adaptive estimation of regression models via moment restrictions abstract this paper considers adaptive estimation of regression models by means of generalized method of moments estimators two models are considered one with an i i d disturbance that is independent of the regressors and one with a conditionally symmetric but possibly heteroskedastic disturbance for both cases the paper develops linearized estimators that are asymptotically efficient if the number and variety of moment conditions are allowed to grow at an appropriate rate with the sample size in the general symmetric case no other adaptive estimator has yet been proposed also results of a small monte carlo study indicate that in the independence case the small sample performance of the generalized method of moments estimator can be quite good vis a vis other estimators previously proposed

series estimation under cross sectional dependence an asymptotic theory is developed for series estimation of nonparametric and semiparametric regression models for cross sectional data under conditions on disturbances that allow for forms of cross sectional dependence and hetero geneity including conditional and unconditional heteroskedascity along with conditions on regressors that allow dependence and do not require existence of a density the conditions aim to accommodate various settings plausible in economic applications and can apply also to panel spatial and time series data a mean square rate of convergence of nonparametric regression estimates is established followed by asymptotic normality of a quite general statistic data driven studentizations that rely on single or double indices to order the data are justified in a partially linear model setting monte carlo investigation of finite sample properties and two empirical applications are carried out

asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

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

efficient estimation of a semiparametric partially linear varying coefficient model in this paper we propose a general series method to estimate a semiparametric partially linear varying coefficient model we establish the consistency and sqrt n normality property of the estimator of the finite dimensional parameters of the model we further show that when the error is conditionally homoskedastic this estimator is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator of the finite dimensional parameter reaches the semiparametric efficiency bound of this model a small scale simulation is reported to examine the finite sample performance of the proposed estimator and an empirical application is presented to illustrate the usefulness of the proposed method in practice we also discuss how to obtain an efficient estimation result when the error is conditional heteroskedastic

the distribution of zeros of all solutions of first order neutral differential equations this paper is concerned with the distribution of zeros of all solutions of the first order neutral differential equation x t p t x t q t x t 0 t t 0 where p c t 0 0 q c t 0 0 and r new estimations for the distance between adjacent zeros of this neutral equation are obtained via comparison with a corresponding differential inequality these results extend some known results from the non neutral to the neutral case and improve other published results as well

correction to list decoding of generalized reed solomon codes over commutative rings in the above titled paper ibid vol 51 no 1 pp 411 419 jan 05 lemma 6 is incorrect due to an error on the proof consequently proposition 2 is restated here

nonparametric specification testing via the trinity of tests tests are developed for inference on a parameter vector whose dimension grows slowly with sample size the statistics are based on the lagrange multiplier wald and pseudo likelihood ratio principles admit standard normal asymptotic distributions under the null and are straightforward to compute they are shown to be consistent and possessing non trivial power against local alternatives the settings considered include multiple linear regression panel data models with fixed effects and spatial autoregressions when a nonparametric regression function is estimated by series we use our statistics to propose specification tests and in semiparametric adaptive estimation we provide a test for correct error distribution specification these tests are nonparametric but handled in practice with parametric techniques a monte carlo study suggests that our tests perform well in finite samples two empirical examples use them to test for correct shape of an electricity distribution cost function and linearity and equality of engel curves

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

profile quasi maximum likelihood estimation of partially linear spatial autoregressive models abstract we propose profile quasi maximum likelihood estimation of spatial autoregressive models that are partially linear the rate of convergence of the spatial parameter estimator depends on some general features of the spatial weight matrix of the model the estimators of other finite dimensional parameters in the model have the regular n rate of convergence and the estimator of the nonparametric component is consistent but with different restrictions on the choice of bandwidth parameter associated with different natures of the spatial weights monte carlo simulations verify our theory and indicate that our estimators perform reasonably well in finite samples

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

efficient estimation of the semiparametric spatial autoregressive model efficient semiparametric and parametric estimates are developed for a spatial autoregressive model containing non stochastic explanatory variables and innovations suspected to be non normal the main stress is on the case of distribution of unknown nonparametric form where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest these estimates are as efficient as the ones based on a correct form in particular they are more efficient than pseudo gaussian maximum likelihood estimates at non gaussian distributions two different adaptive estimates are considered relying on somewhat different regularity conditions a monte carlo study of finite sample performance is included

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

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

testing the goodness of fit of a linear model via nonparametric regression techniques abstract this article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model the large sample properties of parametric goodness of fit tests for linearity are considered the inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression large sample theory is derived for two variants of this type of statistic the results demonstrate that such tests are consistent against all fixed smooth alternatives to linearity but are incapable of detecting local alternatives converging to a linear model at the parametric rate n 1 2 simulation experiments involving a test based on fitting cubic smoothing splines to residuals reveals that this test has good power properties against several reasonable alternatives

asymptotic behavior of m estimators of p regression parameters when p 2 n is large ii normal approximation in a general linear model y x beta r with y and r n dimensional x a n times p matrix and beta p dimensional let hat beta be an m estimator of beta satisfying 0 sum x i psi y i x i beta let p rightarrow infty such that p log n 3 2 n rightarrow 0 then max i x i hat beta beta rightarrow p 0 and it is possible to find a uniform normal approximation for the distribution of hat beta under which arbitrary linear combinations a n hat beta beta are asymptotically normal when appropriately normalized and hat beta beta x x hat beta beta is approximately chi 2 p

sieve wald and qlr inferences on semi nonparametric conditional moment models this paper considers inference on functionals of semi nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals which include all of the nonlinear nonparametric instrumental variables iv as special cases these models are often ill posed and hence it is difficult to verify whether a possibly nonlinear functional is root n estimable or not we provide computationally simple unified inference procedures that are asymptotically valid regardless of whether a functional is root n estimable or not we establish the following new useful results 1 the asymptotic normality of a plug in penalized sieve minimum distance psmd estimator of a possibly nonlinear functional 2 the consistency of simple sieve variance estimators for the plug in psmd estimator and hence the asymptotic chi square distribution of the sieve wald statistic 3 the asymptotic chi square distribution of an optimally weighted sieve quasi likelihood ratio qlr test under the null hypothesis 4 the asymptotic tight distribution of a non optimally weighted sieve qlr statistic under the null 5 the consistency of generalized residual bootstrap sieve wald and qlr tests 6 local power properties of sieve wald and qlr tests and of their bootstrap versions 7 asymptotic properties of sieve wald and sqlr for functionals of increasing dimension simulation studies and an empirical illustration of a nonparametric quantile iv regression are presented

pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension pseudo maximum likelihood estimates are developed for higher order spatial autoregressive models with increasingly many parameters including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component and regression models with spatial autoregressive disturbances consistency and asymptotic normality of the estimates are established monte carlo experiments examine finite sample behaviour

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

efficiency improvements in inference on stationary and nonstationary fractional time series we consider a time series model involving a fractional stochastic component whose integration order can lie in the stationary invertible or nonstationary regions and be unknown and an additive deterministic component consisting of a generalized polynomial the model can thus incorporate competing descriptions of trending behavior the stationary input to the stochastic component has parametric autocorrelation but innovation with distribution of unknown form the model is thus semiparametric and we develop estimates of the parametric component which are asymptotically normal and achieve an m estimation efficiency bound equal to that found in work using an adaptive lam lan approach a major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies this is relevant also when the innovation density is parameterized and we provide a result for that case also our semiparametric estimates employ nonparametric series estimation which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models our work thus also contributes to methods and theory for nonfractional time series models such as autoregressive moving averages a monte carlo study of finite sample performance of the semiparametric estimates is included

asymptotics for semiparametric econometric models via stochastic equicontinuity this paper provides a general framework for proving the square root of t consistency and asymptotic normality of a wide variety of semiparametric estimators the class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator the method of proof exploits results concerning the stochastic equicontinuity of stochastic processes the results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models primitive conditions are given for square root of t consistency and asymptotic normality of this estimator copyright 1994 by the econometric society

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

inference on higher order spatial autoregressive models with increasingly many parameters this paper develops consistency and asymptotic normality of parameter estimates for a higher order spatial autoregressive model whose order and number of regressors are allowed to approach infinity slowly with sample size both least squares and instrumental variables estimates are examined and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied besides allowing the number of parameters to increase with the data this has the advantage of accommodating some asymptotic regimes that are suggested by certain spatial settings several of which are discussed a small empirical example is also included and a monte carlo study analyses various implications of the theory in finite samples

semiparametric estimation of count regression models this paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity we use the generalized laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a poisson mixture model we establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated censored and zero inflated count regression models monte carlo evidence shows that the finite sample behavior of the estimator is quite good the paper applies the method to a model of individual shopping behavior