on completeness and consistency in nonparametric instrumental variable models this paper provides positive testability results for the identification condition in a nonparametric instrumental variable model known as completeness and it links the outcome of the test to properties of an estimator of the structural function in particular i show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator this is the case for a large class of complete distributions as well as certain incomplete distributions as a byproduct the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself

end to end distance from the green s function for a hierarchical self avoiding walk in four dimensions in bei92 we introduced a levy process on a hierarchical lattice which is four dimensional in the sense that the green s function for the process equals frac 1 x 2 if the process is modified so as to be weakly self repelling it was shown that at the critical killing rate mass squared c the green s function behaves like the free one now we analyze the end to end distance of the model and show that its expected value grows as a constant times sqrt t log frac 1 8 t left 1 o left frac log log t log t right right which is the same law as has been conjectured for self avoiding walks on the simple cubic lattice 4 the proof uses inverse laplace transforms to obtain the end to end distance from the green s function and requires detailed properties of the green s function throughout a sector of the complex plane these estimates are derived in a companion paper bi02

regression discontinuity design with continuous measurement error in the running variable abstract since the late 90s regression discontinuity rd designs have been widely used to estimate local average treatment effects late when the running variable is observed with continuous measurement error identification fails assuming non differential measurement error we propose a consistent nonparametric estimator of the late when the discrepancy between the true running variable and its noisy measure is observed in an auxiliary sample of treated individuals and when there are treated individuals at any value of the true running variable two sided fuzzy designs we apply our method to estimate the effect of receiving unemployment benefits

identification and estimation of triangular simultaneous equations models without additivity this paper uses control variables to identify and estimate models with nonseparable multidimensional disturbances triangular simultaneous equations models are considered with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable also for any control variable identification results are given for quantile average and policy effects bounds are given when a common support assumption is not satisfied estimators of identified objects and bounds are provided and a demand analysis empirical example is given

the broken supersymmetry phase of a self avoiding random walk we consider a weakly self avoiding random walk on a hierarchical lattice ind 4 dimensions we show that for choices of the killing ratea less than the critical valueacthe dominant walks fill space which corresponds to a spontaneously broken supersymmetry phase we identify the asymptotic density to which walks fill space a to be a supersymmetric order parameter for this transition we prove that a ac a log ac a 1 2 asa ac which is mean field behavior with logarithmic corrections as expected for a system in its upper critical dimension

on the testability of identification in some nonparametric models with endogeneity this paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity the first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions these conditions are typically referred to as completeness conditions the second and third hypothesis testing problems we examine concern testing for identification directly in some nonparametric models with endogeneity involving quantile independence restrictions for each of these hypothesis testing problems we provide conditions under which any test will have power no greater than size against any alternative in this sense we conclude that no nontrivial tests for these hypothesis testing problems exist publication abstract

event history graphs for censored survival data a compact graphical device for combining survival and time varying covariate information is proposed the proposed graph contains the kaplan meier estimator for right censored data and a simultaneous display of the behaviour of time dependent covariate s and the lifetime for each subject in the sample the observed levels of time dependent covariates are possibly subjected to an initial dimension reduction or smoothing step to produce a continuous covariate function values of this function are plotted on a horizontal bar for the length of the lifetime of the subject covariate information for censored data is also incorporated the union of the horizontal bars forms the kaplan meier estimator of the survival function our graphical method is implemented with a new s plus function and demonstrated in several applications copyright 2001 john wiley sons ltd

green s function for a hierarchical self avoiding walk in four dimensions this is the second of two papers on the end to end distance of a weakly self repelling walk on a four dimensional hierarchical lattice it completes the proof that the expected value grows as a constant times sqrt t log frac 1 8 t left 1 o left frac log log t log t right right which is the same law as has been conjectured for self avoiding walks on the simple cubic lattice 4 apart from completing the program in the first paper the main result is that the green s function is almost equal to the green s function for the markov process with no self repulsion but at a different value of the killing rate which can be accurately calculated when the interaction is small furthermore the green s function is analytic in in a sector in the complex plane with opening angle greater than

survival probabilities with time dependent treatment indicator quantities and non parametric estimators the landmark and simon and makuch non parametric estimators of the survival function are commonly used to contrast the survival experience of time dependent treatment groups in applications such as stem cell transplant versus chemotherapy in leukemia however the theoretical survival functions corresponding to the second approach were not clearly defined in the literature and the use of the simon and makuch estimator was criticized in the biostatistical community here we review the landmark approach showing that it focuses on the average survival of patients conditional on being failure free and on the treatment status assessed at the landmark time we argue that the simon and makuch approach represents counterfactual survival probabilities where treatment status is forced to be fixed the patient is thought as under chemotherapy without possibility to switch treatment or as under transplant since the beginning of the follow up we argue that the simon and makuch estimator leads to valid estimates only under the markov assumption which is however less likely to occur in practical applications this motivates the development of a novel approach based on time rescaling which leads to suitable estimates of the counterfactual probabilities in a semi markov process the method is also extended to deal with a fixed landmark time of interest

nonparametric instrumental variables estimation of a quantile regression model we consider nonparametric estimation of a regression function that is identified by requiring a specified quantile of the regression error conditional on an instrumental variable to be zero the resulting estimating equation is a nonlinear integral equation of the first kind which generates an ill posed inverse problem the integral operator and distribution of the instrumental variable are unknown and must be estimated nonparametrically we show that the estimator is mean square consistent derive its rate of convergence in probability and give conditions under which this rate is optimal in a minimax sense the results of monte carlo experiments show that the estimator behaves well in finite samples

finite sample confidence envelopes for shape restricted densities a conservative finite sample simultaneous confidence envelope for a density can be found by solving a finite set of finite dimensional linear programming problems if the density is known to be monotonic or to have at most k modes relative to a positive weight function the dimension of the problems is at most n log n 1 3 where n is the number of observations the linear programs find densities attaining the largest and smallest values at a point among cumulative distribution functions in a confidence set defined using the assumed shape restriction and differences between the empirical cumulative distribution function evaluated at a subset of the observed points bounds at any finite set of points can be extrapolated conservatively using the shape restriction the optima are attained by densities piecewise proportional to the weight function with discontinuities at a subset of the observations and at most five other points if the weight function is constant and the density satisfies a local lipschitz condition with exponent the width of the bounds converges to zero at the optimal rate log n n 1 2 outside every neighborhood of the set of modes if a bandwidth parameter is chosen correctly the integrated width of the bounds converges at the same rate on intervals where the density satisfies a lipschitz condition if the intervals are strictly within the support of the density the approach also gives algorithms to compute confidence intervals for the support of monotonic densities and for the mode of unimodal densities lower confidence intervals on the number of modes of distribution and conservative tests of the hypothesis of k modality we use the method to compute confidence bounds for the probability density of aftershocks of the 1984 morgan hill ca earthquake assuming aftershock times are an inhomogeneous poisson point process with decreasing intensity

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

prevalence a translation invariant almost every on infinite dimensional spaces we present a measure theoretic condition for a property to hold almost everywhere on an infinite dimensional vector space with particularemphasis on function spaces such as c k and l p like the concept of lebesgue almost every on an infinite dimensional spaces our notion of prevalence is translation invariant instead of using a specific measure on the entire space we define prevalence in terms of the class of all probability measures with compact support prevalence is a more appropriate condition than the topological concepts of open and dense or generic when one desires a probabilistic result on the likelihood of a given property on a function space

direct instrumental nonparametric estimation of inverse regression functions abstract this paper treats the estimation of the inverse g 1 of a monotonic function g satisfying e y g x w 0 where x w is continuously distributed using instrumental restrictions many parameters of interest in econometrics can be expressed as inverses of functions satisfying such a conditional moment as far as i know consistent estimators are available only if g x e y x which precludes endogenous models this and other technical concerns motivates a methodology for estimating g 1 in one step from the data when w contains components excluded from x the presented estimator achieves this objective by identifying g 1 as the solution of a nonlinear integral equation whose sample analog can be estimated nonparametrically the existence of a well behaved joint density function for x w produces an ill posed problem namely the solution is discontinuous in the data to solve this the estimator is regularized with the tikhonov technique if g 1 is smooth in a certain sense then the mse rate of convergence in a global metric is equal to n r 2 r 1 where is a continuous function with 0 0 and r 1 denotes the number of partial derivatives for the joint density of x w with respect to its second argument the analytical expression of depends on a link function characterizing the smoothness of g 1 this result holds for a broad class of link functions belonging to a suitable space

generalized reduced rank tests using the singular value decomposition we propose a novel statistic to test the rank of a matrix the rank statistic overcomes deficiencies of existing rank statistics like a kronecker covariance matrix for the canonical correlation rank statistic of anderson annals of mathematical statistics 1951 22 327 351 sensitivity to the ordering of the variables for the ldu rank statistic of cragg and donald journal of the american statistical association 1996 91 1301 1309 and gill and lewbel journal of the american statistical association 1992 87 766 776 a limiting distribution that is not a standard chi squared distribution for the rank statistic of robin and smith econometric theory 2000 16 151 175 usage of numerical optimization for the objective function statistic of cragg and donald journal of econometrics 1997 76 223 250 and ignoring the non negativity restriction on the singular values in ratsimalahelo 2002 rank test based on matrix perturbation theory unpublished working paper u f r science economique university de franche comte in the non stationary cointegration case the limiting distribution of the new rank statistic is identical to that of the johansen trace statistic

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals this paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables this is a nonparametric nonlinear instrumental variables iv problem we propose a class of penalized sieve minimum distance psmd estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space some of the psmd procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty others use large dimensional sieves with lower semicompact and or convex penalties we establish their consistency and the convergence rates in banach space norms such as a sup norm or a root mean squared norm allowing for possibly noncompact infinite dimensional parameter spaces for both mildly and severely ill posed nonlinear inverse problems our convergence rates in hilbert space norms such as a root mean squared norm achieve the known minimax optimal rate for the nonparametric mean iv regression we illustrate the theory with a nonparametric additive quantile iv regression we present a simulation study and an empirical application of estimating nonparametric quantile iv engel curves

injectivity of a class of integral operators with compactly supported kernels abstract injectivity of integral operators is related to completeness conditions of their corresponding kernel functions completeness provides a useful way of obtaining nonparametric identification in various models including nonparametric regression models with instrumental variables nonclassical measurement error models and auction models etc however the condition is quite abstract for empirical work and lacks a proper economic interpretation we rely on known results regarding the volterra equation to provide sufficient conditions for completeness conditions for densities with compact support our conditions include various smoothness assumptions and monotonously moving support assumptions on the kernel function of the operator we apply our results to establish nonparametric identification in nonparametric iv regression models nonclassical measurement error models and auction models with an accessible interpretation and without specific functional form restrictions

inference for parameters defined by moment inequalities using generalized moment selection the topic of this paper is inference in models in which parameters are defined by moment inequalities and or equalities the parameters may or may not be identified this paper introduces a new class of confidence sets and tests based on generalized moment selection gms gms procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative the power of gms tests is compared to that of subsampling m out of n bootstrap and plug in asymptotic pa tests the latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size in a uniform sense for the moment inequality equality model gms tests are shown to have asymptotic power that dominates that of subsampling m out of n bootstrap and pa tests subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of pa tests

weighted local regression and kernel methods for nonparametric curve fitting abstract weighted local regression a popular technique for smoothing scatterplots is shown to be asymptotically equivalent to certain kernel smoothers since both methods are local weighted averages of the data it is proved that in the fixed design regression model given a weighted local regression procedure with any weight function there is a corresponding kernel method such that the quotients of weights distributed by both methods tend uniformly to 1 as the number of observations increases to infinity it is demonstrated by examples that in some instances the weights are nearly the same for both methods even for small samples the asymptotic equivalence allows the derivation of the leading terms of the mean squared error and of the local limit distribution for weighted local regression further a close correspondence is found between the orders of the polynomial to be locally fitted in weighted local regression and the order number of vanishing moments of the kernel employed in the kernel smoot

examples of l2 complete and boundedly complete distributions abstract completeness and bounded completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non classical measurement error models however distributions that are known to be complete or boundedly complete are somewhat scarce in this paper we consider an l 2 completeness condition that lies between completeness and bounded completeness we construct broad nonparametric classes of distributions that are l 2 complete and boundedly complete the distributions can have any marginal distributions and a wide range of strengths of dependence examples of l 2 incomplete distributions also are provided

some results on the lil in banach space with applications to weighted empirical processes we examine the cluster set of s n a n for banach space valued random variables and investigate the relationship between the central limit theorem and the law of the iterated logarithm in this setting in the case of hilbert space valued random variables necessary and sufficient conditions are given for the law of the iterated logarithm some interesting examples are also included we then apply our results to weighted empiricals both in the supremum norm and the l 2 lbrack 0 1 rbrack norm

confidence bands in density estimation given a sample from some unknown continuous density f we construct adaptive confidence bands that are honest for all densities in a generic subset of the union of t holder balls 0 t r where r is a fixed but arbitrary integer the exceptional nongeneric set of densities for which our results do not hold is shown to be nowhere dense in the relevant holder norm topologies in the course of the proofs we also obtain limit theorems for maxima of linear wavelet and kernel density estimators which are of independent interest

adaptive nonparametric confidence sets we construct honest confidence regions for a hilbert space valued parameter in various statistical models the confidence sets can be centered at arbitrary adaptive estimators and have diameter which adapts optimally to a given selection of models the latter adaptation is necessarily limited in scope we review the notion of adaptive confidence regions and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation applications include the finite normal mean model the white noise model density estimation and regression with random design institute of mathematical statistics 2006

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

self avoiding walk enumeration via the lace expansion we introduce a new method for the enumeration of self avoiding walks based on the lace expansion we also introduce an algorithmic improvement called the two step method for self avoiding walk enumeration problems we obtain significant extensions of existing series on the cubic and hypercubic lattices in all dimensions d 3 we enumerate 32 step self avoiding polygons in d 3 26 step self avoiding polygons in d 4 30 step self avoiding walks in d 3 and 24 step self avoiding walks and polygons in all dimensions d 4 we analyze these series to obtain estimates for the connective constant and various critical exponents and amplitudes in dimensions 3 d 8 we also provide major extensions of 1 d expansions for the connective constant and for two critical amplitudes

critical φ 4 3 e the euclidean 4 3 e model in r3 corresponds to a perturbation by a 4 interaction of a gaussian measure on scalar fields with a covariance depending on a real parameter e in the range 0 e 1 for e 1 one recovers the covariance of a massless scalar field in r3 for e 0 4 is a marginal interaction for 0 e 0 sufficiently small there exists a non gaussian fixed point with one unstable direction of the renormalization group iterations we construct the stable critical manifold near this fixed point and prove that under renormalization group iterations the critical theories converge to the fixed point

pivotal statistics for testing structural parameters in instrumental variables regression we propose a novel statistic for testing the structural parameters in instrumental variables regression the statistic is straightforward to compute and has a limiting distribution that is pivotal with a degrees of freedom parameter that is equal to the number of tested parameters it therefore differs from the anderson rubin statistic whose limiting distribution is pivotal but has a degrees of freedom parameter that is equal to the number of instruments and the likelihood based wald likelihood ratio and lagrange multiplier statistics whose limiting distributions are not pivotal we analyze the relationship between the statistic and the concentrated likelihood of the structural parameters and show that its limiting distribution is not affected by weak instruments we discuss examples of the non standard shapes of the asymptotically pivotal confidence sets that can be constructed using the statistic and investigate its power properties to show its importance for practical purposes we apply the statistic to the angrist krueger 1991 data and find similar results as in staiger and stock 1997 this discussion paper has resulted in a publication in econometrica 2002 70 5 1781 1803

heterogeneity and selection in dynamic panel data abstract the data generating process dgp for generic dynamic panel data consists of a law of state dynamics g a selection or attrition rule h and an initial condition f i study nonparametric identifiability of this complete dgp g h f using short unbalanced panel data allowing for nonseparability between observed states and unobserved heterogeneity in each of g h and f for t 3 the dgp is identified by using a proxy variable for t 6 the three additional periods construct a proxy and thus the dgp is identified without an auxiliary variable

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

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

renormalization group analysis of the self avoiding paths on the d dimensional sierpinski gaskets notion of the renormalization group dynamical system the self avoiding fixed point and the critical trajectory are mathematically defined for the set of self avoiding walks on the d dimensional pre sierpinski gaskets n simplex lattices such that their existence imply the asymptotic behaviors of the self avoiding walks such as the existence of the limit distributions of the scaled path lengths of canonical ensemble the connectivity constant exponential growth of path numbers with respect to the length and the exponent for mean square displacement we apply the so defined framework to prove these asymptotic behaviors of the restricted self avoiding walks on the 4 dimensional pre sierpinski gasket

polymers in a weak random potential in dimension four rigorous renormalization group analysis correlation functions of the edwards model of polymers at weak coupling are defined and studied at the critical point in dimension four by a rigorous renormalization group method which validates at any order perturbative renormalization group results on their behaviour at large distances remainders are controlled by a new argument which enlarges the use of methods of constructive field theory to models of statistical physics

testing the rank and definiteness of estimated matrices with applications to factor state space and arma models abstract consider any consistent asymptotically normal estimate of an arbitrary rectangular or square matrix a this article derives an explicit test for the rank of a and a related test of semi definiteness of a potential applications include testing for identification of structural models testing for the number of state variables in state space models including tests for the order of autoregressive moving average arma processes consumer demand analysis applications and testing for the number of factors in factor analysis and related procedures the test is based on the gaussian elimination lower diagonal upper triangular ldu decomposition the test is illustrated with an empirical application to testing the order of arma processes

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

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

overidentification in regular models in the unconditional moment restriction model of hansen specification tests and more efficient estimators are both available whenever the number of moment restrictions exceeds the number of parameters of interest we show that a similar relationship between potential refutability of a model and existence of more efficient estimators is present in much broader settings specifically a condition we name local overidentification is shown to be equivalent to both the existence of specification tests with nontrivial local power and the existence of more efficient estimators of some smooth parameters in general semi nonparametric models under our notion of local overidentification various locally nontrivial specification tests such as hausman tests incremental sargan tests or optimally weighted quasi likelihood ratio tests naturally extend to general semi nonparametric settings we further obtain simple characterizations of local overidentification for general models of nonparametric conditional moment restrictions with possibly different conditioning sets the results are applied to determining when semi nonparametric models with endogeneity are locally testable and when nonparametric plug in and semiparametric two step gmm estimators are semiparametrically efficient examples of empirically relevant semi nonparametric structural models are presented

inferring the rank of a matrix abstract this paper considers methods of inference concerning the rank of matrix a based on an asymptotically normal estimate of and some identifiable specification for one such specification is 0 in which case one is interested in the rank of we first propose and examine the properties of a test of the hypothesis that the rank is of a given size against the alternative that the rank is larger we then look at the problem of estimating the rank of this matrix using model selection procedures and sequential hypothesis testing conditions for consistency of such procedures are obtained some economic applications are discussed and the various methods are compared in a monte carlo experiment

self avoiding walk in five or more dimensions i the critical behaviour we use the lace expansion to study the standard self avoiding walk in thed dimensional hypercubic lattice ford 5 we prove that the numbercn ofn step self avoiding walks satisfiescn a n where is the connective constant i e 1 and that the mean square displacement is asymptotically linear in the number of steps i e v 1 2 a bound is obtained forcn x the number ofn step self avoiding walks ending atx the correlation length is shown to diverge asymptotically like z 1 2 the critical two point function is shown to decay at least as fast as x 2 and its fourier transform is shown to be asymptotic to a multiple ofk 2 ask 0 i e 0 we also prove that the scaling limit is gaussian in the sense of convergence in distribution to brownian motion the infinite self avoiding walk is constructed in this paper we prove these results assuming convergence of the lace expansion the convergence of the lace expansion is proved in a companion paper

integrated square error properties of kernel estimators of regression functions weak laws of large numbers and central limit theorems are proyed for integrated square error of kernel estimators of regression functions the regressor is assumed to take values in rp and the regressand x to be real valued it is shown that in many cases integrated square error is asymptotically normally distributed and independent of the x sample as an application a test for the regression function such as that proposed by konakov is seen to be asymptotically independent of an arbitrary test based on the xsample the proofs involve martingale methods

logarithmic correction for the susceptibility of the 4 dimensional weakly self avoiding walk a renormalisation group analysis we prove that the susceptibility of the continuous time weakly self avoiding walk on mathbb z d in the critical dimension d 4 has a logarithmic correction to mean field scaling behaviour as the critical point is approached with exponent frac 1 4 for the logarithm the susceptibility has been well understood previously for dimensions d 5 using the lace expansion but the lace expansion does not apply when d 4 the proof begins by rewriting the walk two point function as the two point function of a supersymmetric field theory the field theory is then analysed via a rigorous renormalisation group method developed in a companion series of papers by providing a setting where the methods of the companion papers are applied together the proof also serves as an example of how to assemble the various ingredients of the general renormalisation group method in a coordinated manner