on the volume of the wiener sausage let w t varepsilon be the varepsilon wiener sausage i e the varepsilon neighborhood of the trace of the brownian motion up to time t it is shown that the results of donsker and varadhan on the behavior of e exp nu w t varepsilon nu 0 remain true if varepsilon depends on t and converges to 0 with a certain rate

nonparametric estimation in case of endogenous selection this paper addresses the problem of estimation of a nonparametric regression function from selectively observed data when selection is endogenous our approach relies on independence between covariates and selection conditionally on potential outcomes endogeneity of regressors is also allowed for in the exogenous and endogenous case consistent two step estimation procedures are proposed and their rates of convergence are derived pointwise asymptotic distribution of the estimators is established in addition bootstrap uniform confidence bands are obtained finite sample properties are illustrated in a monte carlo simulation study and an empirical illustration

some mixed hodge structures on l 2 cohomology groups of coverings of kahler manifolds we give methods to compute l 2 cohomology groups of a covering manifold obtained by removing the pullback of a normal crossing divisor to a covering of a compact kahler manifold we prove that in suitable quotient categories these groups admit natural mixed hodge structure whose graded pieces are given by the expected gysin maps

invariants de von neumann des faisceaux analytiques coherents in order to study the group of l 2 holomorphic sections of the pull back to the universal covering space of an holomorphic vector bundle on a compact complex manifold it would be convenient to have a cohomological formalism generalizing atiyah s l 2 index theorem in eys99 such a formalism is proposed in a restricted context to each coherent analytic sheaf cal f on a n dimensionnal smooth projective variety x n and each galois infinite unramified covering pi tilde x to x whose galois group is denoted by gamma l 2 cohomology groups denoted by h q 2 tilde x cal f are attached such that

applied nonparametric instrumental variables estimation instrumental variables are widely used in applied econometrics to achieve identification and carry out estimation and inference in models that contain endogenous explanatory variables in most applications the function of interest e g an engel curve or demand function is assumed to be known up to finitely many parameters e g a linear model and instrumental variables are used identify and estimate these parameters however linear and other finite dimensional parametric models make strong assumptions about the population being modeled that are rarely if ever justified by economic theory or other a priori reasoning and can lead to seriously erroneous conclusions if they are incorrect this paper explores what can be learned when the function of interest is identified through an instrumental variable but is not assumed to be known up to finitely many parameters the paper explains the differences between parametric and nonparametric estimators that are important for applied research describes an easily implemented nonparametric instrumental variables estimator and presents empirical examples in which nonparametric methods lead to substantive conclusions that are quite different from those obtained using standard parametric estimators

random walks in a random field of decaying traps we study random walks on d d 1 containing traps subject to decay the initial trap distribution is random in the course of time traps decay independently according to a given lifetime distribution we derive a necessary and sufficient condition under which the walk eventually gets trapped with probability 1 we prove bounds and asymptotic estimates for the survival probability as a function of time and for the average trapping time these are compared with some well known results for nondecaying traps

moderate deviations for the volume of the wiener sausage for a 0 let wa t be the a neighbourhood of standard brownian motion in rd starting at 0 and observed until time t it is well known that elwa t l ikat t oc for d 3 with kea the newtonian capacity of the ball with radius a we prove that lm t d 2 d log p wa t l oc this is markedly different from the optimal strategy for large deviations iwa t i 5 is nonanalytic at some critical point in 0 kia above which it follows a pure power law this crossover is associated with a collapse transition in the optimal strategy we also derive the analogous moderate deviation result for d 2 in this case eiwa t 2wrt logt t oc and we prove that

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

tikhonov regularization for nonparametric instrumental variable estimators abstract we study a tikhonov regularized tir estimator of a functional parameter identified by conditional moment restrictions in a linear model with both exogenous and endogenous regressors the nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivatives after showing its consistency in the sobolev norm and uniform consistency under an embedding condition we derive the expression of the asymptotic mean integrated square error and the rate of convergence the optimal value of the regularization parameter is characterized in two examples we illustrate our theoretical findings and the small sample properties with simulation results finally we provide an empirical application to estimation of an engel curve and discuss a data driven selection procedure for the regularization parameter

testing a parametric model against a nonparametric alternative with identification through instrumental variables this paper is concerned with inference about a function g that is identified by a conditional moment restriction involving instrumental variables the paper presents a test of the hypothesis that g belongs to a finite dimensional parametric family against a nonparametric alternative the test does not require nonparametric estimation of g and is not subject to the ill posed inverse problem of nonparametric instrumental variables estimation under mild conditions the test is consistent against any alternative model in large samples its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is o n 1 2 where n is the sample size in monte carlo simulations the finite sample power of the new test exceeds that of existing tests

survival asymptotics for brownian motion in a poisson field of decaying traps let w t be the wiener sausage in mathbb r d that is the a neighborhood for some a 0 of the path of brownian motion up to time t it is shown that integrals of the type int t 0 nu s d w s with t rightarrow nu t nonincreasing and nu t sim nu t gamma t rightarrow infty have a large deviation behavior similar to that of w t established by donsker and varadhan such a result gives information about the survival asymptotics for brownian motion in a poisson field of spherical traps of radius a when the traps decay independently with lifetime distribution nu t nu 0 there are two critical phenomena i in d geq 3 the exponent of the tail of the survival probability has a crossover at gamma 2 d ii in d geq 1 the survival strategy changes at time s lbrack gamma 1 gamma rbrack t provided gamma 1 2 d 1 respectively gamma 2 d d geq 2

goodness of fit tests based on series estimators in nonparametric instrumental regression this paper proposes several tests of restricted specification in nonparametric instrumental regression based on series estimators test statistics are established that allow for tests of the general model against a parametric or nonparametric specification as well as a test of exogeneity of the vector of regressors the tests asymptotic distributions under correct specification are derived and their consistency against any alternative model is shown under a sequence of local alternative hypotheses the asymptotic distributions of the tests are derived moreover uniform consistency is established over a class of alternatives whose distance to the null hypothesis shrinks appropriately as the sample size increases a monte carlo study examines finite sample performance of the test statistics

constistent specification testing via nonparametric series regression this paper proposes two consistent one sided specification tests for parametric regression models one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values the other based on the difference in sums of squared residuals between the parametric and nonparametric models we estimate the nonparametric model by series regression the new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate n 1 2 under misspecification while avoiding weighting sample splitting and non nested testing procedures used elsewhere in the literature asymptotically our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regression model are zero where the dependent variable is the residual from the parametric model and the series terms are functions of the explanatory variables chosen so as to support nonparametric estimation of a conditional expectation we specifically consider fourier series and regression splines and present a monte carlo study of the finite sample performance of the new tests in comparison to consistent tests of bierens 1990 eubank and spiegelman 1990 jayasuriya 1990 wooldridge 1992 and yatchew 1992 the results show the new tests have good power performing quite well in some situations we suggest a joint bonferroni procedure that combines a new test with those of bierens and wooldridge to capture the best features of the three approaches

an index theorem on open manifolds ii on decrit et on applique un nouveau theoreme d indice pour des operateurs elliptiques sur certaines varietes non compactes on calcule un indice a valeur reelle pour des operateurs de type dirac sur des varietes non compactes de geometrie bornee

localization of a two dimensional random walk with an attractive path interaction we consider an ordinary symmetric continuous time random walk on the two dimensional lattice mathbb z 2 the distribution of the walk is transformed by a density which discounts exponentially the number of points visited up to time t this introduces a self attracting interaction of the paths we study the asymptotic behavior for t rightarrow infty it turns out that the displacement is asymptotically of order t 1 4 the main technique for proving the result is a refined analysis of large deviation probabilities a partial discussion is given also for higher dimensions

random media and eigenvalues of the laplacian let be a fixed number 1 we remove m balls of centersw1 w m beta with the same radius m from a bounded domain inr3 we consider the asymptotic behaviour of thekth eigenvalue of the laplacian in omega backslash overline m beta balls under the dirichlet condition as a random variable on a probability space w 1 w m beta in omega m beta whenm

inference in nonparametric instrumental variables with partial identification this paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework we construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction the same test statistic can be employed under identification in which case the hypothesis is whether the true model satisfies the posited property an almost sure consistent bootstrap procedure is provided for obtaining critical values possible applications include testing for semiparametric specifications as well as building confidence regions for certain functionals on the identified set as an illustration we obtain confidence intervals for the level and slope of brazilian fuel engel curves a monte carlo study examines finite sample performance

nonparametric instrumental regression the focus of this paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions that stem from a structural econometric model e y f z w 0 and involve endogenous variables y and z and instruments w the function f is the solution of an ill posed inverse problem and we propose an estimation procedure based on tikhonov regularization the paper analyzes identification and overidentification of this model and presents asymptotic properties of the estimated nonparametric instrumental regression function

semi nonparametric iv estimation of shape invariant engel curves this paper studies a shape invariant engel curve system with endogenous total expenditure in which the shape invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric engel curves we focus on the identification and estimation of both the nonparametric shapes of the engel curves and the parametric specification of the demographic scaling parameters the identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions allowing for endogeneity we establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support root n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of low level sufficient conditions our empirical application using the u k family expenditure survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of engel curves

lifschitz tail and wiener sausage ii the present paper is a continuation of 23 we present here two examples of situations where the method developed in 23 applies the first example is that of a periodic diffusion z in r n 1 with generator l isia dj where a is a c2 z periodic elliptic matrix we consider the wiener sausage w u0 c u i z c where c is a nonpolar compact subset of r for instance a closed ball or disc in r if a denotes the constant matrix of homogenized coefficients of the periodic diffusion see 1 i we show that

specification testing in nonparametric instrumental variable estimation abstract in nonparametric instrumental variable estimation the function being estimated is the solution to an integral equation a solution may not exist if for example the instrument is not valid this paper discusses the problem of testing the null hypothesis that a solution exists against the alternative that there is no solution we give necessary and sufficient conditions for existence of a solution and show that uniformly consistent testing of an unrestricted null hypothesis is not possible uniformly consistent testing is possible however if the null hypothesis is restricted by assuming that any solution to the integral equation is smooth many functions of interest in applied econometrics including demand functions and engel curves are expected to be smooth the paper presents a statistic for testing the null hypothesis that a smooth solution exists the test is consistent uniformly over a large class of probability distributions of the observable random variables for which the integral equation has no smooth solution the finite sample performance of the test is illustrated through monte carlo experiments

testing conditional moment restrictions let x z be a pair of observable random vectors we construct a new smoothed empirical likelihood based test for the hypothesis e g z x 0 w p 1 where g is a vector of known functions and an unknown finite dimensional parameter we show that the test statistic is asymptotically normal under the null hypothesis and derive its asymptotic distribution under a sequence of local alternatives furthermore the test is shown to possess an optimality property in large samples simulation evidence suggests that it also behaves well in small samples