root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

asymptotic optimality of generalized cl cross validation and generalized cross validation in regression with heteroskedastic errors abstract the problem considered here is that of using a data driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter in contrast to other papers on this subject we consider models with heteroskedastic errors the results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators nearest neighbor estimators and local regression estimators among others generalized c l gc l cross validation cv and generalized cross validation gcv procedures are analyzed the gc l and cv criteria are shown to be asymptotically optimal under general conditions a feasible version of gc l however is available only in some applications the gcv criterion is found to be asymptotically optimal only under a condition that is satisfied in some applications but not in others for example it is satisfied in the nearest neighbor estimation context but not in the series estimation local regression estimation or model selection contexts thus the cv criterion is the only feasible criterion of the three that is asymptotically optimal under general conditions the proofs rely heavily on results of li 1987

finite size effects for the ising model on random graphs with varying dilution abstract we investigate the finite size corrections to the equilibrium magnetization of an ising model on a random graph with n nodes and n edges with 1 2 by conveniently rescaling the coupling constant the free energy is made extensive as expected the system displays a phase transition of the mean field type for all the considered values of at the transition temperature of the fully connected curie weiss model finite size corrections are investigated for different values of the parameter using two different approaches a replica based finite n expansion and a cavity method numerical simulations are compared with theoretical predictions the cavity based analysis is shown to agree better with numerics

functional coefficient instrumental variables models we consider estimation of nonparametric structural models under a functional coefficient representation for the regression function under this representation models are linear in the endogenous components with coefficients given by unknown functions of the predetermined variables a nonparametric generalization of random coefficient models the functional coefficient restriction is an intermediate approach between fully nonparametric structural models that are ill posed when endogenous variables are continuously distributed and partially linear models over which they have appreciable flexibility we propose two step estimators that use local linear approximations in both steps the first step is to estimate a vector of reduced forms of regression models and the second step is local linear regression using the estimated reduced forms as regressors our large sample results include consistency and asymptotic normality of the proposed estimators the high practical power of estimators is illustrated via both a monte carlo simulation study and an application to returns to education

efficiency of weighted average derivative estimators and index models weighted average derivatives are useful parameters for semiparametric index models and nonparametric demand analysis this paper gives efficiency results for average derivative estimators including formulating estimators that have high efficiency our analysis is carried out in three steps first we derive the efficiency bound for weighted average derivatives of conditional location functionals such as the conditional mean and median second we derive the efficiency bound for semiparametric index models where the location measure depends only on indices or linear combinations of the regressors third we compare the bound for index models with the asymptotic variance of weighted average derivative estimators of the index coefficients we characterize the form of the optimal weight function when the distribution of the regressors is elliptically symmetric in more general cases we discuss how to combine estimators with different weight functions to achieve efficiency we derive a general condition for approximate efficiency of pooled minimum chi square estimators for index model coefficients based on weighted average derivatives finally we discuss ways of selecting the type and number of weighting functions to achieve high efficiency

nonparametric identification under discrete variation this paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates the function delivers values of a discrete or continuous outcome and instruments may be discrete valued application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions the results are used to investigate the nonparametric identifying power of the quarter of birth instruments used in angrist and krueger s 1991 study of the returns to schooling

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

sieve instrumental variable quantile regression estimation of functional coefficient models abstract in this paper we consider sieve instrumental variable quantile regression ivqr estimation of functional coefficient models where the coefficients of endogenous regressors are unknown functions of some exogenous covariates we estimate the functional coefficients by the sieve ivqr technique and establish the uniform consistency and asymptotic normality of the estimators based on the sieve estimates we propose a nonparametric specification test for the constancy of the functional coefficients and study its asymptotic we conduct simulations to evaluate the finite sample behavior of our estimator and test statistic and apply our method to study the estimation of quantile engel curves

stochastic bifurcations in the nonlinear parallel ising model we investigate the phase transitions of a nonlinear parallel version of the ising model characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one this model arises in problems of opinion formation the mean field approximation shows chaotic oscillations by changing the couplings or the connectivity the spatial model shows bifurcations in the average magnetization similar to that seen in the mean field approximation induced by the change of the topology after rewiring short range to long range connection as predicted by the small world effect these coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins induced by long range couplings similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution degree of asynchronism of the updating we also examined the effects of inhomogeneity mixing ferromagnetic and antiferromagnetic coupling which induces an unexpected bifurcation diagram with a bubbling behavior as also happens for dilution

nonparametric iv estimation of local average treatment effects with covariates in this paper nonparametric instrumental variable estimation of local average treatment effects late is extended to incorporate covariates estimation of late is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models including covariates in the estimation of late is necessary when the instrumental variable itself is confounded such that the iv assumptions are valid only conditional on covariates previous approaches to handle covariates in the estimation of late relied on parametric or semiparametric methods in this paper a nonparametric estimator for the estimation of late with covariates is suggested that is root n asymptotically normal and efficient

output dead beat controllers and function dead beat observers for linear periodic discrete time systems in this paper two problems are considered that of finding a possibly dynamic linear periodic controller such that both the regulated output and the control input of a linear periodic discrete time system become and remain zero and that of designing a dead beat observer of a linear function of the state of the system for both these problems necessary and sufficient conditions for the existence of a solution are given and synthesis procedures of both the controller and the observer are provided by the sufficiency proofs such conditions are very simple and concise when expressed in terms of controllable and or unreconstructible states

estimation of average treatment effects with misclassification this paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified failure to account for misclassification is shown to result in attenua tion bias in the estimated treatment effect an identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect a discrete instrument suffices for nonparametric identification this paper provides conditions for identification and estimation of the av erage effect conditioned on covariates of a binary treatment program or pol icy on a scalar outcome when treatment may be misclassified more generally what is provided is an estimator of the effect of a binary regressor in a con ditional mean regression which may also include other regressors when the binary regressor is observed with error this equals the conditional average treatment effect given a weak unconfoundedness assumption misclassification occurs when a binary variable the treatment indicator is measured with error that is some units are reported to have received treat ment when they actually have not and vice versa for example in a returns to schooling analysis the outcome could be wages the binary variable could be attaining a college degree and misclassification could arise from school tran script reporting errors see e g kane and rouse 1995 and kane rouse and staiger 1999 bollinger 1996 considers misclassification of union status in wage equations if treatment is a job training program misclassification may arise if individuals assigned to the program fail to attend or if those not as signed obtain training elsewhere similarly for medical treatment individuals assigned a drug might fail to take it and those assigned a placebo might obtain treatment from another source more generally misclassification describes any binary variable that is sometimes mismeasured this paper first shows that misclassification causes attenuation bias in esti mated treatment effects analogous to the attenuation bias of classically mis measured variables in linear regression models additional assumptions on

semiparametric instrumental variable estimation of treatment response models this article introduces a new class of instrumental variable iv estimators for linear and nonlinear treatment response models with covariates the rationale for focusing on nonlinear models is that if the dependent variable is binary or limited or if the effect of the treatment varies with covariates a nonlinear model is appropriate in the spirit of roehrig econometrica 56 1988 433 identification is attained nonparametrically and does not depend on the choice of the parametric specification for the response function of interest one virtue of this approach is that it allows the researcher to construct estimators that can be interpreted as the parameters of a well defined approximation to a treatment response function under functional form misspecification in contrast to some usual iv models heterogeneity of treatment effects is not restricted by the identification conditions the ideas and estimators in this article are illustrated using iv to estimate the effects of 401 k retirement programs on savings

testing for separability in structural equations abstract separability is an important feature of structural equations as it implies the absence of unobservable heterogeneity of effects and has significant implications for identification and efficiency of estimation this paper provides a nonparametric test for separability in structural equations the test is based on a conditional independence test recently developed by huang et al 2013 building on consistent procedures of bierens 1982 1990 and stinchcombe and white 1998 the test is easy to implement and achieves n local power we apply our test to study interest rate elasticities of loan demand in microfinance and the impact of education on wages

varying coefficient panel data model in the presence of endogenous selectivity and fixed effects this paper considers a exible panel data sample selection model in which i the outcome equation is permitted to take a semiparametric varying coecient form to capture potential parameter heterogeneity in the relationship of interest ii both the outcome and parametric selection equations contain unobserved xed eects and iii selection is generalized to a polychotomous case we propose a two stage estimator given consistent parameter estimates from the selection equation obtained in the rst stage we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time the selection bias term is then asymptotically removed from the equation along with xed eects using kernel based weights the proposed estimator is consistent and asymptotically normal we rst investigate the nite sample properties of the estimator in a small monte carlo study and then apply it to study production technologies of u s retail credit unions from 2002 to 2006

the thermodynamics of the curie weiss model with random couplings we study the curie weiss version of an ising spin system with random positively biased couplings in particular the case where the couplings ij take the values one with probabilityp and zero with probability 1 p which describes the ising model on a random graph is considered we prove that ifp is allowed to decrease with the system sizen in such a way thatnp n asn then the free energy converges after trivial rescaling to that of the standard curie weiss model almost surely similarly the induced measures on the mean magnetizations converge to those of the curie weiss model generalizations of this result to a wide class of distributions are detailed

dummy endogenous variables in weakly separable models in this paper we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term the model is not required to be strictly increasing in the error term and the class of models considered includes limited dependent variable models such as discrete choice models conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions

ising model on networks with an arbitrary distribution of connections we find the exact critical temperature t c of the nearest neighbor ferromagnetic ising model on an equilibrium random graph with an arbitrary degree distribution p k we observe an anomalous behavior of the magnetization magnetic susceptibility and specific heat when p k is fat tailed or loosely speaking when the fourth moment of the distribution diverges in infinite networks when the second moment becomes divergent t c approaches infinity the phase transition is of infinite order and size effect is anomalously strong

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

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

instrumental variables estimators of nonparametric models with discrete endogenous regressors this paper discusses estimation of nonparametric models whose regressor vectors consist of a vector of exogenous variables and a univariate discrete endogenous regressor with finite support both identification and estimators are derived from a transform of the model that evaluates the nonparametric structural function via indicator functions in the support of the discrete regressor a two step estimator is proposed where the first step constitutes nonparametric estimation of the instrument and the second step is a nonparametric version of two stage least squares linear functionals of the model are shown to be asymptotically normal and a consistent estimator of the asymptotic covariance matrix is described for the binary endogenous regressor case it is shown that one functional of the model is a conditional on covariates local average treatment effect that permits both unobservable and observable heterogeneity in treatments finite sample properties of the estimators from a monte carlo simulation study illustrate the practicability of the proposed estimators

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

an elasticity can be estimated consistently without a priori knowledge of functional form we consider an open question in applied price theory without a priori knowledge of a firm s cost function or a consumer s indirect utility function is it possible to estimate price and substitution elasticities consistently by observing a demand system as the work of white 30 guilkey lovell and sickles 19 and others has shown ordinary flexible functional forms such as the translog cannot achieve this objective we find that if one is prepared to assume that elasticities of substitution cannot oscillate wildly over the region of interest then consistent estimation is possible using the fourier flexible form provided the number of fitted parameters increases as the number of observations increases this result obtains with any of the commonly used statistical methods as for example multivariate least squares maximum likelihood and three stage least squares it obtains if the number of fitted parameters is chosen adaptively by observing the data or chosen deterministically according to some fixed rule we approach the problem along the classical lines of estimability considerations as used in the study of less than full rank linear statistical models and thereby discover that the problem has a fascinating structure which we explore in detail

nonparametric identification of a binary random factor in cross section data suppose v and u are two independent mean zero random variables where v has an asymmetric distribution with two mass points and u has a symmetric distribution we show that the distributions of v and u are nonparametrically identifled just from observing the sum v u and provide a rate root n estimator we apply these results to the world income distribution to measure the extent of convergence over time where the values v can take on correspond to country types i e wealthy versus poor countries we also extend our results to include covariates x showing that we can nonparametrically identify and estimate cross section regression models of the form y g x d u where d is an unobserved

functional coefficient regression models for nonlinear time series abstract the local linear regression technique is applied to estimation of functional coefficient regression models for time series data the models include threshold autoregressive models and functional coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross validatory estimation for the expected forecasting errors the proposed methodology is data analytic and of sufficient flexibility to analyze complex and multivariate nonlinear structures without suffering from the curse of dimensionality the asymptotic properties of the proposed estimators are investigated under the mixing condition both simulated and real data examples are used for illustration

smooth coefficient estimation of a seemingly unrelated regression abstract this paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model we discuss the imposition of cross equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection a test of correct functional form for the entire system of equations is also constructed asymptotic and finite sample results are given we illustrate our estimator by applying it to a cost system for us commercial banks our results show that most of the banks are operating under increasing returns to scale but that returns to scale decrease with bank size