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

from concentration to logarithmic sobolev and poincare inequalities abstract we give a new proof of the fact that gaussian concentration implies the logarithmic sobolev inequality when the curvature is bounded from below and also that exponential concentration implies poincare inequality under null curvature condition our proof holds on non smooth structures such as length spaces and provides a universal control of the constants we also give a new proof of the equivalence between dimension free gaussian concentration and talagrand s transport inequality

local łojasiewicz exponents milnor numbers and mixed multiplicities of ideals let g mathbb c n 0 to mathbb c n 0 be a finite analytic map we give an expression for the local ojasiewicz exponent and for the multiplicity of g when the component functions of g satisfy certain condition with respect to a set of n monomial ideals i1 in we give an effective method to compute ojasiewicz exponents based on the computation of mixed multiplicities as a consequence of our study we give a numerical characterization of a class of functions that includes semi weighted homogenous functions and newton non degenerate functions

a characterization of dimension free concentration in terms of transportation inequalities the aim of this paper is to show that a probability measure concentrates independently of the dimension like a gaussian measure if and only if it verifies talagrand s t 2 transportation cost inequality this theorem permits us to give a new and very short proof of a result of otto and villani generalizations to other types of concentration are also considered in particular one shows that the poincare inequality is equivalent to a certain form of dimension free exponential concentration the proofs of these results rely on simple large deviations techniques

robust inference in the negative binomial regression model with an application to falls data summary a popular way to model overdispersed count data such as the number of falls reported during intervention studies is by means of the negative binomial nb distribution classical estimating methods are well known to be sensitive to model misspecifications taking the form of patients falling much more than expected in such intervention studies where the nb regression model is used we extend in this article two approaches for building robust m estimators of the regression parameters in the class of generalized linear models to the nb distribution the first approach achieves robustness in the response by applying a bounded function on the pearson residuals arising in the maximum likelihood estimating equations while the second approach achieves robustness by bounding the unscaled deviance components for both approaches we explore different choices for the bounding functions through a unified notation we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately and provide the asymptotic distributions of the resulting estimators moreover we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter specific to the nb distribution simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model and this for both approaches we present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference

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

integral closure and bounds for quotients of multiplicities of monomial ideals abstract given a pair of monomial ideals i and j of finite colength of the ring of analytic function germs c n 0 c we prove that some power of i admits a reduction formed by homogeneous polynomials with respect to the newton filtration induced by j if and only if the quotient of multiplicities e i e j attains a suitable upper bound expressed in terms of the newton polyhedra of i and j we also explore other connections between mixed multiplicities newton filtrations and the integral closure of ideals

a new characterization of talagrand s transport entropy inequalities and applications we show that talagrand s transport inequality is equivalent to a restricted logarithmic sobolev inequality this result clarifies the links between these two important functional inequalities as an application we give the first proof of the fact that talagrand s inequality is stable under bounded perturbations

extended moment series and the parameters of the negative binomial distribution recent studies indicate that for finite sample sizes moment estimators may be superior to maximum likelihood estimators in some regions of parameter space in this paper a statistic based on the central moment of the sample is expanded in a taylor series using 24 derivatives and many more terms than previous expansions a summary algorithm is required to find meaningful approximants using the higher order coefficients a example is presented and a comparison between theoretical assessment and simulation results is made

the sequence of mixed łojasiewicz exponents associated to pairs of monomial ideals abstract we analyze the sequence l j i of mixed ojasiewicz exponents attached to any pair i j of monomial ideals of finite colength of the ring of analytic function germs c n 0 c in particular we obtain a combinatorial expression for this sequence when j is diagonal we also show several relations of l j i with other numerical invariants associated to i and j

kantorovich duality for general transport costs and applications we introduce a general notion of transport cost that encompasses many costs used in the literature including the classical one and weak transport costs introduced by talagrand and marton in the 90 s and prove a kantorovich type duality theorem as a by product we obtain various applications in different directions we give a short proof of a result by strassen on the existence of a martingale with given marginals we characterize the associated transport entropy inequalities together with the log sobolev inequality restricted to convex concave functions some explicit examples of discrete measures satisfying weak transport entropy inequalities are also given

interval estimation of the over dispersion parameter in the analysis of one way layout of count data the over dispersion parameter is an important and versatile measure in the analysis of one way layout of count data in biological studies for example it is commonly used as an inverse measure of aggregation in biological count data its estimation from finite data sets is a recognized challenge many simulation studies have examined the bias and efficiency of different estimators of the over dispersion parameter for finite data sets see for example clark and perry biometrics 1989 45 309 316 and piegorsch biometrics 1990 46 863 867 but little attention has been paid to the accuracy of the confidence intervals cis of it in this paper we first derive asymptotic procedures for the construction of confidence limits for the over dispersion parameter using four estimators that are specified by only the first two moments of the counts we also obtain closed form asymptotic variance formulae for these four estimators in addition we consider the asymptotic ci based on the maximum likelihood ml estimator using the negative binomial model it appears from the simulation results that the asymptotic cis based on these five estimators have coverage below the nominal coverage probability to remedy this we also study the properties of the asymptotic cis based on the restricted estimates of ml extended quasi likelihood and double extended quasi likelihood by eliminating the nuisance parameter effect using their adjusted profile likelihood and quasi likelihoods it is shown that these cis outperform the competitors by providing coverage levels close to nominal over a wide range of parameter combinations two examples to biological count data are presented copyright 2010 john wiley sons ltd

concentration for multidimensional diffusions and their boundary local times we prove that probability laws of certain multidimensional semimartingales which includes time inhomogenous diffusions under suitable assumptions satisfy quadratic transportation cost inequality under the uniform metric from this we derive concentration properties of lipschitz functions of process paths that depend on the entire history in particular we estimate concentration of boundary local time of reflected brownian motions on a polyhedral domain we work out explicit applications of consequences of measure concentration for the case of brownian motion with rank based drifts

bias corrected maximum likelihood estimator of the negative binomial dispersion parameter nous decrivons un estimateur du maximum de vraisemblance avec correction du premier ordre pour le biais sur le parametre de dispersion d une distribution binomiale negative cet estimateur est compare en terme debiais et d efficacite avec l estimateur du maximum de vraisemblance etudie par piegorsch 1990 biometrics 46 863 867 les estimateurs de moment et du maximum de quasi vraisemblance etendue de clark et perry 1989 biometrics 45 309 316 et un estimateur de double quasi vraisemblance etendue l estimateur du maximum de vraisemblance avec correction du biais a des proprietes de biais et d efficacite superieures dans la plupart des cas pour faciliter la comparaison nous donnons les resultats pour le modele binomial negatif a deux parametres cependant un exemple impliquant la regression binomiale negative est donne

gradient flows on wasserstein spaces over compact alexandrov spaces we establish the existence of euclidean tangent cones on wasserstein spaces over compact alexandrov spaces of curvature bounded below by using this riemannian structure we formulate and construct gradient flows of functions on such spaces if the underlying space is a riemannian manifold of nonnegative sectional curvature then our gradient flow of the free energy produces a solution of the linear fokker planck equation

estimating intraclass correlation for binary data summary this paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study some of the estimators are very specific while others result from general methods such as pseudo likelihood and extended quasi likelihood estimation the simulation study identifies several useful estimators one of which does not seem to have been considered previously for binary data estimators based on extended quasi likelihood are found to have a substantial bias in some circumstances

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

families of distributions for repeated samples of animal counts the criterion of flexibility perry and taylor 1985 journal of animal ecology 54 931 953 that families of distributions with n 2 parameters should fit adequately to all n samples of animal counts over the full range of population densities usually encountered was misinterpreted by kemp 1987 biometrics 43 693 699 this criterion of goodness of fit is examined here for perry and taylor s ades family and one of kemp s alternatives a family of constrained negative binomial c n b distributions using extensive literature data while the ades fitted better than the c n b in 15 of 22 sets the evidence is not overwhelming because in 13 sets the difference was negligible or both families fitted adequately however of the remainder the ades fitted notably better to seven sets these mainly comprised long tailed distributions with large means typical of pest species its use in practical applications with such data is discussed and the importance of its superior reliability stressed kemp s method of fitting is not recommended

characterization of talagrand s like transportation cost inequalities on the real line abstract in this paper we give necessary and sufficient conditions for talagrand s like transportation cost inequalities on the real line this brings a new wide class of examples of probability measures enjoying a dimension free concentration of measure property another byproduct is the characterization of modified log sobolev inequalities for log concave probability measures on r

estimation of the shape parameter k of the negative binomial distribution using approximate bayesian methods an estimator of the shape parameter of the negative binomial distribution is introduced most of the available estimators of this parameter such as the method of moment and the maximum likelihood estimators mme and mle give inadmissible values when the mean of the observed sample is larger than its variance in this case the mme gives values while the mle is infinite such observed sample in not unlikely when the mean of the population is close to its variance the suggested estimator always has valid values and turned out to be more efficient for most values of the parameter space family size data is used for illustration of the procedure

a simple proof of the blowing up lemma corresp the blowing up lemma says that if the probability with respect to a product measure of a set a subseteq cal x n cal x finite n large is not exponentially small then its l n neighborhood has probability almost one for some l n o n here an information theoretic proof of the blowing up lemma generalizing it to continuous alphabets is given

poincare s inequalities and talagrand s concentration phenomenon for the exponential distribution we present a simple proof based on modified logarithmic sobolev inequalities of talagrand s concentration inequality for the exponential distribution we actually observe that every measure satisfying a poincare inequality shares the same concentration phenomenon we also discuss exponential integrability under poincare inequalities and its consequence to sharp diameter upper bounds on spectral gaps

properties of isoperimetric functional and transport entropy inequalities via concentration various properties of isoperimetric functional transport entropy and concentration inequalities are studied on a riemannian manifold equipped with a measure whose generalized ricci curvature is bounded from below first stability of these inequalities with respect to perturbation of the measure is obtained the extent of the perturbation is measured using several different distances between perturbed and original measure such as a one sided l bound on the ratio between their densities wasserstein distances and kullback leibler divergence in particular an extension of the holley stroock perturbation lemma for the log sobolev inequality is obtained and the dependence on the perturbation parameter is improved from linear to logarithmic second the equivalence of transport entropy inequalities with different cost functions is verified by obtaining a reverse jensen type inequality the main tool used is a previous precise result on the equivalence between concentration and isoperimetric inequalities in the described setting of independent interest is a new dimension independent characterization of transport entropy inequalities with respect to the 1 wasserstein distance which does not assume any curvature lower bound

families of discrete distributions satisfying taylor s power law count data in entomological studies can often be described by some form of contagious distribution such as the negative binomial neyman type a or polya aeppli these are all clustered poisson distributions their distributional forms are given in section 2 arising when groups of individuals occur at random i e are poissonian and individuals within a group have their own distribution whilst pahl 1969 found strong evidence that the negative binomial distribution gives good fits to his 35 samples of data on the chrysomelid beetle paropsis atomaria martin and katti 1965 fitted a number of distributions to a variety of insect plant and animal data and observed for instance that mcguire brindley and bancroft s 1957 data on the european cornborer pyrausta nubilalis and beall s 1940 data on the beet webworm loxostege sticticalis are fitted well not only by the negative binomial but also by the neyman type a and other distributions in such circumstances the fits given by different distributions are often very similar and the exact choice is not critical see kemp and kemp 1965 the recent work of tripathi gurland and bhalerao 1986 gives further guidance on the choice of an appropriate distribution when this is not clearly indicated by the ecological context the negative binomial neyman type a and polya aeppli distributions all have two parameters when there are many samples of data in one data set anscombe 1949 and bliss and owen 1958 suggested fitting a model that is parsimonious in parameters by keeping one of them constant from sample to sample their use of a common exponent parameter k when fitting families of negative binomials was criticised by taylor woiwod and perry 1979 who considered that k is an unstable parameter whose relationship with aggregation is doubtful much empirical evidence has accumulated in support of taylor s power law

a new index of aggregation for animal counts a new index is described that is especially appropriate for measuring the aggregation of entomological data in the form of counts per sample unit and that can make use of spatial information when it is available calculation of the index is based on a comparison of the effort required of individuals in a sample to achieve complete crowding with that to achieve complete randomness the power of tests of randomness based on this index is found to be greater than those based on the index of dispersion especially when spatial information is available

multistage estimation compared with fixed sample size estimation of the negative binomial parameter k the negative binomial distribution often fits biological data well since the mean is of primary interest the parameterization in terms of the mean and a parameter k has become almost standard given a precise estimate of k sequential methods of estimating the mean are available however precise estimation of k has been elusive in this paper estimators of k by the method of moments and by maximum likelihood estimation based on samples of size 50 and 100 are investigated by using monte carlo methods although the maximum likelihood estimators tend to have smaller mean square errors than the method of moments estimators neither can be considered good a multistage approach to the estimation of k is presented and monte carlo results indicate that this procedure gives a mean square error less than that of comparable fixed sample size estimators two truncation rules for the multistage procedure are also given and compared

fitting the negative binomial distribution this note is a reaction to recent papers in this journal by willson folks and young 1984 and bowman 1984 for the biometrical analysis of certain kinds of observations such as insect counts accident counts or cave entrance counts when only nonnegative integers are observable it is expedient to restrict attention to those random variables which are restricted to the lattice of nonnegative integers cf noack 1950 with an admitted loss of generality one may substantially simplify the procedure by a further restriction using as a frame of reference the family of binomial frequency functions hoel 1947 within this frame of reference the use of the modem restatement of the time honored occam s razor principle wrinch and jeffreys 1921 quoted by popper 1959 p 171 leads rather straightforwardly to a null hypothesis which may be discussed expediently in terms of the number n of distinct but not necessarily all unequal observations rj of r j 1 n writing

modified logarithmic sobolev inequalities and transportation inequalities we present a class of modified logarithmic sobolev inequality interpolating between poincare and logarithmic sobolev inequalities suitable for measures of the type exp x or exp x log 2 x 1 2 and which lead to new concentration inequalities these modified inequalities share common properties with usual logarithmic sobolev inequalities as tensorisation or perturbation and imply as well poincare inequality we also study the link between these new modified logarithmic sobolev inequalities and transportation inequalities

a new characterization of quadratic transportation information inequalities it is known that a quadratic transportation information inequality mathrm w 2 mathrm i interpolates between the talagrand s inequality mathrm w 2 mathrm h and the log sobolev inequality lsi for short the aim of this paper is threefold 1 to prove the equivalence of mathrm w 2 mathrm i and the lyapunov condition which gives a new characterization inspired by cattiaux et al probab theory relat fields 148 1 2 285 304 2010 2 to prove the stability of mathrm w 2 mathrm i under bounded perturbations which gives a transference principle in the sense of holley stroock 3 to prove mathrm w 2 mathrm h through a restricted mathrm w 2 mathrm i which gives a counterpart of the restricted lsi presented by gozlan et al ann probab 39 3 857 880 2011