirable properties and some investigators may find the odds ratio is easier to interpret we discuss modelling the association between binary responses at pairs of times with the odds ratio we then modify the estimating equations of prentice to estimate the odds ratios in simulations the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization

estimating equations for parameters in means and covariances of multivariate discrete and continuous responses generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response these equations are to be solved jointly with score equations from a generalized linear model for mean parameters a class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion and proposals for the use of such equations are developed comments on the relative merits of the ad hoc and model based approaches to estimation are given and a regression illustration with a bivariate response is provided

a simple method for the adjustment of profile likelihoods summary we propose a simple adjustment for profile likelihoods the aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods such as bias inconsistency and overoptimistic variance estimates the adjustment is applied to the profile loglikelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function for cases in which explicit calculation of the adjustments is difficult we give two methods to simplify their computation an automatic simulation method that requires as input only the profile loglikelihood and its first few derivatives first order asymptotic expressions some examples are provided and a comparison is made with the conditional profile log likelihood of cox and reid

local model uncertainty and incomplete data bias with discussion problems of the analysis of data with incomplete observations are all too familiar in statistics they are doubly difficult if we are also uncertain about the choice of model we propose a general formulation for the discussion of such problems and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation the increase in variance when an assumed model is correct the bias in estimation when the model is incorrect examples include non ignorable missing data hidden confounders in observational studies and publication bias in meta analysis doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of undetectably small departures from the model the problem of assessing the risk of lung cancer from passive smoking is used as a motivating example

a mollification approach for inverting the spherical mean radon transform the filtered backprojection algorithm is still one of the most important reconstruction methods in computed tomography it is based on explicit formulas for recovering mollified versions of the original unknown function in this paper we derive such formulas for the spherical mean radon transform with centers restricted to the boundary of a ball in two spatial dimensions we present an efficient implementation strategy that leads to a stable reconstruction algorithm of filtered backprojection type

constructive algorithm for system immersion into non linear observer form there exists a class of non linear systems which cannot be transformed into a non linear observer form an observable linear system up to output injection via diffeomorphism but can be immersed into a higher dimensional non linear observer form this class of systems can be characterized by a differential equation called characteristic equation if the system is an n dimensional system and it is immersible into n m dimensional observer form the characteristic equation involves n m 1 unknowns where n m unknowns are for the state immersion and one for the output transformation in general one should solve these unknowns simultaneously which makes the characterization difficult after investigating the algebraic structure of the characteristic equation we present an algorithm to check the immersibility under a constant rank assumption using the algorithm one can check the immersibility iteratively since only one unknown is involved at each step of the algorithm

on the probability of observing misleading statistical evidence abstract the law of likelihood explains how to interpret statistical data as evidence specifically it gives to the discipline of statistics a precise and objective measure of the strength of statistical evidence supporting one probability distribution vis a vis another that measure is the likelihood ratio but evidence even when properly interpreted can be misleading observations can truly constitute strong evidence supporting one distribution when the other is true what makes statistical evidence valuable to science is that this cannot occur very often here we examine two bounds on the probability of observing strong misleading evidence one is a universal bound applicable to every pair of probability distributions the other bound much smaller applies to all pairs of distributions within fixed dimensional parametric models in large samples the second bound comes from examining how the probability of strong misleading evidence varies as a function of the alternative value of the parameter we

sampling conditions for the circular radon transform recovering a function from circular or spherical mean values is the basis of many modern imaging technologies such as photo and thermoacoustic computed tomography or ultrasound reflection tomography recently much progress has been made concerning the problem of recovering a function from its circular mean values its circular radon transform in particular theoretically exact inversion formulas of the back projection type have been discovered using continuously sampled data in practical applications however only a discrete number of circular mean values can be collected in this paper we address this issue in the context of the shannon sampling theory we derive sharp sampling conditions for the number of angular and radial samples such that any essentially b0 bandlimited function can be recovered from a finite number of such circular mean values

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

observer linearization by output dependent time scale transformations we study the problem of observer linearization for single output dynamical systems in the presence of output dependent time scaling changes an alternative algorithm for the solution of the observer linearization problem is introduced the algorithm employs an exterior calculus approach that provides a simple procedure for the solution of the observer linearization problem by means of an output dependent time scale transformation

the universal back projection formula for spherical means and the wave equation on certain quadric hypersurfaces abstract in many tomographic applications and elsewhere there arises a need to reconstruct a function from the data on the boundary of some domain given either by the spherical means of the function or by the corresponding solution of the free space wave equation in this paper we show that the so called universal back projection formulas provide exact recovery of the unknown function with compact support for data on any quadric hypersurfaces that can be approximated by elliptic hypersurfaces these quadric hypersurfaces include elliptic paraboloid as well as parabolic and elliptic cylinders

new algebraic geometric conditions for the linearization by input output injection the goal of this paper is twofold it unifies and generalizes existing results on input output injection linearization of nonlinear systems the problem is solved as a realization problem since it is based on the analysis of the structure of the input output differential equation the necessary and sufficient conditions are derived from a simplified and constructive procedure for clarity the paper is limited to the case of single output systems exterior differential systems are extensively used throughout the paper giving constructive conditions

a robust effect size index effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size existing effect size indices are developed for particular parametric models or population parameters here we propose a robust effect size index based on m estimators this approach yields an index that is very generalizable because it is unitless across a wide range of models we demonstrate that the new index is a function of cohen s d formula see text and standardized log odds ratio when each of the parametric models is correctly specified we show that existing effect size estimators are biased when the parametric models are incorrect e g under unknown heteroskedasticity we provide simple formulas to compute power and sample size and use simulations to assess the bias and standard error of the effect size estimator in finite samples because the new index is invariant across models it has the potential to make communication and comprehension of effect size uniform across the behavioral sciences

assigning a value to a power likelihood in a general bayesian model summarybayesian robustness under model misspecification is a current area of active research among recent ideas is that of raising the likelihood function to a power in this paper we discuss the choice of appropriate power and provide examples

nonlinear observer design by dynamic observer error linearization in this note we address the problem of transforming a nonlinear system into nonlinear observer canonical form in the extended state space with the aid of dynamic system extension and introduction of virtual outputs as an intermediate step for the general problem we consider a restricted structure of dynamic extension which is obtained roughly speaking by adding the chains of integrators to the outputs of original system we propose sufficient conditions which can be verified using the system dynamics expressed in their original coordinates an illustrative example is included that demonstrates the advantage of the proposed method over the conventional method

parametric robust inferences for correlated ordinal data the aim of this article is to provide asymptotically valid likelihood inferences about regression parameters for correlated ordinal response variables the legitimacy of this novel approach requires no knowledge of the underlying joint distributions so long as their second moments exist the efficacy of the proposed parametric approach is demonstrated via simulations and the analyses of two real data sets

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

universal back projection algorithm for photoacoustic computed tomography we report results of a reconstruction algorithm for three dimensional photoacoustic computed tomography a universal back projection formula is presented for three types of imaging geometries planar spherical and cylindrical surfaces a solid angle weighting factor is introduced in the back projection formula to compensate for the variations of detection views a method for implementing this algorithm is described numerical simulation is used to demonstrate the performance of the algorithm

marginally specified logistic normal models for longitudinal binary data summary likelihood based inference for longitudinal binary data can be obtained using a generalized linear mixed model breslow n and clayton d g 1993 journal of the american statistical association88 9 25 wolfinger r and o connell m 1993 journal of statistical computation and simulation48 233 243 given the recent improvements in computational approaches alternatively fitzmaurice and laird 1993 biometrika80 141 151 molenberghs and lesaffre 1994 journal of the american statistical association89 633 644 and heagerty and zeger 1996 journal of the american statistical association91 1024 1036 have developed a likelihood based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and or marginal higher moment assumptions each of these marginal approaches is computationally intense and currently limited to small cluster sizes in this manuscript an alternative parameterization of the logistic normal random effects model is adopted and both likelihood and estimating equation approaches to parameter estimation are studied a key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual level predictions or contrasts an example is presented where scientific interest is in both the mean response and the covariance among repeated measurements

observer design for nonlinear triangular systems with unobservable linearisation the article deals with the observer design problem for a wide class of triangular time varying nonlinear systems with unobservable linearisation sufficient conditions are derived for the existence of a luenberger type observer when it is a priori known that the initial state of the system belongs to a given nonempty bounded subset of the state space for the general case the state estimation is exhibited by means of a switching sequence of time varying dynamics

exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface two universal reconstruction methods for photoacoustic also called optoacoustic or thermoacoustic computed tomography are derived applicable to an arbitrarily shaped detection surface in photoacoustic tomography acoustic pressure waves are induced by illuminating a semitransparent sample with pulsed electromagnetic radiation and are measured on a detection surface outside the sample the imaging problem consists in reconstructing the initial pressure sources from those measurements the first solution to this problem is based on the time reversal of the acoustic pressure field with a second order embedded boundary method the pressure on the arbitrarily shaped detection surface is set to coincide with the measured data in reversed temporal order in the second approach the reconstruction problem is solved by calculating the far field approximation a concept well known in physics where the generated acoustic wave is approximated by an outgoing spherical wave with the reconstruction point as center numerical simulations are used to compare the proposed universal reconstruction methods with existing algorithms

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

on constructing nonlinear observers two algorithmic approaches to constructing nonlinear observers currently exist here one of these is improved by finding an explicit solution to the partial differential equations describing the change of state coordinates thereby avoiding expensive bracket computations this simplifies the algorithm and has implications for system identification

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

is a curved flight path in sar better than a straight one in the plane we study the transform r gamma f of integrating an unknown function f over circles centered at a given curve gamma this is a simplified model of synthetic aperture radar sar when the radar is not directed but has other applications like thermoacoustic tomography for example we study the problem of recovering the wave front set wf f if the visible singularities of f hit gamma once we show that wf f cannot be recovered i e the artifacts cannot be resolved if gamma partial omega is the boundary of a strictly convex domain omega we show that this is still true on the other hand in the latter case if f is known a priori to have singularities in a compact set then we show that one can recover wf f omega and moreover this can be done in a simple explicit way using backpropagation for the wave equation

on autocorrelation in a poisson regression model summary this paper develops a practical approach to diagnosing the existence of a latent stochastic process in the mean of a poisson regression model the asymptotic distribution of standard generalised linear model estimators is derived for the case where an autocorrelated latent process is present simple formulae for the effect of autocovariance on standard errors of the regression coefficients are also provided methods for adjusting for the severe bias in previously proposed estimators of autocovariance are derived and their behaviour is investigated applications of the methods to time series of monthly polio counts in the u s a and daily asthma presentations at a hospital in sydney are used to illustrate the results and methods

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 likelihood based method for analysing longitudinal binary responses summary in this paper we discuss a likelihood based method for analysing correlated binary responses based on a multivariate model it is related to the pseudo maximum likelihood approach suggested recently by zhao prentice 1990 their parameterization results in a simple pairwise model in which the association between responses is modelled in terms of correlations while the present paper uses conditional log odds ratios with this approach higher order associations can be incorporated in a natural way one important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence we describe an iterative two stage procedure for obtaining the maximum likelihood estimates two examples are presented to illustrate this methodology

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

an inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions abstract in the articles 1 and 2 of d finch m haltmeier s patch and d rakesh inversion formulas were found in any dimension greater than or equal to 2 for recovering a smooth function with compact support in the unit ball from spherical means centered on the unit sphere the aim of this article is to show that the methods used in 1 2 can be modified in order to get similar inversion formulas from spherical means centered on an ellipsoid in two and three dimensional spaces

on repeated measures analysis with misspecified covariance structure in recent years various sophisticated methods have been developed for the analysis of repeated measures or longitudinal data the more traditional approach based on a normal likelihood function has been shown to be unsatisfactory in the sense of yielding asymptotically biased estimates when the covariance structure is misspecified more recent methodology based on generalized linear models and quasi likelihood estimation has gained widespread acceptance as generalized estimating equations however this also has theoretical problems in this paper a suggestion is made for improving the asymptotic behaviour of estimators by using the older approach implemented via gaussian estimation the resulting estimating equations include the quasi score function as one component so the methodology proposed can be viewed as a combination of gaussian estimation and generalized estimating equations which has a firmer asymptotic basis than either alone has

effect of omitted confounders on the analysis of correlated binary data summary marginal analysis using the generalized estimating equation approach is widely applied to correlated observations as occur in studies with clusters and in longitudinal follow up of individuals in this article we investigate the effect of confounding in such models we assume that a risk factor x and a confounder z are related by a generalized linear model to the outcome y which can be binary or ordinal in order to investigate confounding arising from the omission of z a joint structure for x and z must be specified modeling normally distributed x z as sums of between and within individual or cluster components allows us to incorporate different degrees of betweenand within individual correlation such a structure includes as special cases cohort and period effects in longitudinal settings and random intercept models the latter situation corresponds to allowing z to vary only on the between individual or cluster level and to be uncorrelated with x and leads to attenuation of the coefficient of x in marginal models with the logit and probit links more complex situations occur when z is allowed to also vary on the within individual or cluster level and when z is correlated with x we examine the model specification and the expected bias when fitting a marginal model in the presence of the omitted confounder z we derive general formulas and interpret the parameters and results in an ongoing cohort study testing for omitted covariates is also discussed

towards a unification of second order theory for likelihood and marginal composite likelihood an adjustment for marginal composite likelihoods is derived to match the second order theory of the likelihood when inference is for a vector valued parameter in the absence of nuisance components the adjustment overcomes the failure of bartlett identities for marginal composite likelihoods and leads to a bartlett correctable marginal composite likelihood ratio statistic

testing for omitted variables and non linearity in regression models for longitudinal data when fitting regression models to investigate the relationship between an outcome variable and independent variables of primary interest there is often concern whether omitted variables or assuming a different functional relationship could have changed the conclusion or interpretation of the results in longitudinal studies of aging the concern with omitted variables is well known in the context of cohort and period effects which refer to unmeasured variables systematically related to the individual s year of birth and secular trends in outcome respectively we present and compare three approaches to detecting omitted confounders and non linearity in the random effects model for longitudinal data laird and ware 1982 with random slope and intercept across individuals the first approach compares simple unweighted within and between regression coefficients the second is the hausman specification test for regression models and the third approach involves testing directly the significance of functions of individual specific covariate means means i in the random effects regression model this last approach is motivated by the models that arise when cohort or period effects are ignored we compare the three approaches and illustrate their application

erratum nonlinear observer design in the siegel domain there is an error in the proof of the main result of our paper siam j control optim 41 2002 pp 932 953 an additional assumption is needed for the main result to hold in this erratum we supply a corrected version of the main result

the spherical radon transform with centers on cylindrical surfaces abstract recovering a function from its spherical radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies including sar ultrasound imaging and photo and thermoacoustic tomography in this paper we study an inversion of the spherical radon transform with centers of integration restricted to cylindrical surfaces of the form r m where is a hypersurface in r n we show that this transform can be decomposed into two lower dimensional spherical radon transforms one with centers on and one with a planar center set in r m 1 together with explicit inversion formulas for the spherical radon transform with a planar center set and existing algorithms for inverting the spherical radon transform with a center set this yields reconstruction procedures for general cylindrical domains in the special case of spherical or elliptical cylinders we obtain novel explicit inversion formulas for three spatial dimensions these inversion formulas can be implemented efficiently by backprojection type algorithms only requiring o n 4 3 floating point operations where n is the total number of unknowns to be recovered we present numerical results demonstrating the efficiency of the derived algorithms

immersion of non linear systems into linear systems up to output injection characteristic equation approach there exists a class of non linear systems which cannot be transformed into non linear observer form via diffeomorphism but can be immersed into higher dimensional non linear observer form this paper investigates when n dimensional non linear systems can be immersed into n m dimensional non linear systems in non linear observer form and provides a necessary and sufficient condition we also present an algorithm to check the immersibility in general at the first step of the algorithm one should solve a differential equation with m 1 unknowns rather than solving one with n m unknowns simultaneously when a solution to the differential equation can be obtained the immersibility can be checked by a recursive algorithm moreover when 2m n a straightforward algorithm is provided to check the immersibility

inversion of n dimensional spherical averages in this paper we give a simple inversion formula for determining the even part of a function from its averages over the surfaces of spheres in mathbb r n centered on a hyperplane y 0 we emphasize the relation between the backprojection approximation to the function and the full inversion result a simple necessary and sufficient condition for data to correspond to the spherical averages of a function is given

output regulation with nonlinear internal models this paper addresses the problem of semi global nonlinear output regulation for a class of nonlinear systems possessing a nonlinear internal model it is shown that under appropriate and verifiable hypotheses the standard assumption that the feed forward inputs needed to keep the zero error manifold invariant satisfy a linear differential equation can be weakened

nonlinear system immersion observers and finite dimensional filters abstract nonlinear deterministic and stochastic systems which can be immersed into linear observable ones are identified by necessary and sufficient conditions those systems are shown to admit observers in the deterministic case and exact finite dimensional filters in the stochastic case the sufficient conditions obtained generalize earlier results in both cases

likelihood for statistically equivalent models in likelihood inference we usually assume that the model is fixed and then base inference on the corresponding likelihood function often however the choice of model is rather arbitrary and there may be other models which fit the data equally well we study robustness of likelihood inference over such statistically equivalent models and suggest a simple envelope likelihood to capture this aspect of model uncertainty robustness depends critically on how we specify the parameter of interest some asymptotic theory is presented illustrated by three examples

immersion of nonlinear systems into linear systems modulo output injection the problem of the immersion of a siso system into a linear up to an output injection one is studied in order to design luenberger like observers necessary and sufficient conditions are stated within a very general framework effective computations and examples are then provided

on the use of a working correlation matrix in using generalised linear models for repeated measures summary in a seminal paper liang zeger 1986 extended the use of generalised linear models to repeated measures data they based the analysis on specifications for the means and variances of the observations as usual for generalised linear models but showed how specifications for the correlations between measurements made on the same unit could be avoided by using a working correlation matrix in some cases the parameters involved in this matrix are subject to an uncertainty of definition which can lead to a breakdown of the asymptotic properties of the estimators

comparing several means of dependent populations of count a parametric robust approach we propose a parametric robust procedure for comparing several means of dependent populations of counts the validity of the proposed method requires no knowledge of the true underlying joint distributions so long as they have finite second moments the efficacy of this novel technique is demonstrated by simulations and the analysis of a data set from the taiwan national health insurance research database our new parametric robust method is also compared with the popular semi parametric generalized estimating equations approach

simultaneous control of error rates in fmri data analysis the key idea of statistical hypothesis testing is to fix and thereby control the type i error false positive rate across samples of any size multiple comparisons inflate the global family wise type i error rate and the traditional solution to maintaining control of the error rate is to increase the local comparison wise type ii error false negative rates however in the analysis of human brain imaging data the number of comparisons is so large that this solution breaks down the local type ii error rate ends up being so large that scientifically meaningful analysis is precluded here we propose a novel solution to this problem allow the type i error rate to converge to zero along with the type ii error rate it works because when the type i error rate per comparison is very small the accumulation or global type i error rate is also small this solution is achieved by employing the likelihood paradigm which uses likelihood ratios to measure the strength of evidence on a voxel by voxel basis in this paper we provide theoretical and empirical justification for a likelihood approach to the analysis of human brain imaging data in addition we present extensive simulations that show the likelihood approach is viable leading to cleaner looking brain maps and operational superiority lower average error rate finally we include a case study on cognitive control related activation in the prefrontal cortex of the human brain

modelling and generating correlated binary variables summary many applications use simple parametric models for the correlation structure of binary responses which are observed in clusters the usual approach to use correlation models appropriate for normally distributed responses suffers from two drawbacks when the marginal probabilities within the clusters differ first as it does not explicitly take into account constraints on the second moments which must be satisfied for binary responses it may fail to model realistically the range of correlations present in the data secondly computer simulation of observations from these models is very difficult we present an alternative class of correlation models which reflect the binary nature of the responses and allow for simple simulation some key wor ds binary variable computer simulation correlation structure generalised estimating equation

multinomial n mixture models for removal sampling multinomial n mixture models are commonly used to fit data from a removal sampling protocol if the mixing distribution is negative binomial the distribution of the counts does not appear to have been identified and practitioners approximate the requisite likelihood by placing an upper bound on the embedded infinite sum in this paper the distribution which underpins the multinomial n mixture model with a negative binomial mixing distribution is shown to belong to the broad class of multivariate negative binomial distributions specifically the likelihood can be expressed in closed form as the product of conditional and marginal likelihoods and the information matrix shown to be block diagonal as a consequence the nature of the maximum likelihood estimates of the unknown parameters and their attendant standard errors can be examined and tests of the hypothesis of the poisson against the negative binomial mixing distribution formulated in addition appropriate multinomial n mixture models for data sets which include zero site totals can also be constructed two illustrative examples are provided

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

statistical evidence for glm regression parameters a robust likelihood approach when a likelihood ratio is used to measure the strength of evidence for one hypothesis over another its reliability i e how often it produces misleading evidence depends on the specification of the working model when the working model happens to be the true or correct model the probability of observing strong misleading evidence is low and controllable but this is not necessarily the case when the working model is misspecified royall and tsou j r stat soc ser b 2003 65 391 404 show how to adjust working models to make them robust to misspecification likelihood ratios derived from their robust adjusted likelihood are just as reliable asymptotically as if the working model were correctly specified in the first place in this paper we apply and extend these ideas to the generalized linear model glm regression setting we provide several illustrations both from simulated data and real data concerning rates of parasitic infection in philippine adolescents show how the required adjustment factor can be obtained from standard statistical software and draw some connections between this approach and the sandwich estimator for robust standard errors of regression parameters this substantially broadens the availability and the viability of likelihood methods for measuring statistical evidence in regression settings copyright 2007 john wiley sons ltd

observer with linear error dynamics for nonlinear multi output systems based upon nonlinear state coordinate transformations and a condensed dual brunovsk form for multi output systems a method for designing nonlinear state observers with linear error dynamics is presented necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained

mixed poisson likelihood regression models for longitudinal interval count data summary in many longitudinal studies it is desired to estimate and test the rate over time of a particular recurrent event often only the event counts corresponding to the elapsed time intervals between each subject s successive observation times and baseline covariate data are available the intervals may vary substantially in length and number between subjects so that the corresponding vectors of counts are not directly comparable a family of poisson likelihood regression models incorporating a mixed random multiplicative component in the rate function of each subject is proposed for this longitudinal data structure a related empirical bayes estimate of random effect parameters is also described these methods are illustrated by an analysis of dyspepsia data from the national cooperative gallstone study

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

inference of bioequivalence for log normal distributed data with unspecified variances two drugs are bioequivalent if the ratio of a pharmacokinetic pk parameter of two products falls within equivalence margins the distribution of pk parameters is often assumed to be log normal therefore bioequivalence be is usually assessed on the difference of logarithmically transformed pk parameters in the presence of unspecified variances test procedures such as two one sided tests tost use sample estimates for those variances bayesian models integrate them out in the posterior distribution these methods limit our knowledge on the extent that inference about be is affected by the variability of pk parameters in this paper we propose a likelihood approach that retains the unspecified variances in the model and partitions the entire likelihood function into two components f statistic function for variances and t statistic function for demonstrated with published real life data the proposed method not only produces results that are same as tost and comparable with bayesian method but also helps identify ranges of variances which could make the determination of be more achievable our findings manifest the advantages of the proposed method in making inference about the extent that be is affected by the unspecified variances which cannot be accomplished either by tost or bayesian method

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

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

nonlinear observer design in the siegel domain we extend the method of kazantzis and kravaris systems control lett 34 1998 pp 241 247 for the design of an observer to a larger class of nonlinear systems the extended method is applicable to any real analytic observable nonlinear system it is based on the solution of a first order singular nonlinear pde this solution yields a change of state coordinates which linearizes the error dynamics under very general conditions the existence and uniqueness of the solution is proved lyapunov s auxiliary theorem and siegel s theorem are obtained as corollaries the technique is constructive and yields a method for constructing approximate solutions