on the asymptotic behavior for a certain nonlinear evolution equation let x be a real banach space we shall say that an operator a with domain d a and range r a in x is accretive if lx x2 11 0 and yi e axi i 1 2 and that a satisfies the range condition if r z i 1 d a the closure of d a for all a 0 where 1 denotes the identity let g 0 co 0 co be a nonincreasing continuous function such that lim r13 g t 0 let x e x and consider the following initial value problem

generalizing weak instrument robust iv statistics towards multiple parameters unrestricted covariance matrices and identification statistics abstract we generalize the weak instrument robust score or lagrange multiplier and likelihood ratio instrumental variables iv statistics towards multiple parameters and a general covariance matrix so they can be used in the generalized method of moments gmm the gmm extension of moreira s 2003 a conditional likelihood ratio test for structural models econometrica 71 1027 1048 conditional likelihood ratio statistic towards gmm preserves its expression except that it becomes conditional on a statistic that tests the rank of a matrix we analyze the spurious power decline of kleibergen s 2002 pivotal statistics for testing structural parameters in instrumental variables regression econometrica 70 1781 1803 2005 testing parameters in gmm without assuming that they are identified econometrica 73 1103 1124 score statistic and show that an independent misspecification pre test overcomes it we construct identification statistics that reflect if the confidence sets of the parameters are bounded a power study and the possible shapes of confidence sets illustrate the analysis

a regression model for multivariate random length data multivariate random length data occur when we observe multiple measurements of a quantitative variable and the variable number of these measurements is also an observed outcome for each experimental unit for example for a patient with coronary artery disease we may observe a number of lesions in that patient s coronary arteries along with percentage of blockage of each lesion barnhart and sampson first proposed the multiple population model to analyse multivariate random length data without covariates this paper extends their approach to deal with multiple covariates we propose a new multiple population regression model with covariates and discuss the estimation issues we analyse data from the type ii coronary intervention study to illustrate the methodology

the importance of assessing measurement reliability in multivariate regression abstract in many contexts involving multivariate linear regression models some or all of the independent predictor variables are measured with error it is argued that if the goal is to assess the relationship of the dependent variables to the true predictor variables then it is important to determine the reliability matrix of the measurement x of the vector of true predictors if is singular then the slope matrix b is not identifiable if is nearly singular then b cannot be accurately estimated a two step estimation procedure is proposed in which is estimated from data on the measured predictors x and on prior information from reliability studies on these predictors and the parameters of the latent linear relationship are estimated by classical linear regression methods this approach not only allows the use of available software but also lends itself to traditional diagnostic methods large sample properties of the estimators resulting from this approach are derived it is shown how a c

unbounded behavior and convergence of solutions of nonlinear volterra equations in banach spaces soit x un espace de banach reel de norme et a un operateur m accretif dans x on etudie le comportement asymptotique des solutions de l equation de volterra non lineaire g t u t b au t t r 0 ou b r r g r x sont donnees et est la convolution

the average distances in random graphs with given expected degrees abstract random graph theory is used to examine the small world phenomenon any two strangers are connected through a short chain of mutual acquaintances we will show that for certain families of random graphs with given expected degrees the average distance is almost surely of order log n log d where d is the weighted average of the sum of squares of the expected degrees of particular interest are power law random graphs in which the number of vertices of degree k is proportional to 1 k for some fixed exponent for the case of 3 we prove that the average distance of the power law graphs is almost surely of order log n log d however many internet social and citation networks are power law graphs with exponents in the range 2 3 for which the power law random graphs have average distance almost surely of order log log n but have diameter of order log n provided having some mild constraints for the average distance and maximum degree in particular these graphs contain a dense subgraph which we call the core having nc log log n vertices almost all vertices are within distance log log n of the core although there are vertices at distance log n from the core

inferential methods for elasticity estimates abstract elasticities are often estimated from the results of demand analysis however drawing inferences from them may involve assumptions that could influence the outcome in this paper we investigate one of the most common forms of elasticity which is defined as a ratio of estimated relationships and demonstrate how the fieller method for the construction of confidence intervals can be used to draw inferences we estimate the elasticities of expenditure from engel curves using a variety of estimation models parametric engel curves are modelled using ols mm robust regression and tobit semiparametric engel curves are estimated using a penalized spline regression we demonstrate the construction of confidence intervals of the expenditure elasticities for a series of expenditure levels as well as the estimated cumulative density function for the elasticity evaluated for a particular household

estimation and inference with weak semi strong and strong identification this paper analyzes the properties of standard estimators tests and confidence sets cs s for parameters that are unidentified or weakly identified in some parts of the parameter space the paper also introduces methods to make the tests and cs s robust to such identification problems the results apply to a class of extremum estimators and corresponding tests and cs s that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification this covers a class of models estimated using maximum likelihood ml least squares ls quantile generalized method of moments generalized empirical likelihood minimum distance and semi parametric estimators the consistency lack of consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions the asymptotic sizes in a uniform sense of standard and identification robust tests and cs s are established the results are applied to the arma 1 1 time series model estimated by ml and to the nonlinear regression model estimated by ls in companion papers the results are applied to a number of other models

contact processes on random graphs with power law degree distributions have critical value 0 if we consider the contact process with infection rate on a random graph on n vertices with power law degree distributions mean field calculations suggest that the critical value c of the infection rate is positive if the power 3 physicists seem to regard this as an established fact since the result has recently been generalized to bipartite graphs by gomez gardenes et al proc natl acad sci usa 105 2008 1399 1404 here we show that the critical value c is zero for any value of 3 and the contact process starting from all vertices infected with a probability tending to 1 as n maintains a positive density of infected sites for time at least exp n 1 for any 0 using the last result together with the contact process duality we can establish the existence of a quasi stationary distribution in which a randomly chosen vertex is occupied with probability it is expected that c as 0 here we show that 1 2 3 and so 2 for 3 thus even though the graph is locally tree like does not take the mean field critical value 1

confidence regions in linear functional relationships a unified approach to deriving confidence regions in linear functional relationship models is presented based on the conditional likelihood ratio method of knowles siegmund and zhang in the case of a single latent predictor the confidence region for the slope produced by this approach is the familiar one of fieller and creasy however here it is shown how to derive a confidence region for the slope when it is known that the slope is positive that improves on merely intersecting the region for an unrestricted slope with 0 oo a geometric interpretation is given for fieller creasy confidence region for the ratio of population means fieller creasy problem regions are also derived for simultaneous estimation of the slope and intercept in the model with a single latent predictor and for the slopes in a model with two latent predictors

asymptotic behavior of solutions to nonlinear volterra integral equations in section 2 we establish the existence of solutions to 1 1 and to related equations theorems 2 1 and 2 3 in contrast with previous papers e g 7 we do not assume that a is m accretive instead we require a to satisfy a weaker cone condition certain other facts are also included in this section throughout this paper we also assume that b is completely positive 6 in the third section we present two mean ergodic theorems for the solutions of 1 1 in hilbert space the first theorem theorem 3 1 deals with weak almost convergence and the second theorem 3 4 with strong almost convergence these results improve upon those of 1 and include the known results for nonlinear semigroups 191 it is important to establish almost convergence because it then follows that the solution is summed by every strongly regular kernel corollaries 3 3 and 3 5 a weak convergence criterion corollary 3 2 is also obtained if the banach space x is reflexive and strictly convex and 0 e r a then

efficient estimation in the errors in variables model we consider efficient estimation of the slope in the errors in variables model with normal error when either the ratio of error variances is known and the distribution of the independent is arbitrary and unknown or the distribution of the independent variable is not gaussian or degenerate we calculate information bounds and exhibit estimates achieving these bounds using an initial minimum distance estimate and suitable estimates of the efficient score function

admissible pairs and integral equations abstract the aim of this paper is to show how a general convergence principle of bruck and reich can be applied to the study of the asymptotic behavior of solutions to nonlinear volterra integral equations

asymptotic behavior of solutions of nonlinear volterra equations and mean points abstract in this paper we study the asymptotic behavior of solutions to a nonlinear volterra equation in banach spaces first we deal with the mean point concerning an invariant mean on 0 for the unbounded behavior of solutions in a reflexive banach space using the mean point we obtain the weak and strong convergences for the unbounded behavior of solutions in a reflexive and strictly convex banach space and in the dual space which has a frechet differentiable norm respectively

the limiting distribution of least squares in an errors in variables regression model abstract there is a substantial literature concerning linear regression when some of the predictors independent variables are measured with error such models are of importance in econometrics instrumental variables models psychometrics correction for attenuation models of change and in instrumental calibration studies in medicine and industry recent theoretical work concerning maximum likelihood estimation in such models appears in healy 1980 fuller 1980 and anderson 1984 while reilly and patino leal 1981 take a bayesian approach in an applied context an investigator may either overlook the measurement errors in the predictors or choose the classical ordinary least squares ols estimator of the parameters because of its familiarity and ease of use certainly the methodology of classical least squares theory confidence intervals multiple comparisons tests of hypotheses residual analysis is considerably more developed than the corresponding errors in variables methodology particularly in samples of moderate size in this paper it is shown that under reasonable regularity conditions such linear combinations are jointly asymptotically normally distributed

epidemic dynamics in finite size scale free networks many real networks present a bounded scale free behavior with a connectivity cutoff due to physical constraints or a finite network size we study epidemic dynamics in bounded scale free networks with soft and hard connectivity cutoffs the finite size effects introduced by the cutoff induce an epidemic threshold that approaches zero at increasing sizes the induced epidemic threshold is very small even at a relatively small cutoff showing that the neglection of connectivity fluctuations in bounded scale free networks leads to a strong overestimation of the epidemic threshold we provide the expression for the infection prevalence and discuss its finite size corrections the present paper shows that the highly heterogeneous nature of scale free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes

asymptotic behavior of solutions of a nonlinear evolution equation the purpose of this paper is to study the asymptotic behavior of the solutions of a certain nonlinear evolution equation in banach spaces see 1 below this time dependent initial value problem involves an accretive operator a and a function g r f r it was first considered by browder in 11 and was the basis of the iterative procedures for constructing zeros of accretive operators presented in 2 and 5 these papers treat only the case when 0 e r a we begin with several results e g theorems 3 and 6 that are of interest when 0 r a these results are in some sense analogs of known results for nonlinear semigroups and resolvents there is however a difference see for example corollary 4 then we show that under certain mild restrictions 0 e r a if and only if the solutions to 1 are bounded theorem 7 when an additional condition is imposed on g we can shown that a is zero free if and only if lim u t co for each solution of 1 theorem 8 and proposition 9 in the last part of the paper we assume that 0 e r a and obtain several strong convergence results for solutions of 1 e g theorem 12 these results show that the asymptotic behavior of the solutions to 1 resembles the behavior of resolvents more than that of nonlinear semigroups theorem 12 yields improvements of the convergence results for the iterative procedure of s and leads to a geometric result concerning the fixed point set of a nonexpansive mapping corollary 13 we also mention that the sequence constructed from the iterative procedure of 5 imitates the behavior of the solutions of 1 not only when 0 e r a but also when a is zero free finally we remark that many of our results are new even in hilbert space let e be a real banach space and let i denote the identity operator recall that a subset a of e x e with domain d a and range r a is said to be accretive if lx x2 0 we denote the closure of a subset d of e by cl d its closed convex hull by clco d and its distance from a point x in e by d x 0 we 43 0022 247x 81 090043 11 02 00 0

on the asymptotic behavior of nonlinear semigroups and the range of accretive operators ii abstract it is known that certain problems in partial differential equations may be interpreted as initial value problems for ordinary differential equations in banach spaces when such an evolution equation is governed by an accretive operator then its solutions give rise to a nonlinear contraction semigroup in this paper we study certain aspects of the asymptotic behavior of nonlinear semigroups and or resolvents of accretive operators we also derive new results on their behavior at the origin it turns out that the behavior of a nonlinear semigroup resembles that of the resolvent of its generator both at infinity and at the origin author

ising models on power law random graphs we study a ferromagnetic ising model on random graphs with a power law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite degree exponent 2 for which the random graph has a tree like structure for this we closely follow the analysis by dembo and montanari ann appl probab 20 2 565 592 2010 which assumes finite variance degrees 3 adapting it when necessary and also simplifying it when possible our results also apply in cases where the degree distribution does not obey a power law

confidence intervals associated with tests for bioequivalence summary previously the connection between bioequivalence tests and their associated confidence intervals was not well understood in fact the oc level two one sided tests approach was thought to be associated with a 1 20c confidence interval in this paper we build up connections which allow us to construct 1 oc confidence intervals from cx level tests and vice versa when applied to the cc level two one sided tests the resultant 1 oc confidence intervals are properly contained in westlake s 1 oc symmetric interval 1976 our approach is readily generalized to different settings including the nonparametric setting the ratio parameter setting and the repeated confidence interval setting

asymptotic behavior of solutions to a class of nonlinear evolution equations on etudie les equations de la chaleur a controle de temperature a l interieur ou sur la frontiere du domaine pour cela on considere un type de problemes variationnels paraboliques avec obstacles

the nonexistence of 100 1 alpha confidence sets of finite expected diameter in errors in variables and related models on montre que pour certains modeles il est impossible de construire des intervalles de confiance pour les parametres cles qui aient a la fois une confiance positive et une longueur esperee finie

the contact process on trees the contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter is varied for small values of a single infection eventually dies out for larger the infection lives forever with positive probability but eventually leaves any finite set the survival probability is a continuous function of and the proof of this is much easier than it is for the contact process on d dimensional integer lattices for still larger the infection converges in distribution to a nontrivial invariant measure for an n ary tree with n large the first of these transitions occurs when 1 n and the second occurs when 1 2 n e n nonhomogeneous trees whose vertices have degrees varying between 1 and n behave essentially as homogeneous n ary trees provided that vertices of degree n are not too rare in particular letting n go to galton watson trees whose vertices have degree n with probability that does not decrease exponentially with n may have both phase transitions occur together at 0 the nature of the second phase transition is not yet clear and several problems are mentioned in this regard

asymptotic behavior of solutions of nonlinear volterra equations 0 recently baillon and clement 3 established mean ergodic theorems for solutions of nonlinear volterra equations in hilbert space in the present paper we study the asymptotic behavior of solutions of 1 1 by using nonlinear ergodic theorems the first mean ergodic theorem was given by baillon l and it was improved by several authors 3 8 141 163

almost convergence of solutions of nonlinear volterra equations in banach space a l aide d un theoreme ergodique on etudie le comportement asymptotique des solutions des problemes aux valeurs initiales dans des espaces de banach on applique le resultat obtenu a l etude du comportement asymptotique des solutions des equations de volterra non lineaires dans des espaces de banach

high prevalence regimes in the pair quenched mean field theory for the susceptible infected susceptible model on networks reckoning of pairwise dynamical correlations significantly improves the accuracy of mean field theories and plays an important role in the investigation of dynamical processes in complex networks in this work we perform a nonperturbative numerical analysis of the quenched mean field theory qmf and the inclusion of dynamical correlations by means of the pair quenched mean field pqmf theory for the susceptible infected susceptible model on synthetic and real networks we show that the pqmf considerably outperforms the standard qmf theory on synthetic networks of distinct levels of heterogeneity and degree correlations providing extremely accurate predictions when the system is not too close to the epidemic threshold while the qmf theory deviates substantially from simulations for networks with a degree exponent 2 5 the scenario for real networks is more complicated still with pqmf significantly outperforming the qmf theory however despite its high accuracy for most investigated networks in a few cases pqmf deviations from simulations are not negligible we found correlations between accuracy and average shortest path while other basic network metrics seem to be uncorrelated with the theory accuracy our results show the viability of the pqmf theory to investigate the high prevalence regimes of recurrent state epidemic processes in networks a regime of high applicability

small sample ld50 confidence intervals using saddlepoint approximations confidence intervals for the median lethal dose ld50 and other dose percentiles in logistic regression models are developed using a generalization of the fieller theorem for exponential families and saddlepoint approximations simulation results show that in terms of one tailed and two tailed coverage the proposed methodology generally outperforms competing confidence intervals obtained from the classical fieller likelihood ratio and score methods in terms of two tailed coverage the proposed method is comparable to the bartlett corrected likelihood ratio method but generally outperforms it in terms of one tailed coverage an extension to the competing risk setting is presented that allows binary response adjustments to be made using observed censoring times supplementary materials for this article are available online at http pubs amstat org

on the asymptotic behavior of solutions of nonlinear volterra equations where a is an m accretive operator in x b is a given real kernel and g is a given x valued function in what follows we make the same assumptions on b and g as in 2 5 71 hl beac r r b o o b ebv r r h2 ge w r y g el r x g o ed a h3 b is completely positive on r and b m 0 we may assume without loss of generality that b 0 1 sine b t and a may be replaced by b t b o and b o a respectively note that if h 1 holds the first statement in h3 is equivalent to the fact that there exists a k e l r r nonnegative and nonincreasing satisfying b t k b t 1 for t e r moreover in this case lim o b t b cc exists and b m 0 if and only if kel r r see 2 5 71 now define g u for u e c r x or c 0 t x t 0 as follows

robust multivariate regression we introduce a robust method for multivariate regression based on robust estimation of the joint location and scatter matrix of the explanatory and response variables as a robust estimator of location and scatter we use the minimum covariance determinant mcd estimator of rousseeuw based on simulations we investigate the finite sample performance and robustness of the estimator to increase the efficiency we propose a reweighted estimator selected from several possible reweighting schemes the resulting multivariate regression does not need much computation time and is applied to real datasets we show that the multivariate regression estimator has the appropriate equivariance properties has a bounded influence function and inherits the breakdown value of the mcd estimator these theoretical robustness properties confirm the good finite sample results obtained from the simulations

assessing individual bioequivalence using the structural equation model the structural equation model sem is introduced as a useful approach for assessing individual bioequivalence sem parameters are estimated using a partial likelihood analysis and the hypotheses of individual bioequivalence is evaluated in a disaggregate way testing separately the hypothesis concerning sem parameters and assessing the overall hypothesis of individual bioequivalence using the intersection union principle limits of bioequivalence for sem parameters are proposed and a power analysis is carried out

robust confidence sets in the presence of weak instruments abstract this paper considers instrumental variable regression with a single endogenous variable and the potential presence of weak instruments i construct confidence sets for the coefficient on the single endogenous regressor by inverting tests robust to weak instruments i suggest a numerically simple algorithm for finding the conditional likelihood ratio clr confidence sets full descriptions of possible forms of the clr anderson rubin ar and lagrange multiplier lm confidence sets are given i show that the clr confidence sets have nearly the shortest expected arc length among similar symmetric invariant confidence sets in a circular model i also prove that the clr confidence set is asymptotically valid in a model with non normal errors

measurement error and ancova functional and structural relationship approaches this article discusses alternative procedures to the standardf test for ancova in case the covariate is measured with error both a functional and a structural relationship approach are described examples of both types of analysis are given for the simple two group design several cases are discussed and special attention is given to issues of model identifiability an approximate statistical test based on the functional relationship approach is described on the basis of monte carlo simulation results it is concluded that this testing procedure is to be preferred to the conventionalf test of the ancova null hypothesis it is shown how the standard null hypothesis may be tested in a structural relationship approach it is concluded that some knowledge of the reliability of the covariate is necessary in order to obtain meaningful results

critical value for the contact process with random recovery rates and edge weights on regular tree abstract in this paper we are concerned with contact processes with random recovery rates and edge weights on rooted regular trees t n let and be two nonnegative random variables such that p m 1 for some m 0 for each vertex x on t n x is an independent copy of while for each edge e on t n e is an independent copy of an infected vertex x becomes healthy at rate x while an infected vertex y infects an healthy neighbor z at rate proportional to y z for this model we prove that the critical value under the annealed measure approximately equals n e e 1 1 as n grows to infinity furthermore we show that the critical value under the quenched measure equals that under the annealed measure when the cluster containing the root formed with edges with positive weights is infinite

robustness and fragility of the susceptible infected susceptible epidemic models on complex networks we analyze two alterations of the standard susceptible infected susceptible sis dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree all models have the same epidemic thresholds in mean field theories but depending on the network properties simulations yield a dual scenario in which the epidemic thresholds of the modified sis models can be either dramatically altered or remain unchanged in comparison with the standard dynamics for uncorrelated synthetic networks having a power law degree distribution with exponent 5 2 differences are more remarkable for 3 where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one this duality is elucidated in terms of epidemic lifespan on star graphs we verify that the activation of the modified sis models is triggered in the innermost component of the network given by a k core decomposition for 3 the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard sis the duality also appears in the finite size scaling of the critical quantities where mean field behaviors are observed for the modified but not for the original dynamics our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models

nature of the epidemic threshold for the susceptible infected susceptible dynamics in networks we develop an analytical approach to the susceptible infected susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks we find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold in particular small world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit

on the asymptotic behaviour of solutions of volterra equations in hilbert space u 0 x 1 1 where a is a nonlinear maximal monotone possibly multi valued operator on a real hilbert space h f z 0 4 h x e d a and g is a given mapping g c o d a o t h vo t 0 1 2 by a recent result of crandall nohel 5 theorem 11 the problem 1 1 has a unique generalized solution u e c o 0 h p rovided that g satisfies a lipschitz type condition the present note is concerned with the asymptotic behaviour as t m of generalized solutions of 1 1 at the expense of appropriate assumptions on g see 2 3 2 4 below we are able to derive natural analogs of results by several authors concerning the asymptotic properties of nonlinear contraction semigroups in hilbert space the plan of the paper is as follows the results are presented in section 2 and the proofs are given in section 3 although we deal with solutions of l l we have always in mind the related nonlinear volterra equation

errors in variables estimation in multivariate calibration a set of q responses y y 1 y 2 y q t is related to a set of p explanatory variables x x 1 x 2 x p t through the classical linear regression model y t a t x t b e t first the unknown parameters a and b are estimated using a calibrafion set the statistical problem that is considered here is that of estimating the vector x o that underlies a new observed vector of responses y o using the parameter estimates obtained from the first procedure these two procedures are commonly referred to as calibration and prediction or inverse prediction and sometimes jointly referred to as calibration the prediction procedure can be viewed as parameter estimation in errors in variables regression the maximum likelihood estimator assuming normally distributed measurement errors is proposed for the prediction procedure unlike the classical estimator used in the prediction procedure the proposed estimator is consistent with respect to the number of response variables the performan

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

variable selection for partially linear models with measurement errors this article focuses on variable selection for partially linear models when the covariates are measured with additive errors we propose two classes of variable selection procedures penalized least squares and penalized quantile regression using the nonconvex penalized principle the first procedure corrects the bias in the loss function caused by the measurement error by applying the so called correction for attenuation approach whereas the second procedure corrects the bias by using orthogonal regression the sampling properties for the two procedures are investigated the rate of convergence and the asymptotic normality of the resulting estimates are established we further demonstrate that with proper choices of the penalty functions and the regularization parameter the resulting estimates perform asymptotically as well as an oracle procedure as proposed by fan and li choice of smoothing parameters is also discussed finite sample performance of the proposed variable selection procedures is asse

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

a conditional likelihood ratio test for structural models this paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced form covariance matrix these tests are shown to be similar under weak instrument asymptotics when the reduced form covariance matrix is estimated and the errors are non normal the conditional test based on the likelihood ratio statistic is particularly simple and has good power properties like the score test it is optimal under the usual local to null asymptotics but it has better power when identification is weak

impossibility results for nondierentiable functionals we examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution this situation arises in a number of applications of bounds analysis and moment inequality models and in recent work on estimating optimal dynamic treatment regimes drawing on earlier work relating dierentiability to the existence of unbiased and regular estimators we show that if the target object is not continuously dierentiable in the parameters of the data distribution there exist no locally asymptotically unbiased estimators and no regular estimators this places strong limits on estimators bias correction methods and inference procedures

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

asymptotic behavior of the solutions of a class of functional differential equations remarks on a related volterra equation on etudie la convergence asymptotique forte quand t des solutions de u t au t g u t f t t 0 u 0 u 0 a est un operateur monotone maximal defini sur un sous ensemble d a contenu dans un espace de hilbert reel h u 0 d a f l 1 0 h et g est une application donnee

multiplicative errors in variables models with applications to recent data released by the u s department of energy abstract in an errors in variables model the predicting variables are observed with errors traditionally the errors are assumed to be additive in this article i consider the case in which the error is multiplicative a situation that arises when analyzing some recent data released by the u s department of energy a consistent estimator is provided for regression coefficients by correcting the asymptotic bias of the least squares estimate it is shown that after being normalized by an estimate of its covariance is asymptotically normally distributed this can therefore be used to construct approximate tests and confidence sets for the results are essentially nonparametric

on estimating linear relationships when both variables are subject to errors this paper discusses the problem of estimating a linear relationship between two variables observed with errors it focuses on confidence intervals for the slope parameter and confidence regions for the intercept and slope parameters in gaussian models a compendium of existing results as well as new results are presented

contact processes with random connection weights on regular graphs abstract in this paper we study the asymptotic critical value of contact processes with random connection weights sitting on a degree increasing sequence of r regular graph g r we propose a method to generalize the asymptotics results for c z d and c t d of classical contact processes as well as of recent work for contact processes on complete graphs with random connection weights only the lower bound is rigorously proved it is conjectured however that the lower bound gives the right asymptotic behavior for comparison purposes we also introduce binary contact path processes with random connection weights whose asymptotic behavior of the critical value is obtained

critical value for contact processes on clusters of oriented bond percolation in this paper we are concerned with contact processes on open clusters of oriented bond percolation in zd where the disease spreads along the direction of open edges we show that the two critical values in the quenched and annealed cases are equal with probability one and are asymptotically equal to dp 1 as the dimension d grows to infinity where p is the probability that the edge is open

phase transition of the susceptible infected susceptible dynamics on time varying configuration model networks we present a degree based theoretical framework to study the susceptible infected susceptible sis dynamics on time varying rewired configuration model networks using this framework on a given degree distribution we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the sis process this analysis is suitable for the characterization of the phase transition and leads to three main contributions 1 we obtain a self consistent expression for the absorbing state threshold able to capture both collective and hub activation 2 we recover the predictions of a number of existing approaches as limiting cases of our analysis providing thereby a unifying point of view for the sis dynamics on random networks 3 we obtain bounds for the critical exponents of a number of quantities in the stationary state this allows us to reinterpret the concept of hub dominated phase transition within our framework it appears as a heterogeneous critical phenomenon observables for different degree classes have a different scaling with the infection rate this phenomenon is followed by the successive activation of the degree classes beyond the epidemic threshold

the contact process on a finite set ii in this paper we complete the work started in part i we show that if sigma n is the time that the contact process on 1 ldots n first hits the empty set then for lambda lambda c the critical value for the process on z there is a positive constant gamma lambda so that log sigma n n rightarrow gamma lambda in probability as n rightarrow infty we also give a new simple proof that sigma n e sigma n converges to a mean one exponential the keys to the proof of the first result are a planar graph duality for the contact process and an observation of j chayes and l chayes that exponential decay rates for connections in strips approach the decay rates in the plane as the width of the strip goes to infty

the invariance of some score tests in the linear model with classical measurement error the linear model with classical measurement error is an alternative to the standard regression model in which it is assumed that the independent variables are subject to error this assumption can cause statistical inferences and parameter estimators to differ dramatically from those obtained by the standard regression model however in some cases inferences remain unchanged even though the independent variables are assumed to be subject to error this article investigates the invariance property of score tests for assessing heteroscedasticity first order autoregressive disturbance and the need for a box cox power transformation under specific constraints we show that the score tests for measurement error models are identical to the corresponding well established tests derived from standard regression models hence practitioners can assess assumptions of constant variance and independent errors as well as the need for a box cox transformation irrespective of whether or not the variables are measu

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

confidence intervals for partially identified parameters recently a growing body of research has studied inference in settings where parameters of interest are partially identified in many cases the parameter is real valued and the identification region is an interval whose lower and upper bounds may be estimated from sample data for this case confidence intervals cis have been proposed that cover the entire identification region with fixed probability here we introduce a conceptually different type of confidence interval rather than cover the entire identification region with fixed probability we propose cis that asymptotically cover the true value of the parameter with this probability however the exact coverage probabilities of the simplest version of our new cis do not converge to their nominal values uniformly across different values for the width of the identification region to avoid the problems associated with this we modify the proposed ci to ensure that its exact coverage probabilities do converge uniformly to their nominal values we motivate this modified ci through exact results for the gaussian case

some impossibility theorems in econometrics with applications to structural and dynamic models general characterizations of valid confidence sets and tests in problems which involve locally almost unidentified lau parameters are provided and applied to several econo metric models two types of inference problems are studied i inference about parame ters which are not identifiable on certain subsets of the parameter space and ii inference about parameter transformations with discontinuities when a lau parameter or parametric function has an unbounded range it is shown under general regularity conditions that any valid confidence set with level 1 a for this parameter must be unbounded with probability close to 1 a in the neighborhood of nonidentification subsets and will have a nonzero probability of being unbounded under any distribution compatible with the model no valid confidence set which is almost surely bounded does exist these properties hold even if identifying restrictions are imposed similar results also obtain for parameters with bounded ranges consequently a confidence set which does not satisfy this characterization has zero coverage probability level this will be the case in particular for wald type confidence intervals based on asymptotic standard errors furthermore wald type statistics for testing given values of a lau parameter cannot be pivotal functions i e they have distributions which depend on unknown nuisance param eters and even cannot be usefully bounded over the space of the nuisance parameters these results are applied to several econometric problems inference in simultaneous equations instrumental variables iv regressions linear regressions with autoregressive errors inference about long run multipliers and cointegrating vectors for example it is shown that standard asymptotically justified confidence intervals based on iv estimators such as two stage least squares and the associated standard errors have zero coverage probability and the corresponding t statistics have distributions which cannot be bounded by any finite set of distribution functions a result of interest for interpreting iv regressions with weak instruments furthermore expansion methods e g edgeworth expansions and bootstrap techniques cannot solve these difficulties finally in a number of cases where wald type methods are fundamentally flawed e g iv regressions with poor instruments it is observed that likelihood based methods e g likelihood ratio tests and confidence sets combined with projection techniques can easily yield valid tests and confidence sets

impact of the heterogeneity of adoption thresholds on behavior spreading in complex networks abstract individuals always exhibit distinct personal profiles ranging from education social experiences to risk tolerance which induces a vastly different response in the behavior spreading dynamics to describe this phenomenon a widely used method is to assign a distinct adoption threshold for each individual which so far has eluded theoretical analysis in this paper we propose a behavior spreading model to describe the heterogeneity of individuals in adopting the behavior in which the adoption threshold follows the gaussian distribution based on the edge based compartmental theory the theoretical solutions of the behavior spreading size and the threshold are given for discontinuous and continuous phase transitions through theoretical analysis and extensive numerical simulations the impact of the heterogeneity of adoption thresholds on behavior spreading is demonstrated and we find that the phase transition depends on the mean and standard deviation of the adoption thresholds for small values of the mean adoption threshold the system exhibits a continuous phase transition for large values of the mean adoption threshold the phase transition is discontinuous continuous for the small large standard deviation of the adoption thresholds there is a remarkable agreement between theoretical predictions and numerical simulations

measurement methods comparisions and linear statistical relationship the linear statistical relationship model can be used to compare two measurement procedures crude methods are now typically used in practice because the statistical concepts are often not understood by practitioners to clarify concepts we define three types of equivalency based on accuracy and precision of the measurement methods and show that the confidence interval for slope depends on sample size and information size these insights lead to obtaining bounded confidence intervals and equivalence tests the derived results provide the basis for designing and analyzing a comparison experiment an example from practice is used to illustrate the methodology

estimation of censored linear errors in variables models this paper deals with a linear errors in variables model where the dependent variable is censored a two step procedure is proposed to estimate the model and the corresponding asymptotic covariance matrices are derived the framework covers the usual error free tobit model as a special case it is shown that under normality and a certain identifying condition this model can be uniquely reduced to an error free censored regression model and hence the existing estimators for the tobit model can be used to obtain estimators for this model in particular the maximum likelihood estimator is derived in this way the small sample behavior of the two estimators and their sensitivities to misspecified identifying information are studied through monte carlo simulations

projection based statistical inference in linear structural models with possibly weak instruments it is well known that standard asymptotic theory is not applicable or is very unreliable in models with identification problems or weak instruments one possible way out consists of using a variant of the anderson rubin 1949 ar procedure the latter allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation but not for individual coefficients this problem may in principle be overcome by using projection methods dufour 1997 dufour and jasiak 2001 at first sight however this technique requires the application of costly numerical algorithms in this paper we give a general necessary and sufficient condition that allows one to check whether an ar type confidence set is bounded furthermore we provide an analytic solution to the problem of building projection based confidence sets from ar type confidence sets the latter involves the geometric properties of quadrics and can be viewed as an extension of usual confidence intervals and ellipsoids only least squares techniques are needed to build the confidence intervals

discrete stochastic modeling for epidemics in networks in this paper we construct a microscopic mechanism for the epidemic processes in heterogeneous populations which contains two basic assumptions all edges of the network are broken and reconnected at every time step among the epidemic process the probability of randomly chosen two half edges to make a pair is identical we define the stochastic epidemic process and get the epidemic distributions numerically according to the transmission probability two different phases are observed which means the onset of phase transition and the threshold value is very small under the thermodynamic limit the process can be approximated by a deterministic dynamical system about this deterministic system we get the analytical threshold value which is consistent with the numerical results of the epidemic distributions

tests with correct size when instruments can be arbitrarily weak abstract this paper applies classical exponential family statistical theory to develop a unifying framework for testing structural parameters in the simultaneous equations model under the assumption of normal errors with known reduced form variance matrix the results can be divided into the limited information and full information categories in the limited information model it is possible to characterize the entire class of similar tests in a model with only one endogenous explanatory variable in the full information framework this paper proposes a family of similar tests for subsets of endogenous variables coefficients for both limited and full information models there exist power upper bounds for unbiased tests when the model is just identified the anderson rubin score and pseudo conditional likelihood ratio tests are optimal when the model is over identified the pseudo conditional likelihood ratio test has power close to the power envelope when identification is strong

asymptotic properties of solutions of time dependent volterra integral equations abstract the asymptotic properties of the bounded solutions of a time dependent nonlinear volterra equation are studied in a hilbert space an application of physical interest is also given

sequential confidence regions in inverse regression problems for the inverse regression problem and more generally the set estimation of a ratio of regression parameters we construct a 1 confidence sequence applying such a confidence sequence we can construct a 1 sequential confidence interval with the length less than a prespecified quantity

on the asymptotic behavior of solutions of evolution equations associated with nonlinear volterra equations soit x un espace de banach reel on considere le probleme aux valeurs initiales f t du t dt au t g u t r 0 u 0 u 0 ou a est un operateur m accretif dans x f l loc 1 r x u 0 d a et g une application donnee