non parametric analysis of panel data models with endogenous variables abstract this paper considers the estimation of panel data models by first differences in the presence of endogenous variables and under an instrumental variables condition this framework leads to the resolution of linear inverse problems solved using a tikhonov regularization with l 2 or sobolev penalty rates of convergence and data driven selection of the regularization parameters are proposed the practical implementation of our estimators is presented and some monte carlo simulations show the potential of the method

a conditional kolmogorov test this paper introduces a conditional kolmogorov test of model specification for parametric models with covariates regressors the test is an extension of the kolmogorov test of goodness of fit for distribution functions the test is shown to have power against 1 n local alternatives and all fixed alternatives to the null hypothesis a parametric bootstrap procedure is used to obtain critical values for the test

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

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

an adaptive rate optimal test of linearity for median regression models this article is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness we develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest possible rate the test does not require knowledge of the distribution of the model s random noise component and it permits conditional heteroscedasticity of unknown form the numerical performance and usefulness of the test are illustrated by the results of monte carlo experiments and an empirical example

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

structure and stability of the equilibrium set in potential driven flow networks abstract in this paper we address local bifurcation properties of a family of networked dynamical systems specifically those defined by a potential driven flow on a directed graph these network flows include linear consensus dynamics or kuramoto models of coupled nonlinear oscillators as particular cases as it is well known for consensus systems these networks exhibit a somehow unconventional dynamical feature namely the existence of a line of equilibria following from a well known property of the graph laplacian matrix in connected networks with positive weights negative weights which arise in different contexts e g in consensus models in signed graphs or in kuramoto models with antagonistic actors may on the one hand lead to higher dimensional manifolds of equilibria and on the other be responsible for bifurcation phenomena in this direction we prove a saddle node bifurcation theorem for a broad family of potential driven flows in networks with one or more negative weights the goal is to state the conditions in structural terms that is in terms of the expressions defining the flowrates and the graph theoretic properties of the network not only the eigenvalue requirements but also the nonlinear transversality assumptions supporting the bifurcation motivate an analysis of independent interest concerning the rank degeneracies of nodal matrices arising in the linearized dynamics this analysis is performed in terms of the contraction deletion structure of spanning trees and uses several results from matrix analysis different examples illustrate the results some linear problems including signed graphs are aimed at illustrating the analysis of nodal matrices whereas in a nonlinear framework we apply the characterization of saddle node bifurcations to networks with a sinusoidal kuramoto like flow

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

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

goodness of fit tests for parametric regression models several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives these tests formally check if the bias vector of residuals from parametric fits is negligible by using the adaptive neyman test and other methods the testing procedures formalize the traditional model diagnostic tools based on residual plots we examine the rates of contiguous alternatives that can be detected consistently by the adaptive neyman test applications of the procedures to the partially linear models are thoroughly discussed our simulation studies show that the new testing procedures are indeed powerful and omnibus the power of the proposed tests is comparable to the f test statistic even in the situations where the f test is known to be suitable and can be far more powerful than the f test statistic in other situations an application to testing linear models versus additive models is also discussed

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

a simple consistent bootstrap test for a parametric regression function abstract a simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form it is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result we also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative monte carlo simulations suggest that the bootstrap test performs well based on wild bootstrap critical values

test of significance based on wavelet thresholding and neyman s truncation abstract traditional nonparametric tests such as the kolmogorov smirnov test and the cramer von mises test are based on the empirical distribution functions although these tests possess root n consistency they effectively use only information contained in the low frequencies this leads to low power in detecting fine features such as sharp and short aberrants as well as global features such as high frequency alternations the drawback can be repaired via smoothing based test statistics in this article we propose two such kind of test statistics based on the wavelet thresholding and the neyman truncation we provide extensive evidence to demonstrate that the proposed tests have higher power in detecting sharp peaks and high frequency alternations while maintaining the same capability in detecting smooth alternative densities as the traditional tests similar conclusions can be made for two sample nonparametric tests of distribution functions in that case the traditional linear rank tests such as th

perturbation of spectral subspaces and solution of linear operator equations abstract let a and b be normal operators on a hilbert space let k a and k b be subsets of the complex plane at distance at least from each other let e be the spectral projector for a belonging to k a and let f be the spectral projector for b belonging to k b our main results are estimates of the form ef c e a b f in some special situations the constant c is as low as 1 as an application we prove for an absolute constant d that if the space is finite dimensional and if a and b are normal with a b d then the spectrum of b can be obtained from that of a multiplicities counted by moving each eigenvalue by at most our main results have equivalent formulations as statements about the operator equation aq qb s let a and b be normal operators on perhaps different hilbert spaces assume a k a and b k b where k a k b and are as before then we give estimates of the forms q c aq qb

semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors abstract this paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes which is of empirical importance we show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest which has been observed in linear parametric models two step consistent estimators of the parameters of interest are proposed we also show that the proposed estimators are consistent with a rate faster than n 1 4 under a certain metric and the proposed estimators of the finite dimensional unknown parameters obtain root n asymptotic normality monte carlo evidences show that the proposed estimators perform well under a variety of identification conditions an application to instrumental variables estimation of engel curves illustrates the usefulness of our method it supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful engel curves

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

tests of specification for parametric and semiparametric models abstract this paper provides a general framework for constructing specification tests for parametric and semiparametric models the paper develops new specification tests using the general framework in particular specification tests for semiparametric partially linear regression and sample selection models are introduced the results apply in time series and cross sectional contexts the method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes

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

smoothing of stokes s discontinuity for the generalized bessel function ii this is a continuation of an earlier paper in which we investigated the superasymptotics and hyperasymptotics of the generalized bessel function z l 0 z l l 1 l where 0 x and g may be real or complex in this paper we consider the case 1 0 the analysis in the two cases is not quite the same here we shall see that contributions towards hyperasymptotic expansions not only come from adjacent saddles but also from curves that are not even steepest descent paths through any saddles

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