robust bounded influence tests in general parametric models abstract we introduce robust tests for testing hypotheses in a general parametric model these are robust versions of the wald scores and likelihood ratio tests and are based on general m estimators their asymptotic properties and influence functions are derived it is shown that the stability of the level is obtained by bounding the self standardized sensitivity of the corresponding m estimator furthermore optimally bounded influence tests are derived for the wald and scores type tests applications to real and simulated data sets are given to illustrate the tests performance

weak majorization inequalities and convex functions abstract let f be a convex function defined on an interval i 0 1 and a b n n complex hermitian matrices with spectrum in i we prove that the eigenvalues of f a 1 b are weakly majorized by the eigenvalues of f a 1 f b further if f is log convex we prove that the eigenvalues of f a 1 b are weakly majorized by the eigenvalues of f a f b 1 as applications we obtain generalizations of the famous golden thomson trace inequality a representation theorem and a harmonic geometric mean inequality some related inequalities are discussed

periodic solutions of the lienard equation with one sided growth restrictions in this article we are concerned with the problem of the existence of periodic solutions to the periodically forced scalar lienard equation x f x x g x e t d dt 1 where f g e r r are continuous functions and e is periodic we are looking for solutions of 1 having the same period of the forcing term e throughout the paper we assume without loss of generality see e g 22 36 p 693 that

contributions to coincidence degree theory of asymptotically homogeneous operators in this paper we give contributions to the coincidence degree theory of asymptotically homogeneous operators applications are given to the periodic problem for second order functional differential equations

robust gmm tests for structural breaks we propose a class of new robust generalized method of moments gmm tests for endogenous structural breaks the tests are based on supremum average and exponential functionals derived from robust gmm estimators with bounded influence function we study the theoretical local robustness properties of the new tests and show that they imply a uniformly bounded asymptotic sensitivity of size and power under general local deviations from a reference model we then analyze the finite sample performance of the new robust tests via monte carlo simulations and compare it with that of classical gmm tests for structural breaks in large samples we find that the performance of classical asymptotic gmm tests can be quite unstable under slight departures from some given reference distribution in particular the loss in power can be substantial in some models robust asymptotic tests for structural breaks yield important power improvements both in exactly identified and overidentified model settings in small samples bootstrapped versions of the classical and the robust gmm tests provide accurate and stable empirical levels also for quite small sample sizes however bootstrapped robust gmm tests are found to provide again a higher finite sample efficiency

periodic solutions of second order equations via rotation numbers abstract we consider the problem of the existence and multiplicity of periodic solutions associated to a class of scalar equations of the form x f t x 0 the class considered is such that the behaviour of its solutions near zero and infinity can be compared two suitable piecewise linear systems we show how a rotation number approach together with the poincare birkhoff theorem and the phase plane analysis of the spiral properties allows to obtain multiplicity results in terms of the gap between the rotation numbers of the referred piecewise linear systems at zero and at infinity these systems may also be resonant in particular our approach can be used to deal with the problems without both global existence of the cauchy problems associated to the equation and the sign assumption on f the typical example is a partially superlinear second order equation our main result generalizes some classical results of jacobowitz and hartman among others

gel estimation for heavy tailed garch models with robust empirical likelihood inference abstract we construct a generalized empirical likelihood estimator for a garch 1 1 model with a possibly heavy tailed error the estimator imbeds tail trimmed estimating equations allowing for over identifying conditions asymptotic normality efficiency and empirical likelihood based confidence regions for very heavy tailed random volatility data we show the implied probabilities from the tail trimmed continuously updated estimator elevate weight for usable large values assign large but not maximum weight to extreme observations and give the lowest weight to non leverage points we derive a higher order expansion for gel with imbedded tail trimming gelitt which reveals higher order bias and efficiency properties available when the garch error has a finite second moment higher order asymptotics for gel without tail trimming requires the error to have moments of substantially higher order we use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample we also present robust versions of generalized empirical likelihood ratio wald and lagrange multiplier tests and an efficient and heavy tail robust moment estimator with an application to expected shortfall estimation finally we present a broad simulation study for gel and gelitt and demonstrate profile weighted expected shortfall for the russian ruble us dollar exchange rate we show that tail trimmed cue gmm dominates other estimators in terms of bias mse and approximate normality

robust linear model selection based on least angle regression in this article we consider the problem of building a linear prediction model when the number of candidate predictors is large and the data possibly contain anomalies that are difficult to visualize and clean we want to predict the nonoutlying cases therefore we need a method that is simultaneously robust and scalable we consider the stepwise least angle regression lars algorithm which is computationally very efficient but sensitive to outliers we introduce two different approaches to robustify lars the plug in approach replaces the classical correlations in lars by robust correlation estimates the cleaning approach first transforms the data set by shrinking the outliers toward the bulk of the data which we call multivariate winsorization and then applies lars to the transformed data we show that the plug in approach is time efficient and scalable and that the bootstrap can be used to stabilize its results we recommend using bootstrapped robustified lars to sequence a number of candidate pred

hermite hadamard s type inequalities for operator convex functions some hermite hadamard s type inequalities for operator convex functions of selfadjoint operators in hilbert spaces are given applications for particular cases of interest are also provided

nonsmooth analysis and frechet differentiability of m functionals abstract a necessary requirement for existence of the frechet derivative is that the defining psi function is uniformly bounded and this naturally excludes those nonrobust estimators such as the maximum likelihood estimator in normal parametric models in this paper the methods of nonsmooth analysis described in the book by f h clarke 1983 are introduced to the theory of statistical expansions and are used here in the proofs of weak continuity and frechet differentiability of m functionals subsequently the conditions for frechet differentiability given in clarke 1983 can be relaxed to include most popular m functionals additional keywords distribution functions m estimators robustness gross error sensitivity weak continuity asymptotic expansions asymptotic normality selection functional local uniqueness author

assessing robustness of generalised estimating equations and quadratic inference functions in the presence of data contamination or outliers some empirical studies have indicated that the two methods of generalised estimating equations and quadratic inference functions appear to have rather different robustness behaviour this paper presents a theoretical investigation from the perspective of the influence function to identify the causes for the difference we show that quadratic inference functions lead to bounded influence functions and the corresponding m estimator has a redescending property but the generalised estimating equation approach does not we also illustrate that unlike generalised estimating equations quadratic inference functions can still provide consistent estimators even if part of the data is contaminated we conclude that the quadratic inference function is a preferable method to the generalised estimating equation as far as robustness is concerned this conclusion is supported by simulations and real data examples

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

continuation theorems for periodic perturbations of autonomous systems it is first shown in this paper that whenever it exists the coincidence degree of the left hand member of an autonomous differential equation x g x 0 in the space of periodic functions with fixed period omega can be computed in terms of the brouwer degree of g this result provides efficient continuation theorems specially for omega periodic perturbations of autonomous systems extensions to differential equations in flow invariant enr s are also given

infinitesimal robustness for autoregressive processes we define the influence function and construct optimal robust estimators for autoregressive processes we show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination this function is called the influence function it is unique only up to an equivalence relation but there is a natural unique version which describes the limiting influence of an additional observation given the previous observations moreover with this version the asymptotic variance at the true model can be expressed in a simple form optimal robust estimators minimize this asymptotic variance under a constraint on the influence function as in the i i d case they are found by truncating a multiple of the influence function of the maximum likelihood estimator

robust alternatives to the f test in mixed linear models based on mm estimates mixed linear models are commonly used to analyze data in many settings these models are generally fitted by means of restricted maximum likelihood techniques relying heavily on normality the sensitivity of the resulting estimators and related tests to this underlying assumption has been identified as a weakness that can even lead to wrong interpretations very recently a highly robust estimator based on a scale estimate that is an s estimator has been proposed for general mixed linear models it has the advantage of being easy to compute and allows the computation of a robust score test however this proposal cannot be used to define a likelihood ratio type test that is certainly the most direct route to robustify an f test as the latter is usually a key tool of hypothesis testing in mixed linear models we propose two new robust estimators that allow the desired extension they also lead to resistant wald type tests useful for testing contrasts and covariate effects we study their properties theoretically and by means of simulations the analysis of a real data set illustrates the advantage of the new approach in the presence of outlying observations

branches of forced oscillations for periodically perturbed second order autonomous odes on manifolds where h tm r and f r tm r are continuous vector fields tangent to a differentiable manifold m embedded in some euclidean space r and f is t periodic in t here x represents the component of the acceleration parallel to m this equation governs the motion of a constrained mechanical system with configuration space m acted on by the sum of two forces an autonomous one h and a periodic perturbation f this motion problem reduces to that of 3 and 2 when h 0 nevertheless our results do not include those of 3 unless the manifold m is compact as in 2 we investigate the properties of the set x of t pairs of 1 i e of those pairs x 0 c t m with x a t periodic solution of 1 in article id jdeq 1998 3557 available online at http www idealibrary com on

instrumental variable estimation based on conditional median restriction abstract we develop a method named the l 1 iv estimator to estimate structural equations based on the conditional median restriction imposed on the error terms we study its asymptotic behavior and show how to estimate its asymptotic covariance matrix we also discuss the point identification in the l 1 iv estimation and propose an over identifying restriction test we further demonstrate the performance of the l 1 iv estimator in comparison with the familiar two stage least squares estimator the proposed method is applied to estimate the labor supply and wage offer functions for working married women

periodic solutions of lienard equations with singular forces of repulsive type in this paper we will use the coincidence degree to give an existence result of periodic solutions for the scalar lienard equations with singular forces of repulsive type the main result of this paper clearly describes what balance conditions between the singular force at the singularity and at the infinity should be imposed if the equation has a periodic solution as an application we will improve the results of ding ye and wang for the brillouin electron beam focusing system

robust inference with gmm estimators the local robustness properties of generalized method of moments gmm estimators and of a broad class of gmm based tests are investigated in a unified framework gmm statistics are shown to have bounded influence if and only if the function defining the orthogonality restrictions imposed on the underlying model is bounded since in many applications this function is unbounded it is useful to have procedures that modify the starting orthogonality conditions in order to obtain a robust version of a gmm estimator or test we show how this can be obtained when a reference model for the data distribution can be assumed we develop a flexible algorithm for constructing a robust gmm rgmm estimator leading to stable gmm test statistics the amount of robustness can be controlled by an appropriate tuning constant we relate by an explicit formula the choice of this constant to the maximal admissible bias on the level or and the power of a gmm test and the amount of contamination that one can reasonably assume given some information on the data finally we illustrate the rgmm methodology with some simulations of an application to rgmm testing for conditional heteroscedasticity in a simple linear autoregressive model in this example we find a significant instability of the size and the power of a classical gmm testing procedure under a non normal conditional error distribution on the other side the rgmm testing procedures can control the size and the power of the test under non standard conditions while maintaining a satisfactory power under an approximatively normal conditional error distribution

infinitesimal robustness for diffusions we develop infinitesimally robust statistical procedures for the general diffusion processes we first prove the existence and uniqueness of the times series influence function of conditionally unbiased m estimators for ergodic and stationary diffusions under weak conditions on the martingale estimating function used we then characterize the robustness of m estimators for diffusions and derive a class of conditionally unbiased optimal robust estimators to compute these estimators we propose a general algorithm which exploits approximation methods for diffusions in the computation of the robust estimating function monte carlo simulation shows a good performance of our robust estimators and an application to the robust estimation of the exchange rate dynamics within a target zone illustrates the methodology in a real data application

periodic solutions of semilinear duffing equations with impulsive effects abstract in this paper we are concerned with the existence of periodic solutions for semilinear duffing equations with impulsive effects firstly for its autonomous equation any motion of the solution is same as the motion of the corresponding equation without impulses until it meets the first impulse time under the influence of impulses these two motions are likely to be quite different we introduce some reasonable assumptions on the impulsive functions to control these differences such that the information valid for the equation without impulses can always be used for the impulsive one basing on poincare birkhoff twist theorem we prove the existence of infinitely many periodic solutions secondly as for the nonautonomous equation where the autonomous case is taken as an auxiliary one we find the relation between the solutions of these two equations and then obtain the existence of infinitely many periodic solutions also by poincare birkhoff twist theorem lastly an example with special impulses satisfying the above assumptions is given

robust score and portmanteau tests of volatility spillover abstract this paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or garch type feedback the tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent we negligibly trim test equations or components of the equations and construct heavy tail robust score and portmanteau statistics trimming is either simple based on an indicator function or smoothed in particular we develop the tail trimmed sample correlation coefficient for robust inference and prove that its gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness further if spillover occurs within a specified horizon our test statistics obtain power of one asymptotically we discuss the choice of trimming portion including a smoothed p value over a window of extreme observations a monte carlo study shows our tests provide significant improvements over extant garch based tests of spillover and we apply the tests to financial returns data finally based on ideas in patton 2011 we construct a heavy tail robust forecast improvement statistic which allows us to demonstrate that our spillover test can be used as a model specification pre test to improve volatility forecasting

better bounds on the numerical radii of hilbert space operators abstract kittaneh proved that if a is a bounded linear operator on a complex hilbert space then 1 4 a 2 a 2 2 a where and are the numerical radius and the usual operator norm and a a a 1 2 in this paper we show that 1 4 a 2 a 2 1 2 2 a 1 8 a a a a 2 a meanwhile we give an improvement of the norm inequality presented by bhatia and kittaneh for the positive operators

prevalence of stable periodic solutions for duffing equations abstract we study the prevalence of stable periodic solutions of the duffing equations for external force which guarantees the existence of periodic solutions both the dissipative case and the conservative case are considered the nonlinearity may be periodic or satisfies the condition of landesman lazer type

robust inference for generalized linear models by starting from a natural class of robust estimators for generalized linear models based on the notion of quasi likelihood we define robust deviances that can be used for stepwise model selection as in the classical framework we derive the asymptotic distribution of tests based on robust deviances and we investigate the stability of their asymptotic level under contamination the binomial and poisson models are treated in detail two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures

semiparametric robust estimation of truncated and censored regression models many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares scls are sensitive to outliers and data contamination as we document therefore we propose a semiparametric general trimmed estimator gte of truncated and censored regression which is highly robust but relatively imprecise to improve its performance we also propose data adaptive and one step trimmed estimators we derive the robust and asymptotic properties of all proposed estimators and show that the one step estimators e g one step scls are as robust as gte and are asymptotically equivalent to the original estimator e g scls the finite sample properties of existing and proposed estimators are studied by means of monte carlo simulations

robust and efficient one way manova tests we propose robust tests as alternatives to the classical wilks lambda test in one way manova the robust tests use highly robust and efficient multisample multivariate s estimators or mm estimators instead of the empirical covariances the properties of several robust test statistics are compared under the null hypothesis the distribution of the test statistics is proportional to a chi square distribution as an alternative to the asymptotic distribution we develop a fast robust bootstrap method to estimate the distribution under the null hypothesis we show when it is asymptotically correct to estimate the null distribution in this way and we use simulations to verify the performance of the bootstrap based tests in finite samples we also investigate the power of the new tests as well as their robustness against outliers finally we illustrate the use of these robust test statistics on a real data example some additional results are provided as supplemental material

resistant estimation for simultaneous equations models using weighted instrumental variables in this paper we present a weighted instrumental variables estimator that is resistant2 to heavy tailed errors aberrant data in either the endogenous or exogenous variables and certain other model failures the estimator is analogous to the weighted least squares approach to robustness proposed by krasker and welsch 21 for ordinary regression we will discuss the theory that motivated this estimator derive some of its properties describe our computational algorithm and using an empirical example illustrate the estimator s utility as a tool for data analysis in structural models the evolution of robust estimators for simultaneous equations models has closely resembled the development of robust methods for ordinary regression in both cases research focused at first on the well documented effects of long tailed error distributions on the classical procedures for ordinary regression models statisticians have studied the properties of least absolute deviations lad estimators see bassett and koenker 2 and amemiya 1 and maximum likelihood type estimators called m estimators see huber 14 for simultaneous equations models lad can be generalized in several different ways to modify two stage least squares or instrumental variables amemiya 1 has presented these estimators in a unified framework and powell 31 has proven their asymptotic normality under weak assumptions fair 8 has compared two stage lad estimates of a u s macroeconomic model with two stage least squares and full information maximum likelihood estimates the m estimator concept can also be generalized to simultaneous equations for example prucha and kelejian 32 have considered maximum likelihood estimation under the assumption that the disturbance vector is multivariate student t although lad and m estimators maintain a high efficiency when the error distribution is heavy tailed they are not robust in the stronger sense of hampel 10 which roughly speaking requires an estimator to have a limited sensitivity to any small fraction of the data 3 lad and m estimators fail under this criterion because a single observation whose values for the right side variables are highly anomalous can have an arbitrarily large effect on lad estimates or m estimates just as on the classical procedures consequently these estimators do not provide insurance against the sort of gross errors that occur in some data sets nor do they serve as reliable diagnostics for departures from linearity occurring in extreme regions of the space of right side variables for linear models the estimators that satisfy the strong hampel robustness criterion have become known as bounded influence estimators several such estimators have been

on the set of harmonic solutions of periodically perturbed autonomous differential equations on manifolds where g m r and f r m r are continuous vector fields tangent to a not necessarily closed boundaryless differentiable manifold m r with f t periodic with respect to the first variable we investigate the structure of the set of solution pairs of 1 i e of those pairs x 0 ct m such that x is a necessarily t periodic solution of 1 we give conditions ensuring the existence of a non compact connected component of solution pairs x of 1 which emanates from the set of constant solutions of the unperturbed equation

a note on topological methods for a class of differential algebraic equations abstract we study a particular class of autonomous differential algebraic equations that are equivalent to ordinary differential equations on manifolds under appropriate assumptions we determine a straightforward formula for the computation of the degree of the associated tangent vector field that does not require any explicit knowledge of the manifold we use this formula to study the set of harmonic solutions to periodic perturbations of our equations two different classes of applications are provided

a geometric approach to periodically forced dynamical systems in presence of a separatrix we consider the periodic boundary value problem for the non autonomous scalar second order equation x f x x e t with e a continuous and t periodic forcing term using a continuation theorem adapted from capietto et al trans amer math soc 329 1992 41 72 we propose some new conditions for the existence of t periodic solutions to the forced equation in terms of the dynamical properties of the trajectories of the associated autonomous equation x f x x 0 special emphasis will be addressed to the study of the case in which the presence of an unbounded separatrix for the autonomous system in the phase plane allows to obtain a priori bounds for the t periodic solutions of the homotopic equation x f x x e t

higher order infinitesimal robustness using the von mises expansion we study the higher order infinitesimal robustness of a general m functional and characterize its second order properties we show that second order robustness is equivalent to the boundedness of both the estimator s estimating function and its derivative with respect to the parameter it implies at the same time i variance robustness and ii robustness of higher order saddlepoint approximations to the estimator s finite sample density the proposed construction of second order robust m estimators is fairly general and potentially useful in a variety of relevant settings besides the theoretical contributions we discuss the main computational issues and provide an algorithm for the implementation of second order robust m estimators finally we illustrate our theory by monte carlo simulation and in a real data estimation of the maximal losses of nikkei 225 index returns our findings indicate that second order robust estimators can improve on other widely applied robus

a new fixed point theorem and periodic solutions of nonconservative weakly coupled systems abstract in this paper we prove a new fixed point theorem for the coupling of twist conditions and poincare bohl type conditions as its applications we prove the existence of periodic solutions for various nonconservative mixed type weakly coupled systems

periodic orbits of radially symmetric keplerian like systems a topological degree approach abstract we are concerned with non autonomous radially symmetric systems with a singularity which are t periodic in time by the use of topological degree theory we prove the existence of large amplitude periodic solutions whose minimal period is an integer multiple of t precise estimates are then given in the case of keplerian like systems showing some resemblance between the orbits of those solutions and the circular orbits of the corresponding classical autonomous system

periodic solutions for ordinary differential equations with sublinear impulsive effects abstract the continuation method of topological degree is used to investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects the applications of the abstract approach include the generalizations of some classical nonresonance theorem for impulsive equations for instance the existence theorem for asymptotically positively homogeneous differential systems and the existence theorem for second order equations with landesman lazer conditions

the existence of periodic solutions for a class of nonautonomous lattices with bounded coupling abstract in this paper by using a definition of topological degree and limiting arguments we study the existence of periodic solutions of a class of one dimensional nonautonomous chains with bounded coupling an approach is developed to deal with the case of lack of the a priori bounds for an infinite lattices

new robust statistical procedures for the polytomous logistic regression models this article derives a new family of estimators namely the minimum density power divergence estimators as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model based on these estimators a family of wald type test statistics for linear hypotheses is introduced robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model the validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies finally an approach for the data driven selection of the robustness tuning parameter is proposed with empirical justifications

generalized method of moments specification testing abstract this paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions it shows that any such test may fail against general misspecification that causes estimator inconsistency the mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived applications to testing for exogeneity of a set of instrumental variables are presented

on b robust instrumental variable estimation of the linear model with panel data the aim of this paper is to demonstrate how to acquire robust consistent estimates of the linear model when the fundamental orthogonality condition is not fulfilled with this end in view we develop two estimation procedures two stage generalized m 2sgm and robust generalized method of moments rgmm both estimators are b robust i e their associated influence function is bounded consistent and asymptotic normally distributed our simulation results indicate that the relatively efficient rgmm estimator in regressions with heteroskedastic and or autocorrelated errors provides accurate parameter estimates of a panel data model with all variables subject to measurement errors even if a substantial portion of the data is contaminated with aberrant observations the traditional estimation techniques such as 2sls and gmm break down when outliers corrupt the data

a natural robustification of the ordinary instrumental variables estimator summary instrumental variables estimators are designed to provide consistent parameter estimates for linear regression models when some covariates are correlated with the error term we propose a new robust instrumental variables estimator riv which is a natural robustification of the ordinary instrumental variables estimator oiv specifically we construct riv using a robust multivariate location and scatter s estimator to robustify the solution of the estimating equations that define oiv riv is computationally inexpensive and readily available for applications through the r library riv it has attractive robustness and asymptotic properties including high resilience to outliers bounded influence function consistency under weak distributional assumptions asymptotic normality under mild regularity conditions and equivariance we further endow riv with an iterative algorithm which allows for the estimation of models with endogenous continuous covariates and exogenous dummy covariates we study the performance of riv when the data contains outliers using an extensive monte carlo simulation study and by applying it to a limited access dataset from the framingham heart study cohort to estimate the effect of long term systolic blood pressure on left atrial size

periodic solutions of superlinear impulsive differential equations a geometric approach abstract a geometric method is introduced to study superlinear second order differential equations with impulsive effects basing on a reference continuous polar lifting of a planar orientation preserving homeomorphism we prove via the poincare birkhoff twist theorem the existence of infinitely many periodic solutions of conservative superlinear second order equations with the finite twist impulsive terms we also prove by developing a new twist fixed point theorem the existence of periodic solutions for non conservative superlinear second order equations with degenerate impulsive terms

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

multiplicity of forced oscillations for the spherical pendulum acted on by a retarded periodic force abstract we prove a multiplicity result for forced oscillations of a spherical pendulum that is a massive point moving on a sphere subject to a periodic action with or without friction allowed to depend on the whole past of the motion the approach is based on topological methods in particular when the unperturbed forcing term is the gravity we obtain two harmonic forced oscillations regardless of the presence of friction and of the form of the perturbing force field

forced oscillations on manifolds and multiplicity results for periodically perturbed autonomous systems some qualitative results for forced oscillations on differentiable manifolds are obtained which cannot be deduced via variational or implicit function methods

robust indirect inference in this article we develop robust indirect inference for a variety of models in a unified framework we investigate the local robustness properties of indirect inference and derive the influence function of the indirect estimator as well as the level and power influence functions of indirect tests these tools are then used to design indirect inference procedures that are stable in the presence of small deviations from the assumed model although indirect inference was originally proposed for statistical models whose likelihood is difficult or even impossible to compute and or to maximize we use it here as a device to robustify the estimators and tests for models where this is not possible or is difficult with classical techniques such as m estimators examples from financial applications time series and spatial statistics are used for illustration

periodic motion of a system of two or three charged particles we provide necessary and sufficient conditions for the existence of t periodic solutions of a system of second order ordinary differential equations that models the motion of two or three collinear charged particles of the same sign

robust estimators for simultaneous equations models this paper presents a class of robust estimators for linear and non linear simultaneous equations models which are a direct generalization of the maximum likelihood estimator the new estimators are obtained as solutions of a generalized likelihood equation they are resistant to deviations from the model distribution to outlying observations and to some model misspecifications an optimality principle leads to the construction of an optimal robust estimator which is the best trade off between efficiency at the model and robustness

robust inference in sample selection models the problem of non random sample selectivity often occurs in practice in many fields the classical estimators introduced by heckman are the backbone of the standard statistical analysis of these models however these estimators are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice we develop a general framework to study the robustness properties of estimators and tests in sample selection models we derive the influence function and the change of variance function of heckman s two stage estimator and we demonstrate the non robustness of this estimator and its estimated variance to small deviations from the model assumed we propose a procedure for robustifying the estimator prove its asymptotic normality and give its asymptotic variance both cases with and without an exclusion restriction are covered this allows us to construct a simple robust alternative to the sample selection bias test we illustrate the use of our new methodology in an analysis of ambulatory expenditures and we compare the performance of the classical and robust methods in a monte carlo simulation study

inequalities between f a b and f a f b abstract the conjecture posed by aujla and silva j s aujla f c silva weak majorization inequalities and convex functions linear algebra appl 369 2003 217 233 is proved it is shown that for any m tuple of positive semidefinite n n complex matrices a j and for any non negative convex function f on 0 with f 0 0 the inequality f a 1 f a 2 f a m f a 1 a 2 a m holds for any unitarily invariant norm it is also proved that f a 1 f a 2 f a m f a 1 a 2 a m where f is a non negative concave function on 0 and is normalized

periodic solutions for planar autonomous systems with nonsmooth periodic perturbations abstract in this paper we consider a class of planar autonomous systems having an isolated limit cycle x 0 of smallest period t 0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1 we consider two functions defined by means of the eigenfunctions of the adjoint of the linearized system and we formulate conditions in terms of them in order to have the existence of two geometrically distinct families of t periodic solutions of the autonomous system when it is perturbed by nonsmooth t periodic nonlinear terms of small amplitude we also show the convergence of these periodic solutions to x 0 as the perturbation disappears and we provide an estimation of the rate of convergence the employed methods are mainly based on the theory of topological degree and its properties that allow less regularity on the data than that required by the approach commonly employed in the existing literature on this subject based on various versions of the implicit function theorem

norm inequalities for certain operator sums abstract we extend to larger classes of norms some inequalities concerning sums of positive operators and sums of operators having orthogonal ranges these inequalities are useful in the theories of best approximation in c algebras and generalized inverses

periodic solutions for functional differential equations of mixed type in this paper we study the existence of periodic solutions for some functional differential equations of mixed type among the main results are the averaging principle and existence theorems for some equations with homogeneous nonlinearities we use here the coincidence degree theory of mawhin

gmm inference when the number of moment conditions is large abstract asymptotic theory typically presumes that the dimensionality of econometric models is independent of the sample size even though this presumption is often quite unrealistic in gmm estimation whenever optimal instruments are not available it can frequently be shown that adding over identifying restrictions moment conditions will increase asymptotic precision however the conventional asymptotics which underlies this view insists that the number of moment conditions remain finite even though the number of available moment conditions may grow without bound we consider the explicit dependence of the number of moment conditions or instruments q n on the sample size n and establish that under conventional regularity conditions for the estimation of a linear model with general heteroskedasticity q n 3 n 0 is a sufficient condition for the validity of conventional asymptotic inference about the gmm estimator

maslov index poincare birkhoff theorem and periodic solutions of asymptotically linear planar hamiltonian systems abstract we study the relationship between the twist condition in the poincare birkhoff fixed point theorem and the assumptions on the maslov index for asymptotically linear planar hamiltonian systems for this aim we develop a variant of the poincare birkhoff theorem which together with its classical version allows to obtain a lower bound for the number of nontrivial periodic solutions in terms of the gap between the maslov indexes associated to the linearizations of the planar system at zero and at infinity