interpolation operators in orlicz sobolev spaces we study classical interpolation operators for finite elements like the scott zhang operator in the context of orlicz sobolev spaces furthermore we show estimates for these operators with respect to quasi norms which appear in the study of systems of p laplace type

instrumental variables estimation in errors in variables models when instruments are correlated with errors abstract consistency of an instrumental variable iv estimator is based on the orthogonality assumption of the iv s and the regression equation errors if this assumption is in doubt there is not much hope left for the iv estimator the assumption can be tested but such a test usually requires another set of iv s for which the assumption holds in this paper it is shown that in an errors in variables model tighter bounds can be found in the presence of iv s even if they are correlated with the regression equation errors and that these bounds can be made tighter still if one has prior information restricting the extent of this correlation moreover the result is used to establish a sufficient condition for the ols estimator to be inconsistent when orthogonality is suspect so that the wu hausman test is not applicable this condition is useful even when the above type of prior information is not directly available

eta invariants and regularized determinants for odd dimensional hyperbolic manifolds with cusps we study eta invariants of dirac operators and regularized determinants of dirac lapla cians over hyperbolic manifolds with cusps and their relations with selberg zeta functions using the selberg trace formula and a detailed analysis of the unipotent orbital integral we show that the eta and zeta functions defined by the relative traces are regular at the origin so that we can define the eta invariant and the regularized determinant we also show that the selberg zeta function of odd type has a meromorphic extension over c prove a relation of the eta invariant and a certain value of the selberg zeta function of odd type and derive a corresponding functional equation these results generalize the earlier work of john millson to hyperbolic manifolds with cusps we also prove that the selberg zeta function of even type has a meromorphic extension over c relate it to the regularized determinant and obtain a corresponding functional equation

analytic torsion for twisted de rham complexes we dene analytic torsion x e h 2 det h x e h for the twisted de rham complex consisting of the spaces of dieren tial forms on a compact oriented riemannian man ifold x valued in a at vector bundle e with a dieren tial given by r e h where r e is a at connection on e h is an odd degree closed dieren tial form on x and h x e h denotes the cohomology of this z2 graded complex the denition uses pseudo dieren tial operators and residue traces we show that when dim x is odd x e h is independent of the choice of metrics on x and e and of the representative h in the cohomology class h we explain the relation to generalized geometry when h is a 3 form we demonstrate some basic func torial properties when h is a top degree form we compute the torsion dene its simplicial counterpart and prove an analogue of the cheeger mtheorem we also establish the rela tionship of an invariant form of the analytic torsion for t dual circle bundles with 3 form uxes

an algorithm for the computation of eigenvalues spectral zeta functions and zeta determinants on hyperbolic surfaces we present a rigorous scheme that makes it possible to compute eigenvalues of the laplace operator on hyperbolic surfaces within a given precision the method is based on an adaptation of the method of particular solutions to the case of locally symmetric spaces and on explicit estimates for the approximation of eigenfunctions on hyperbolic surfaces by certain basis functions it can be applied to check whether or not there is an eigenvalue in an e neighborhood of a given number 0 this makes it possible to find all the eigenvalues in a specified interval up to a given precision with rigorous error estimates the method converges exponentially fast with the number of basis functions used combining the knowledge of the eigenvalues with the selberg trace formula we are able to compute values and derivatives of the spectral zeta function again with error bounds as an example we calculate the spectral determinant and the casimir energy of the bolza surface and other surfaces

identification of complete information games this paper establishes sufficient conditions for point identification of the utility functions in generalized complete information game models these models allow generalized interaction structures and generalized behavioral assumptions the generalized interaction structures allow that the dependence of an agent s utility function on the other agents actions can itself depend on characteristics of the agents including an endogenous network of connections among the agents the generalized behavioral assumptions relax the solution concept from nash equilibrium play to weaker solution concepts like rationalizability the results allow a non parametric specification of the unobservables

bounding parameter estimates with nonclassical measurement error abstract the bias introduced by errors in the measurement of independent variables has increasingly been a topic of interest among researchers estimating economic parameters however studies typically use the assumption of classical measurement error that is the variable of interest and its measurement error are uncorrelated and the expected value of the mismeasured variable is equal to the expected value of the true measure these assumptions often arise from convenience rather than conviction when a variable is bounded it is likely that the measurement error and the true value of the variable are negatively correlated we consider the case of a noisily measured variable with a negative covariance between the measurement error and the true value of the variable we show that asymptotically the parameter in a univariate regression is bounded between the ordinary least squares ols estimator and an instrumental variables iv estimator further we demonstrate that the ols bound can be improved in

affine orlicz polya szego principle for log concave functions abstract the affine l p polya szego principle significantly strengthens the classical polya szego principle it is an open problem whether there exists an affine orlicz polya szego principle which includes the affine l p polya szego principle as special case in this paper an affine orlicz polya szego principle for log concave functions is established by using functional steiner symmetrizations

bounding the effects of proxy variables on regression coefficients we consider a regression in which one of the observed variables is a proxy for some unobserved true variable given a lower bound for the correlation between the proxy and the unobserved true variable for which it substitutes we derive intervals in which the coefficients of the unobserved true regression must lie regardless of any other correlations involving unobserved variables or disturbances we present a simple solution for the important special case in which only the signs of the coefficients are of concern and one seeks the smallest correlation between the proxy and the true variable that guarantees the correctness of the signs of the coefficients in the proxy regression we also present an algorithm for extending these results to the multiple proxy problem attemprs to confront economic theories with data are often hampered by the problem that some of the relevant variables are unavailable or even unobservable in the case of regression models it is customary to substitute proxies for the unavailable variables though the coefficients in the proxy regression will not coincide with those in the regression of the dependent variable on the true explanatory variables it is clear by continuity that the differences will be small if each proxy is sufficiently highly correlated with the unobserved true variable for which it substitutes even if its error is correlated with other errors or variables moreover in many instances the theory predicts not the magnitudes but only the signs of the regression coefficients correct inferences will then be drawn from the model provided that the pairwise correlations between the proxies and the true variables are high enough to guarantee that the signs of the regression coefficients would be unchanged if the proxies were replaced by the true variables in applications econometricians can generally assess those pairwise correlations subjectively but how high do they need to be in this paper we present a complete answer to this question when only one variable is a proxy and describe an algorithm for determining the required correlations when there are several proxies the effects of proxy variables have been extensively studied in the special case of errors in variables eiv in which the differences between the proxies and the corresponding true variables the measurement errors are independent of the true variables of each other and of the disturbances in the true regression we require no such independence in the eiv case it is sometimes possible to guarantee correctness of the signs of the coefficients even without prior information about the variances of the measurement errors for example if the coefficient vector from the direct regression and the coefficient vectors from the reverse regressions as one varies the left side variable all lie in the same orthant then the coefficient vector in the true regression must also lie in that orthant see

twisted perron frobenius theorem and l functions abstract a theorem of perron frobenius type and its twisted version are established in a setting of topological graphs the applications include a partial extension of selberg s results on his zeta functions and a result by parry and pollicott on meromorphic continuations of dynamical zeta functions to certain l functions associated to a dynamical system of anosov type

ruelle zeta function at zero for surfaces we show that the ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the euler characteristic this result was previously known only in constant curvature

meromorphic zeta functions for analytic flows we extend to hyperbolic flows in all dimensions rugh s results on the meromorphic continuation of dynamical zeta functions in particular we show that the ruelle zeta function of a negatively curved real analytic manifold extends to a meromorphic function on the complex plane

consistent sets of estimates for regressions with correlated or uncorrelated measurement errors in arbitrary subsets of all variables over the last decade the problem of measurement errors in the independent variables of a regression equation has attracted renewed interest among econometricians in the fifties and sixties the problem was considered to be more or less hopeless due to its inherent underidentification e g theil 1971 apart from instrumental variables the most frequently cited textbook solution was wald s method of grouping wald 1940 recent insight into the properties of the method of grouping can be interpreted as making this method worthless in most practical cases pakes 1982 since about 1970 new approaches to the problem have been explored basically along three lines viz embedding the error ridden equation into a set of multiple equations e g zellner 1970 goldberger 1972 into a set of simultaneous equations e g hsiao 1976 geraci 1976 and using the dynamics of the equation if present e g maravall and aigner 1977 in view of the underidentification of the basic model it is clear that all these methods invoke additional information of some kind if this information takes the form of exact or stochastic knowledge of certain parameters in the model the construction of consistent estimators is fairly straightforward e g fuller 1980 kapteyn and wansbeek 1984 for an overview of the state of the art see aigner et al 1984 an approach somewhat orthogonal to the ones described above has been to take the model as it is and to use prior ideas about the size of the measurement errors to diagnose how serious the probem is examples are blomqvist 1972 hodges and moore 1972 and davies and hutton 1975 leamer 1983 starts from the opposite direction by asking how serious the measurement error problem has to be in order to render the data useless for inference that is to say when measurement error is large enough to make it impossible to put bounds on regression parameters in an empirical example he shows that even very small measurement errors in some explanatory variables would open up the possibility of perfectly collinear explanatory variables and hence make the data useless for statistical inference at least without additional prior information the most systematic analysis of the information loss caused by measurement error is due to klepper and leamer 1984 they start out by invoking a minimal amount of prior information and then ask the question under what conditions it is still possible to make some inferences regarding the vector of unknown regression parameters p in the special case where the measurement errors are assumed uncorrelated and the k 1 estimates of 3 obtained by regressing each of the k 1 variables involved i e the one dependent variable and the k independent variables on the remaining k variables are all in the same orthant one can bound the ml estimates of p in that case the convex hull of the k 1 regressions contains all possible ml estimates and any point in the hull is a possible ml estimate if the k 1 regressions are not all in the same orthant then the set of ml estimates is unbounded in that case klepper and leamer 1984 introduce extra prior information which allows them to bound the set of maximum likelihood estimates the prior information comes in two forms firstly a researcher is supposed to be able to specify a maximum value of r2 if all exogenous variables were measured accurately it is shown that if this maximum is low enough one can again bound the set of ml estimates by a convex hull secondly if

l2 torsion invariants we discuss a generalisation of reidemeister franz torsion which applies to infinite dimensional representations of the fundamental group by utilising the theory of finite von neumann algebras our results apply to a class of closed oriented manifolds which are l2 acyclic in the sense of having trivial l2 cohomology evidence is presented for equality of the essentially combinatorial torsion introduced here with an analytic l2 ray singer torsion defined by the second named author

consistent estimation of linear panel data models with measurement error abstract measurement error causes a bias towards zero when estimating a panel data linear regression model the panel data context offers various opportunities to derive instrumental variables allowing for consistent estimation we consider three sources of moment conditions i restrictions on the covariance matrix of the errors in the equations ii nonzero third moments of the regressors and iii heteroskedasticity and nonlinearity in the relation between the error ridden regressor and another error free regressor in simulations these approaches appear to work well

a direct approach to orlicz sobolev capacity abstract this paper is motivated by federer and ziemer s potential free approach to sobolev capacity we extend their results to orlicz sobolev spaces and analyze the resulting notion of orlicz sobolev capacity in particular we explore the relationship between the orlicz sobolev capacity of a set and its hausdorff dimension and then establish the quasicontinuity of orlicz sobolev functions

sobolev s inequalities and vanishing integrability for riesz potentials of functions in the generalized lebesgue space lp logl q abstract our aim in this paper is to deal with sobolev s inequalities for riesz potentials of functions belonging to l p log l q to do so we study the boundedness of hardy littlewood maximal functions and apply the hedberg s trick as an application we treat vanishing integrability for riesz potentials

problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak abstract we draw attention to two problems associated with the use of instrumental variables iv the importance of which for empirical work has not been fully appreciated first the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the iv estimates even if only a weak relationship exists between the instruments and the error in the structural equation second in finite samples iv estimates are biased in the same direction as ordinary least squares ols estimates the magnitude of the bias of iv estimates approaches that of ols estimates as the r 2 between the instruments and the endogenous explanatory variable approaches 0 to illustrate these problems we reexamine the results of a recent paper by angrist and krueger who used large samples from the u s census to estimate wage equations in which quarter of birth is used as an instrument for educational attainment we find evidence that despite huge sample sizes th

on certain definite integrals which arise in automorphic lie theory calculates in closed form a family of definite integrals in b a c n 0 1 2 3 which arise in the calculation of regularized functional determinants associated with a compact space form x of a rank 1 riemannian symmetric space in the special case when n 0 b 1 2 a pi c 1 and x is a riemann surface the integral i0 1 2 pi 1 is known for example in the context of polyakov string theory

parameter estimation in regression models with errors in the variables and autocorrelated disturbances abstract for regression models with first order autocorrelated disturbances the traditional prescription of econometricians is to correct for serial correlation by using appropriate estimation techniques such as the cochrane orcutt hildreth lu or prais winsten procedures this suggestion however does not take into account the fact that in most economic applications the independent variables contain measurement errors when there are errors in the variables ordinary least squares without any attempt to correct for serial correlation may in several cases yield less unreliable and misleading results in terms of biases and mean squared errors of the estimators this paradoxical finding is demonstrated analytically for the asymptotic case and illustrated for finite samples by monte carlo experiments for the regression model with a single stationary explanatory variable the monte carlo experiments also suggest that the same conclusion holds if the independent variable follows a random walk at least for medium size samples

homological identities for closed orbits the classical lefschetz formula expresses a relationship between the fixed points of certain transformations and homological invariants when applied to continuous systems one obtains the hopf formula relating the singularities of a flow to the euler characteristic of the underlying manifold the main goal of this paper is to prove an analogous formula that relates the closed orbits of a stable flow to a homological invariant of the manifold there are serious obstruction to finding such a formula for flows the first is that there are flows on any closed manifold of dimension 4 of zero euler characteristic with no periodic orbits whatsoever 27 these flows however are unstable by pugh s c a closing lemma 19 so it is natural to restrict attention to flows that satisfy axiom a and the no cycles property since smale has shown that these flows are o stable 23 secondly there are gradient flows on any closed manifold that are axiom a no cycles and have no closed orbits 24 so it is natural to study only nonsingular flows the possibility that a lefschetz type formula for such flows existed was suggested to us by r bowen even nonsingular morse smale flows however are difficult to deal with since asimov s geometric index is not an invariant of the nonsingular homotopy class 2 we must further restrict the class of flows to assume that the closed orbits relate in some manner to the homology of the underlying manifold we define in sect 2 the class of homology proper flows such a flow has the property that closed orbits of large period lie in large homology classes in sect 7 we show that a homology proper axiom a no cycles flow does satisfy a lefschetz type formula that relates invariants of the closed orbits to a manifold invariant this formula is closely related to franks study of smale flows on s 3 in which the linking numbers of closed orbits are used to compute the alexander polynomial of a certain link indeed the manifold invariant used in sect 7 is a close analogue of an alexander polynomial that we call the alexander

regularized liml for many instruments the use of many moment conditions improves the asymptotic efficiency of the instrumental variables estimators however in finite samples the inclusion of an excessive number of moments increases the bias to solve this problem we propose regularized versions of the limited information maximum likelihood liml based on three different regularizations tikhonov landweber fridman and principal components our estimators are consistent and asymptotically normal under heteroskedastic error moreover they reach the semiparametric efficiency bound assuming homoskedastic error we show that the regularized liml estimators possess finite moments when the sample size is large enough the higher order expansion of the mean square error mse shows the dominance of regularized liml over regularized two staged least squares estimators we devise a data driven selection of the regularization parameter based on the approximate mse a monte carlo study and two empirical applications illustrate the relevance of our estimators

the zeta functions of ruelle and selberg for hyperbolic manifolds with cusps in this paper we study the ruelle zeta function and the selberg zeta functions attached to the fundamental representations for real hyperbolic manifolds with cusps in particular we show that they have meromorphic extensions to mathbb c and satisfy functional equations we also derive the order of the singularity of the ruelle zeta function at the origin to prove these results we completely analyze the weighted unipotent orbital integrals on the geometric side of the selberg trace formula when test functions are defined for the fundamental representations

matrix algebra for higher order moments abstract a large part of statistics is devoted to the estimation of models from the sample covariance matrix the development of the statistical theory and estimators has been greatly facilitated by the introduction of special matrices such as the commutation matrix and the duplication matrix and the corresponding matrix algebra some more extensive models require however estimation based on higher order moments typically third and fourth order moments an example is the popular kenny judd model that includes interactions between latent variables this paper introduces some special matrices that can be used to simplify the model expressions for third fourth and higher order moments gives some relationships between these matrices and related matrices and gives some formulas for kronecker products of three and four matrices the theory is applied to derive convenient expressions for third and fourth order moments of some structural equation models

analytic torsion versus reidemeister torsion on hyperbolic 3 manifolds with cusps for a non compact hyperbolic 3 manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of mathrm sl 2 mathbb c to the corresponding reidemeister torsion while the analytic torsion is a spectral invariant of the manifold the reidemeister torsion is of combinatorial nature our proof rests on an expression of the analytic torsion in terms of special values of ruelle zeta functions as well as on recent work of pere menal ferrer and joan porti

forms on vector bundles over hyperbolic manifolds and the trace anomaly we study gauge theories based on abelian p forms on real compact hyperbolic manifolds an explicit formula for the trace anomaly corresponding to skew symmetric tensor fields is obtained by using zeta function regularization and the trace tensor kernel formula explicit exact and numerical values of the anomaly for p forms of order up to p 4 in spaces of dimension up to n 10 are then calculated

analytic torsion and ruelle zeta functions for hyperbolic manifolds with cusps abstract in this paper we derive a relationship of the leading coefficient of the laurent expansion of the ruelle zeta function at s 0 and the analytic torsion for hyperbolic manifolds with cusps here the analytic torsion is defined by a certain regularized trace following melrose r b melrose the atiyah patodi singer index theorem res notes math vol 4 a k peters ltd wellesley ma 1993 this extends the result of fried which was proved for the compact case in d fried analytic torsion and closed geodesics on hyperbolic manifolds invent math 84 3 1986 523 540 to a noncompact case

nonparametric identification and semiparametric estimation of classical measurement error models without side information virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information e g validation data known error distributions repeated measurements or instruments in contrast we establish that the fully nonparametric classical errors in variables model is identifiable from data on the regressor and the dependent variable alone unless the model takes a very specific parametric form this parametric family includes but is not limited to the linear specification with normally distributed variables as a well known special case this result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions assumptions our approach can handle both monotone and nonmonotone specifications provided the latter oscillate a finite number of times given that the very specific unidentified parametric functional form is arguably the exception rather than the rule this identification r

a class of orlicz sobolev spaces with applications to variational problems involving nonlinear hill s equations necessary and sufficient conditions are proved for a b 2 young function g with independent variable t to be convex resp concave in t2 in terms of inequalities between the second derivative of g and the first derivative of its legendre transform g with independent variable s it is then proven that a young function g is convex resp concave in t2 if and only if g is concave resp convex in s2 these results along with another set of inequalities for functions g convex resp concave in t2 allow the proof of the uniform convexity and thereby of the reflexivity with respect to luxemburg s norm f g inf k 0 d g f k 1 of the orlicz space lg over an open domain rn with lebesgue measure d when applied to g t t pp and g s s p p with p 1 p 1 1 the preceding results lead to the shortest proof to date of two clarkson s inequalities and of the reflexivity of lp spaces for 1 p finally some of these results are used to solve by direct methods variational problems associated with the existence question of periodic orbits for a class of nonlinear hill s equations these variational problems are formulated on suitable orlicz sobolev spaces wmlg and thereby allow for nonlinear terms which may grow faster than any power of the variable

negative orlicz sobolev norms and strongly nonlinear systems in fluid mechanics abstract we prove a version of the negative norm theorem in orlicz sobolev spaces a study of boundedness properties of the bogovski operator between orlicz spaces is a crucial step of independent interest in our approach applications to the problem of pressure reconstruction for non newtonian fluids governed by constitutive laws which are not necessarily of power type are presented a key inequality for a numerical analysis of the underlying elliptic system is also derived

regressor diagnostics for the classical errors in variables model abstract a series of diagnostics are developed which can be used to probe the sensitivity of regression coefficient estimates to measurement error in each regressor when all the regressors may be measured with error the diagnostics are based on the large sample properties of the classical errors in variables model the diagnostics provide information about the bounds on the measurement error variances of the regressors needed to bound any coefficient to a desired interval algorithms to compute the diagnostics are provided and the use of the diagnostics is illustrated in an example

simulated minimum distance estimation of dynamic models with errors in variables abstract empirical analysis often involves using inexact measures of the predictors suggested by economic theory the bias created by the correlation between the mismeasured regressors and the error term motivates the need for instrumental variable estimation this paper considers a class of estimators that can be used in dynamic models with measurement errors when external instruments may not be available or are weak the idea is to exploit the relation between the parameters of the model and the least squares biases in cases when the latter are not analytically tractable a special algorithm is designed to simulate the model without completely specifying the processes that generate the latent predictors the proposed estimators perform well in simulations of the autoregressive distributed lag model the methodology is used to estimate the long run risks model

errors in variables in linear systems this paper extends the simple errors in variable bound to the setting of systems of equations both diagonal and nondiagonal measurement error covariance matrices are considered in the nondiagonal case the analogue of the simple errors in variable interval of estimates is an ellipsoid with diagonal equal to the line segment connecting the direct least squares with a two stage least squares estimate for the diagonal case the set of estimates under some conditions must lie within the convex hull of 2k points

higher moment estimators for linear regression models with errors in the variables abstract this paper proposes consistent instrumental variable estimators for linear regression models with errors in the variables that require no extraneous information these estimators are based on sample moments of order higher than two while similar estimators proposed previously in the literature seem to be quite erratic our experimental f findings suggest that our estimators perform better than ordinary least squares estimators in terms of root mean squared errors and also in terms of size of type i errors of standard tests in many typical situations of economic analyses tests for the presence of errors in the variables are also described

modeling discrete choice with response error food stamp participation abstract validation of food stamp program participation by marquis and moore revealed net bias of 13 in mean estimates of participation in the 1984 survey of income and program participation we extend the analysis incorporating demographic and economic covariates in models for underreporting and overreporting we use the resulting models of response error to refine estimates of participation models using pseudo maximum likelihood estimation methods we find that the probability of underreporting rises with increased family income estimates of the participation model indicate the presence of substantial bias in income and asset related parameters compared to values obtained without incorporating response error

l2 index and the selberg trace formula abstract a method is developed for computing the l 2 index of a locally symmetric elliptic differential operator d acting on a locally symmetric manifold m g k with g semisimple of real rank one and of finite co volume based on applying the selberg trace formula to the difference of the two heat kernels associated to d the applications include an extension of the osborne warner multiplicity formula to certain non integrable discrete series derived from the l 2 spinor formula and showing the existence in some cases of non invariant l 2 cohomology classes in the middle dimension via the l 2 signature formula

on a theorem of osborne and warner multiplicities in the cuspidal spectrum osborne and warner have given a formula for the multiplicity of an integrable discrete series representation in l2 g when g is real rank one semi simple lie group and is a discrete subgroup of co finite volume we simplify and evaluate this formula to show that for most g as above the multiplicity is the formal degree of the representation times the volume of g when it is not we give a simple interpretation of the difference

differentiability properties of functions from higher order orlicz sobolev spaces abstract we analyze pointwise differentiability properties of functions from local orlicz sobolev spaces w loc m a on an open subset of r n n 2 a necessary and sufficient condition on the order of differentiation m and on the young function a is exhibited for any function in w loc m a to admit a differential of order m a e in an optimal approximate differentiability property in integral and norm form is established when such a condition fails

estimates for certain orlicz sobolev capacities of an euclidean ball abstract we calculate certain orlicz sobolev capacities of an euclidian n dimensional ball

partial identification of probability distributions with misclassified data abstract this paper addresses the problem of data errors in discrete variables when data errors occur the observed variable is a misclassified version of the variable of interest whose distribution is not identified inferential problems caused by data errors have been conceptualized through convolution and mixture models this paper introduces the direct misclassification approach the approach is based on the observation that in the presence of classification errors the relation between the distribution of the true but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations in which the coefficient matrix is the matrix of misclassification probabilities formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities such information can have strong identifying power the direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest a method for estimating the identification regions and construct their confidence sets is given and illustrated with an empirical analysis of the distribution of pension plan types using data from the health and retirement study

bounding the effects of measurement error in regressions involving dichotomous variables abstract in a multiple regression involving dichotomous independent variables the effects of measurement error in the dichotomous variables is analyzed unlike the case of classical i e white noise measurement error the measurement error in a dichotomous variable must be correlated with the true variable and any other variables correlated with the true variable nonetheless it is shown that the results for the classical errors in variables model can be used to analyze the implications of measurement error in dichotomous variables it is shown how the bounding procedure developed by klepper and leamer 1984 for the classical errors in variables model can be adapted to bound the coefficients when the regression contains mismeasured dichotomous variables the classical results are also used to analyze the inconsistency in least squares regression coefficient estimators computed from data on the mismeasured variables

errors in survey reports of earnings hours worked and hourly wages abstract using administrative records on earnings hours worked and hourly wages for hourly employees of a single manufacturing firm we found standard assumptions about errors in survey measures to be violated to varying extents errors are correlated with true scores and errors in reports of earnings and hours in different periods are generally positively correlated with one another particularly for reports given in a single interview although a high proportion of reporting errors are from an approximately normal distribution a small proportion comes from a distribution with a much greater variance and these cases often have considerable influence on estimates of relationships between variables

extensions of fisher information and stam s inequality we explain how the classical notions of fisher information of a random variable and fisher information matrix of a random vector can be extended to a much broader setting we also show that stam s inequality for fisher information and shannon entropy as well as the more generalized versions proved earlier by the authors are all special cases of more general sharp inequalities satisfied by random vectors the extremal random vectors which we call generalized gaussians contain gaussians as a limiting case but are noteworthy because they are heavy tailed

a regularization approach to the many instruments problem abstract this paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite in order to improve the small sample properties of standard instrumental variable iv estimators we propose three modified iv estimators based on three different ways of inverting the covariance matrix of the instruments these inverses involve a regularization or smoothing parameter it should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation we show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound higher order analysis of the mse reveals that the bias of the modified estimators does not depend on the number of instruments finally we suggest a data driven method for selecting the regularization parameter interestingly our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument

a characterization of minimal orlicz sobolev norms in the affine class abstract the orlicz sobolev norm is invariant only under rigid motions but is not invariant under volume preserving affine transformations on r n in this paper we will consider the orlicz sobolev norm in the affine class and characterize its minimum

extremal metrics for spectral functions of dirac operators in even and odd dimensions abstract let m n g be a closed smooth riemannian spin manifold and denote by its atiyah singer dirac operator we study the variation of riemannian metrics for the zeta function and functional determinant of 2 and prove finiteness of the morse index at stationary metrics and local extremality at such metrics under general i e not only conformal change of metrics in even dimensions which is also a new case for the conformal laplacian the relevant stability operator is of log polyhomogeneous pseudodifferential type and we prove new results of independent interest on the spectrum for such operators we use this to prove local extremality under variation of the riemannian metric which in the important example when m n g is the round n sphere gives a partial verification of branson s conjecture on the pattern of extremals thus det 2 has a local max max min min when the dimension is 4 k 4 k 1 4 k 2 4 k 3 respectively

optimal sobolev norms in the affine class abstract optimal sobolev norms under volume preserving affine transformations are considered it turns out that this minimal transform is equivalent to the p 2 fisher information matrix defined by lutwak lv yang and zhang furthermore some analytic inequalities regarding to the l p affine and l p sine energies for the optimal function are investigated

selberg zeta functions on odd dimensional hyperbolic manifolds of finite volume we study selberg zeta functions z s associated to locally homogeneous vector bundles over the unit sphere bundle of a complete odd dimensional hyperbolic manifold of finite volume we assume a certain condition on the fundamental group of the manifold a priori the selberg zeta functions are defined only for s in some right halfspace of c we will prove that for any locally homogeneous bundle the functions z s have a meromorphic continuation to c and we will give a complete description of their singularities in terms of spectral data of the underlying manifold our work generalizes results of bunke and olbrich to the non compact situation as an application of our results one can compare the normalized reidemeister torsions on hyperbolic 3 manifolds with cusps which were introduced by menal ferrer and porti to the corresponding regularized analytic torsions

proper posteriors from improper priors for an unidentified errors in variables model the problem considered is inference in a simple errors in variables model where consistent estimation is impossible without introducing additional exact prior information the probabilistic prior information required for bayesian analysis is found to be surprisingly light despirte the model s lack of identification a proper posterior is guaranteed for any bounded prior density including those representing improper priors this result is illustrated with the improper uniform prior which implies marginal posterior densities obtainable by integrating the likelihood function

eta invariant and selberg zeta function of odd type over convex co compact hyperbolic manifolds abstract we show meromorphic extension and give a complete description of the divisors of a selberg zeta function of odd type z o associated to the spinor bundle on an odd dimensional convex co compact hyperbolic manifold h 2 n 1 as a byproduct we do a full analysis of the spectral and scattering theory of the dirac operator on asymptotically hyperbolic manifolds we show that there is a natural eta invariant d associated to the dirac operator d over a convex co compact hyperbolic manifold h 2 n 1 and that exp i d z o 0 thus extending millson s formula to this setting under some assumption on the exponent of convergence of poincare series for the group we also define an eta invariant for the odd signature operator and we show that for schottky 3 dimensional hyperbolic manifolds it gives the argument of a holomorphic function which appears in the zograf factorization formula relating two natural kahler potentials for weil petersson metric on schottky space

heat kernels and super determinants of laplace operators on super riemann surfaces heat kernels of laplacians on superfields of arbitrary tensor weight on super riemann surfaces are constructed and are used to compute the super determinants of these operators in terms of the selberg super zeta function

the fried conjecture in small dimensions we study the twisted ruelle zeta function x s for smooth anosov vector fields x acting on flat vector bundles over smooth compact manifolds in dimension 3 we prove fried conjecture relating reidemeister torsion and x 0 in higher dimensions we show more generally that x 0 is locally constant with respect to the vector field x under a spectral condition as a consequence we also show fried conjecture for anosov flows near the geodesic flow on the unit tangent bundle of hyperbolic 3 manifolds this gives the first examples of non analytic anosov flows and geodesic flows in variable negative curvature where fried conjecture holds true

analytic and topological torsion for manifolds with boundary and symmetry letg be a finite group acting on a riemannian manifoldm by isometries we introduce analytic torsion an m m1 v r z repr g pl torsion pl m m1 v k1 rg poincare torsion pd m m1 v k1 rg and euler characteristic m m1 v repr g for m the disjoint union of m1 and m2 and v an equivariant coefficient system the analytic torsionis defined in terms of the spectrum of the laplace operator the pl torsionis based on the cellular chain complex and poincare torsionmeasures the failure of equivariant poincare duality in the pl setting which does hold in the analytic context denote by repr g the subgroup of repr g generated by the irreducible representations of real or complex type we define an isomorphism

spectral functions special functions and the selberg zeta function the functional determinant of an eigenvalue sequence as defined by zeta regularization can be simply evaluated by quadratures we apply this procedure to the selberg trace formula for a compact riemann surface to find a factorization of the selberg zeta function into two functional determinants respectively related to the laplacian on the compact surface itself and on the sphere we also apply our formalism to various explicit eigenvalue sequences reproducing in a simpler way classical results about the gamma function and the barnesg function concerning the latter our method explains its connection to the selberg zeta function and evaluates the related glaisher kinkelin constanta

some further results on the exact small sample properties of the instrumental variable estimator we present new results on the exact small sample distribution of the instrumental variable estimator in particular we compare the small sample distribution to the asymptotic distribution

bounding the effects of proxy variables on instrumental variables coefficients abstract we consider instrumental variables models in which one of the observed variables is a proxy for some unobserved true variable we seek the smallest correlation between the proxy and the unobserved true variable sufficient to guarantee that regardless of any other correlations involving unobserved variables or disturbances a coefficient s sign has not been reversed by substituting the proxy we derive exact solutions when the proxy is the dependent variable the endogenous explanatory variable whose coefficient is of concern some other endogenous explanatory variable or a solely instrumental variable for an exogenous explanatory proxy we derive either exact solutions or useful lower bounds

orlicz sobolev boundary trace embeddings we prove a sharp trace embedding theorem for orlicz sobolev spaces into orlicz spaces on the boundary an optimal trace embedding into more general rearrangement invariant spaces on the boundary is also established

weighted sobolev spaces and embedding theorems in the present paper we study embedding operators for weighted sobolev spaces whose weights satisfy the well known muckenhoupt a p condition sufficient conditions for boundedness and compactness of the embedding operators are obtained for smooth domains and domains with boundary singularities the proposed method is based on the concept of generalized quasiconformal homeomorphisms homeomorphisms with bounded mean distortion the choice of the homeomorphism type depends on the choice of the corresponding weighted sobolev space such classes of homeomorphisms induce bounded composition operators for weighted sobolev spaces with the help of these homeomorphism classes the embedding problem for non smooth domains is reduced to the corresponding classical embedding problem for smooth domains examples of domains with anisotropic holder singularities demonstrate the sharpness of our machinery comparatively with known results

analytic torsion and closed geodesics on hyperbolic manifolds pour une variete hyperbolique orientee fermee x et une representation orthogonale de 1 x on definit une fonction zeta de type ruelle r s pour re s grand comme le produit sur les geodesiques closes premieres des facteurs det i exp sl ou l est la longueur de on continue analytiquement r s et on calcule son terme principal en s 0

vanishing exponential integrability for functions whose gradients belong to ln log e l α if the gradient of u x is nth power locally integrable on euclidean n space then the integral average over a ball b of the exponential of a constant multiple of u x ub n n 1 ub average of u over b tends to 1 as the radius of b shrinks to zero for quasi almost all center points this refines a result of n trudinger 1967 we prove here a similar result for the class of gradients in ln log e l 0 n 1 the results depend on a capacitary strong type inequality for these spaces

minimum distance estimation of the errors in variables model using linear cumulant equations abstract we consider a multiple mismeasured regressor errors in variables model we develop closed form minimum distance estimators from any number of estimating equations which are linear in the third and higher cumulants of the observable variables using the cumulant estimators alters qualitative inference relative to ordinary least squares in two applications related to investment and leverage regressions the estimators perform well in monte carlos calibrated to resemble the data from our applications although the cumulant estimators are asymptotically equivalent to the moment estimators from erickson and whited 2002 the finite sample performance of the cumulant estimators exceeds that of the moment estimators

estimating a class of triangular simultaneous equations models without exclusion restrictions this paper provides a control function estimator to adjust for endogeneity in the triangular simultaneous equations model where there are no available exclusion restrictions to generate suitable instruments our approach is to exploit the dependence of the errors on exogenous variables e g heteroscedasticity to adjust the conventional control function estimator the form of the error dependence on the exogenous variables is subject to restrictions but is not parametrically specified in addition to providing the estimator and deriving its large sample properties we present simulation evidence which indicates the estimator works well

bounding mean regressions when a binary regressor is mismeasured in this paper i examine identification and estimation of mean regression models when a binary regressor is mismeasured i prove that bounds for the model parameters are identified and provide simple estimators which are consistent and asymptotically normal when stronger prior information about the probability of misclassification is available the bounds can be made tighter again a simple estimator for these cases is provided all results apply to parametric and nonparametric models the paper concludes with a short empirical example

consistent noisy independent component analysis we study linear factor models under the assumptions that factors are mutually independent and independent of errors and errors can be correlated to some extent under the factor non gaussianity second to fourth order moments are shown to yield full identification of the matrix of factor loadings we develop a simple algorithm to estimate the matrix of factor loadings from these moments we run monte carlo simulations and apply our methodology to data on cognitive test scores and financial data on stock returns

identification and estimation of nonlinear models with misclassification error using instrumental variables a general solution abstract this paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables the misclassification error is allowed to be correlated with all the explanatory variables in the model it is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns such a claim requires solving a complicated nonlinear system of equations this paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system the solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions therefore the latent model is nonparametrically identifiable and directly estimable using instrumental variables the results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities an alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting the nonparametric identification in this paper directly leads to a n consistent semiparametric estimator the monte carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data

measurement of higher education in the census and current population survey we examine measurement error in the reporting of higher education in the 1990 decennial census and the post 1991 current population survey cps we document that measurement error in the reporting of higher education is prevalent in census data further these errors violate models of classical measurement error in important ways the level of education is consistently reported as higher than it is errors are not mean 0 errors in the reporting of education are correlated with covariates that appear in earnings regressions and errors in the reporting of education appear correlated with the error term in a model of earnings determination thus neither well known results on classical measurement error nor recent models of nonclassical measurement error are likely valid when using census and cps data we find some evidence that the measurement error is lower in the cps than in the census presumably because first interviews are generally conducted in person

bounding parameters in a linear regression model with a mismeasured regressor using additional information this paper discusses a linear regression model with a mismeasured regressor in which the measurement error is correlated with both the latent variable and the regression error we use a linear structure to capture the correlation between the measurement error and the latent variable this paper shows that the variance of the latent variable is very useful for revealing information on the parameters which otherwise cannot be obtained with such a nonclassical measurement error the main result is that the finite bounds on the parameters can be found using the variance of the latent variable regardless of how severely the measurement error and the regression error are correlated if the mismeasured regressor contains enough information on the latent one this paper also discusses the special but interesting case of the latent variable being dichotomous in this case the mean of the latent variable may even reveal information on the correlation between the measurement error and the regression error all the bounds developed in the paper are tight