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

solution to the inverse regulator problem for discrete time systems a complete solution is given for the inverse problem of lq optimal regulators for the discrete time multi input case the kalman equation for discrete time systems is derived to characterize the optimal regulators it is then shown that this equation holds for some quadratic weighting if and only if the feedback satisfies a condition corresponding to the circle criterion for continuous time systems the optimality criterion given here consists of this condition and an additional condition to ensure detectability an example is given to illustrate the results

a local proof for the characterization of young measures generated by sequences in bv this work presents a new proof of the recent characterization theorem for generalized young measures generated by sequences in bv by kristensen and rindler 2010 14 the present argument is based on a localization technique together with a local hahn banach argument in novel function spaces combined with an application of alberti s rank one theorem this strategy avoids employing a relaxation theorem as in the previously known proof and the new tools introduced in its course should prove useful in other contexts as well in particular we introduce homogeneous young measures separately at regular and singular points which exhibit rather different behavior than the classical homogeneous young measures as an application we show how for bv young measures with an atomic part one can find a generating sequence respecting this structure

rank one property for derivatives of functions with bounded variation when u is a function of bounded variation of the open set r into r du is a measure on which takes values in the space rm n of all m n matrices such that du i j ui xj for every i j with 1 i m 1 j n and we denote by dsu the part of the measure du which is singular with respect to lebesgue measure we recall that the rank of a matrix a rm n is dimension of the space spanned by its columns in r or by its rows in r and in particular the rank of a is one if and only if there exist e r and r with e 6 0 6 0 so that a e i e ai j ei j for all i j cf remark 1 7 when is a measure which takes values in the space rm n and d d denotes the radon nikodym derivative of with respect to the total variation we say that has rank one when the rank of the matrix d d x is one for almost every x in this paper we prove we prove the following statement see theorem 4 5 corollary 4 6 and remark 4 9

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

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

analysis of one way layout of count data with negative binomial variation on derive deux statistiques c neyman 1959 pour tester l egalite des moyennes de plusieurs groupes de donnees de comptage en presence d un parametre de dispersion commun on compare leurs performances avec celles de la statistique du rapport de vraisemblance et de deux autres statistiques basees sur des donnees transformees anscombe 1948

on the structure of a free measures and applications we establish a general structure theorem for the singular part of a free radon measures where a is a linear pde operator by applying the theorem to suitably chosen differential operators a we obtain a simple proof of alberti s rank one theorem and for the first time its extensions to functions of bounded deformation bd we also prove a structure theorem for the singular part of a finite family of normal currents the latter result implies that the rademacher theorem on the differentiability of lipschitz functions can hold only for absolutely continuous measures and that every top dimensional ambrosio kirchheim metric current in rd is a federer fleming flat chain

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

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

explicit characterization oflp young measures the full explicit description of young measures attainable by bounded sequences from the lebesgue spacelp rm was known so far for the casep only in the paper a suitable condition characterizing such measures is isolated also for the case 1 p a generalization of thelp young measures constructed recently by diperna and majda can be thus described also but in special cases only

on heterogeneity tests based on efficient scores summary for cases in which a parameter may be estimated from several independent data sets mather 1935 proposed a heterogeneity test based on the efficient scores for the individual data sets evaluated at the overall maximum likelihood estimator following fisher 1946 a modification of the heterogeneity score test is presented wherein a consistent but inefficient estimator of the parameter of interest is substituted for the overall maximum likelihood estimator the modified test is also derived using the c q theory of neyman 1959 using the modified procedure we derive a test for a common odds ratio in several 2 x 2 tables based on the mantel haenszel estimator

analysis of proportions in the presence of over under dispersion procedures for testing homogeneity of proportions in the presence of over dispersion or underdispersion occurring in several groups in toxicology teratology or mutagenicity or other similar fields are developed we consider c a neyman 1959 in probability and statistics the harold cramer volume pp 213 234 new york wiley or score type tests rao 1947 proceedings of the cambridge philosophical society 44 50 57 based on a parametric model namely the extended beta binomial model prentice 1986 journal of the american statistical association 81 321 327 and two semi parametric models using quasi likelihood wedderburn 1974 biornetrika 61 439447 and extended quasi likelihood nelder and pregibon 1987 biometrika 74 221 232 these procedures and a recent procedure by rao and scott 1992 biometrics 48 577 585 based on the concept of design effect and effective sample size are compared through simulation in terms of size power and robustness for departures from data distribution and dispersion homogeneity to study robustness in terms of departure from data distribution we simulate data from the betabinomial distribution the probit normal binomial distribution and the logit normal binomial distribution simulation shows evidence that for litter sizes and number of litters that may arise in practice a score test based on the quasi likelihood performs best in that it holds nominal level well in all data distribution situations considered here it shows some edge in power over some other statistics in some situations and also shows robustness in presence of moderate dispersion heterogeneity this statistic has a very simple form and it requires estimates of the parameters only under the null hypotheses

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

a direct computation of state deadbeat feedback gains a method for computing a feedback gain that achieves state deadbeat control is given from systems given in the staircase form this method derives the deadbeat gain in a numerically reliable way it is shown that the gain turns out to be lq optimal for some weightings

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

characterization of generalized young measures generated by symmetric gradients this work establishes a characterization theorem for generalized young measures generated by symmetric derivatives of functions of bounded deformation bd in the spirit of the classical kinderlehrer pedregal theorem our result places such young measures in duality with symmetric quasiconvex functions with linear growth the local proof strategy combines blow up arguments with the singular structure theorem in bd the analogue of alberti s rank one theorem in bv which was recently proved by the authors as an application of our characterization theorem we show how an atomic part in a bd young measure can be split off in generating sequences

directional oscillations concentrations and compensated compactness via microlocal compactness forms this work introduces microlocal compactness forms mcfs as a new tool to study oscillations and concentrations in l p bounded sequences of functions decisively mcfs retain information about the location value distribution and direction of oscillations and concentrations thus extending at the same time the theories of generalized young measures and h measures in l p spaces oscillations and concentrations precisely discriminate between weak and strong compactness and thus mcfs allow one to quantify the difference in compactness the definition of mcfs involves a fourier variable whereby differential constraints on the functions in the sequence can also be investigated easily a distinct advantage over young measure theory furthermore pointwise restrictions are reflected in the mcf as well paving the way for applications to tartar s framework of compensated compactness consequently we establish a new weak to strong compactness theorem in a geometric way after developing several aspects of the abstract theory we consider three applications for lamination microstructures the hierarchy of oscillations is reflected in the mcf the directional information retained in an mcf is harnessed in the relaxation theory for anisotropic integral functionals finally we indicate how the theory pertains to the study of propagation of singularities in certain systems of pdes the proofs combine measure theory young measures and harmonic analysis

analysis of proportions of affected foetuses in teratological experiments this paper is concerned with the analysis of proportions affected when an increasing dose of a compound is applied to a group of laboratory animals several sets of data including a set from a teratological experiment at the shell toxicology laboratory sittingbourne are analysed and some simulations are performed among the distributional models the beta binomial model is in general found to be the most sensitive to departures from the binomial for testing the equality of two proportions a comparison is made between the pseudo t test based on the jackknife method and the likelihood ratio test based on the beta binomial model from the limited comparison no definite advantage of one approach over the other has been found at the 5 level of significance both approaches lead to similar conclusions

state deadbeat control of nonlinear systems construction via sets a geometric generalization of the discrete time linear deadbeat control problem is studied the proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively for demonstration derivations of the deadbeat feedback law and tracker dynamics are provided for an example system based on the method a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given

young measures generated by ideal incompressible fluid flows in their seminal paper diperna and majda commun math phys 108 4 667 689 1987 introduced the notion of a measure valued solution for the incompressible euler equations in order to capture complex phenomena present in limits of approximate solutions such as persistence of oscillation and development of concentrations furthermore they gave several explicit examples exhibiting such phenomena in this paper we show that any measure valued solution can be generated by a sequence of exact weak solutions in particular this gives rise to a very large arguably too large set of weak solutions of the incompressible euler equations

characterization of generalized gradient young measures generated by sequences in w1 1 and bv generalized young measures as introduced by diperna and majda commun math phys 108 667 689 1987 provide a quantitative tool for studying the one point statistics of oscillation and concentration in sequences of functions in this work after developing a functional analytic framework for such measures including a compactness theorem and results on the generation of such young measures by l1 bounded sequences or even by sequences of bounded radon measures we turn to investigation of those young measures that are generated by bounded sequences of w1 1 gradients or bv derivatives we provide several techniques to manipulate such measures including shifting averaging and approximation by piecewise homogeneous young measures and then establish the main new result of this work the duality characterization of the set of bv or w1 1 gradient young measures in terms of jensen type inequalities for quasiconvex functions with linear growth at infinity this result is the natural generalization of the kinderlehrer pedregal theorem arch ration mech anal 115 329 365 1991 j geom anal 4 59 90 1994 for classical young measures to the w1 1 and bv case and contains its version for weakly converging sequences in w1 1 as a special case finally we give an application to a new lower semicontinuity theorem in bv

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

a simple method for the analysis of clustered binary data a simple method for comparing independent groups of clustered binary data with group specific covariates is proposed it is based on the concepts of design effect and effective sample size widely used in sample surveys and assumes no specific models for the intracluster correlations it can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing the method is applied to a variety of problems involving clustered binary data testing homogeneity of proportions estimating dose response models and testing for trend in proportions and performing the mantel haenszel chi squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance illustrative applications of the method are also presented

hypothesis testing for proportions with overdispersion summary the properties of likelihood ratio tests and simpler t tests are investigated by simulation under an assumed beta binomial model for parameter values typically found in toxicological studies it is found that likelihood ratio methods are at least as powerful as the simpler approaches and in certain situations can be significantly more powerful

likelihood inference in a correlated probit regression model correlated binary observations arise in a variety of applications for example in animal studies the term litter effect is used to describe the greater alikeness of responses within a litter as compared to that between litters at a given set of experimental conditions in a setting that motivated this work cells on individual atomic bomb survivors were scored as to the presence or absence of chromosomal aberrations the number of aberrant cells varied among subjects at a specified radiation exposure estimate age at exposure city of exposure and sex in a manner that substantially exceeds that consistent with a binomial error structure otake prentice 1984 this extra binomial variation or overdispersion reflects the fact that the binary response of cells from a given survivor tend to be more alike than are the responses of cells from distinct survivors having the same estimated radiation exposure level and other covariate values such overdispersion may result from individual differences in susceptibility to radiation damage from omitted covariates or most plausibly in this setting from substantial random errors in the estimated radiation exposure levels failure to acknowledge overdispersion may lead to serious underestimation of the standard errors associated with regression parameter estimates and to unduly precise inferences

a newton squaring algorithm for computing the negative invariant subspace of a matrix by combining newton s method for the matrix sign function with a squaring procedure a basis for the negative invariant subspace of a matrix can be computed efficiently the algorithm presented is a variant of multiplication rich schemes for computing the matrix sign function such as the well known inversion free schulz method which requires two matrix multiplications per step however by avoiding a complete computation of the matrix sign and instead concentrating only on the negative invariant subspace the final newton steps can be replaced by steps which require only one matrix squaring each this efficiency is attained without sacrificing the quadratic convergence of newton s method

deadbeat control and tracking of discrete time systems a new approach for forcing the state of a linear discrete time system to zero in a minimum number of steps is discussed the problem is formulated as the solution to a steady state optimal control problem with no cost on the control this problem in turn is set up as the solution to an associated eigenvalue problem no special assumption on the open loop system matrix and or the ratio of the number of states to controls is required stable numerical techniques are presented for solving for the feedback gain robust deadbeat tracking is also discussed

technical communique a sparse and condensed qp formulation for predictive control of lti systems the computational burden that model predictive control mpc imposes depends to a large extent on the way the optimal control problem is formulated as an optimization problem we present a formulation where the input is expressed as an affine function of the state such that the closed loop dynamics matrix becomes nilpotent using this approach and removing the equality constraints leads to a compact and sparse optimization problem to be solved at each sampling instant the problem can be solved with a cost per interior point iteration that is linear with respect to the horizon length when this is bigger than the controllability index of the plant the computational complexity of existing condensed approaches grow cubically with the horizon length whereas existing non condensed and sparse approaches also grow linearly but with a greater proportionality constant than with the method presented here