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

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

on the radius of convergence of interconnected analytic nonlinear input output systems a complete analysis is presented of the radii of convergence of the parallel product cascade and feedback interconnections of analytic nonlinear input output systems represented as fliess operators such operators are described by convergent functional series which are indexed by words over a noncommutative alphabet their generating series are therefore specified in terms of noncommutative formal power series given growth conditions for the coefficients of the generating series for the subsystems the radius of convergence of each interconnected system is computed assuming the subsystems are either all locally convergent or all globally convergent in the process of deriving the radius of convergence for the feedback connection it is shown definitively that local convergence is preserved under feedback this had been an open problem in the literature until recently

cross section regression with common shocks this paper considers regression models for cross section data that exhibit cross section dependence due to common shocks such as macroeconomic shocks the paper analyzes the properties of least squares ls estimators in this context the results of the paper allow for any form of cross section dependence and heterogeneity across population units the probability limits of the ls estimators are determined and necessary and sufficient conditions are given for consistency the asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling the t wald and f statistics are found to have asymptotic standard normal x 2 and scaled x 2 distributions respectively under the null hypothesis when the conditions required for consistency of the parameter under test hold however the absolute values of t wald and f statistics are found to diverge to infinity under the null hypothesis when these conditions fail confidence intervals exhibit similarly dichotomous behavior hence common shocks are found to be innocuous in some circumstances but quite problematic in others models with factor structures for errors and regressors are considered using the general results conditions are determined under which consistency of the ls estimators holds and fails in models with factor structures the results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units

a varying coefficient panel data model with fixed effects theory and an application to us commercial banks in this paper we propose a semiparametric varying coefficient categorical panel data model in which covariates variables affecting the coefficients are purely categorical this model has two features first fixed effects are included to allow for correlation between individual unobserved heterogeneity and the regressors second it allows for cross sectional dependence through a general spatial error dependence structure we derive a semiparametric estimator for our model by using a modified within transformation and then show the asymptotic and finite properties for this estimator under large n and t the monte carlo study shows that our methodology works well for both large n and t and large n and small t cases finally we illustrate our model by analyzing the effects of state level banking regulations on the returns to scale of commercial banks in the us our empirical results suggest that returns to scale is higher in more regulated states than in less regulated states

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

sieve estimation of panel data models with cross section dependence abstract in this paper we consider the problem of estimating semiparametric panel data models with cross section dependence where the individual specific regressors enter the model nonparametrically whereas the common factors enter the model linearly we consider both heterogeneous and homogeneous regression relationships when both the time and cross section dimensions are large we propose sieve estimators for the nonparametric regression functions by extending pesaran s 2006 common correlated effect cce estimator to our semiparametric framework asymptotic normal distributions for the proposed estimators are derived and asymptotic variance estimators are provided monte carlo simulations indicate that our estimators perform well in finite samples

computable convergence bounds of series expansions for infinite dimensional linear analytic systems and application this paper deals with the convergence of series expansions of trajectories for semi linear infinite dimensional systems which are analytic in state and affine in input a special case of such expansions corresponds to volterra series which are extensively used for the analysis the simulation and the control of weakly nonlinear finite dimensional systems the main results of this paper give computable bounds for both the convergence radius and the truncation error of the series these results can be used for model simplification and analytic approximation of trajectories with a guaranteed quality they are available for distributed and boundary control systems as an illustration these results are applied to an epidemic population dynamic model in this example it is shown that the truncation of the series at order 2 yields an accurate analytic approximation which can be used for time simulation and control issues the relevance of the method is illustrated by simulations

the observation space and realizations of finite volterra series in this paper we extend the results on the theory of realizations of finite volterra series by exploiting the structural properties of the observation space in general two distinct minimal realizations of a finite volterra series may be constructed one based on the properties of the observation space and the other based on the properties of the lie algebra both these realizations display the canonical structure found earlier for such systems the results given here also yield information on the observation algebra generated by functions in the observation space just as previous work gave information on the lie algebra as an application the structure found here is applied to the finite dimensional filtering problem for these systems

identifiability analysis of an epidemiological model in a structured population we investigate the parameter identifiability problem for a system of nonlinear integro partial differential equations of transport type representing the spread of a disease with a long infectious but undetectable period in an individual population after obtaining the expression of the model input output relationships we give sufficient conditions on the initial and boundary conditions of the system that guarantee the parameter identifiability on a finite time horizon we finally illustrate our findings with numerical simulations

using logistic regression procedures for estimating receiver operating characteristic curves summary estimation of a receiver operating characteristic roc curve is usually based either on a fully parametric model such as a normal model or on a fully nonparametric model in this paper we explore a semiparametric approach by assuming a density ratio model for disease and disease free densities this model has a natural connection with the logistic regression model the proposed semiparametric approach is more robust than a fully parametric approach and is more efficient than a fully nonparametric approach two real examples demonstrate that the roc curve estimated by our semiparametric method is much smoother than that estimated by the nonparametric method

technical communique magnitude bounds of generalized frequency response functions for nonlinear volterra systems described by narx model in order to reveal the relationship between system time domain model parameters and system frequency response functions new magnitude bounds of frequency response functions for nonlinear volterra systems described by narx model are established the magnitude bound of the nth order generalized frequency response function gfrf can be expressed as a simple n degree polynomial function of the magnitude of the first order gfrf whose coefficients are functions of the model parameters and frequency variables thus the system output spectrum can also be bounded by a polynomial function of the magnitude of the first order gfrf these results demonstrate explicitly the analytical relationship between model parameters and system frequency response functions and provide a significant insight into the magnitude based analysis and synthesis of nonlinear systems in the frequency domain

computation of convergence bounds for volterra series of linear analytic single input systems in this paper the volterra series decomposition of a class of single input time invariant systems analytic in state and affine in input is analyzed input to state convergence results are obtained for several typical norms l 0 t l r as well as exponentially weighted norms from the standard recursive construction of volterra kernels new estimates of the kernel norms are derived the singular inversion theorem is then used to obtain the main result of the paper namely an easily computable bound of the convergence radius guaranteed error bounds for the truncated series are also provided the relevance of the method is illustrated in several examples

on the convergence of the volterra series representation of the duffing s oscillators subjected to harmonic excitations abstract this paper is concerned with the investigation of the convergence issue of the volterra series representations of the duffing s oscillator subjected to harmonic inputs a simple criterion is proposed to determine the upper limit of the magnitude of the harmonic inputs a comparison between the new proposed criterion and a criterion suggested by tomlinson et al g r tomlinson g manson g m lee a simple criterion for establishing an upper limit to the harmonic excitation level of the duffing oscillator using the volterra series journal of sound and vibration 190 1996 751 762 was carried out the results show that the new criterion can provide a more accurate prediction about the convergence of the volterra series representation of the duffing s oscillator

semiparametric trending panel data models with cross sectional dependence abstract a semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross sectional dependence in both the regressors and the residuals a pooled semiparametric profile likelihood dummy variable approach based on the first stage local linear fitting is developed to estimate both the parameter vector and the nonlinear time trend function as both the time series length t and the cross sectional size n tend to infinity the resulting estimator of the parameter vector is asymptotically normal with a root n t convergence rate meanwhile the asymptotic distribution for the nonparametric estimator of the trend function is also established with a root n t h convergence rate two simulated examples are provided to illustrate the finite sample performance of the proposed method in addition the proposed model and estimation method are applied to a cpi data set as well as an input output data set

brief series expansions for analytic systems linear in control this paper presents a series expansion for the evolution of a class of nonlinear systems characterized by constant input vector fields we present a series expansion that can be computed via explicit recursive expressions and we derive sufficient conditions for uniform convergence over the finite and infinite time horizon furthermore we present a simplified series and convergence analysis for the setting of second order polynomial vector fields the treatment only relies on elementary notions on analytic functions number theory and operator norms

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

shrinkage estimation of the varying coefficient model the varying coefficient model is a useful extension of the linear regression model nevertheless how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood to solve the problem we propose here a novel method which combines the ideas of the local polynomial smoothing and the least absolute shrinkage and selection operator lasso the new method can do nonparametric estimation and variable selection simultaneously with a local constant estimator and the adaptive lasso penalty the new method can identify the true model consistently and that the resulting estimator can be as efficient as the oracle estimator numerical studies clearly confirm our theories extension to other shrinkage methods e g the scad i e the smoothly clipped absolute deviation and other smoothing methods is straightforward

smooth semiparametric receiver operating characteristic curves for continuous diagnostic tests we propose a semiparametric kernel distribution function estimator based on which a new smooth semiparametric estimator of the receiver operating characteristic roc curve is constructed we derive the asymptotic bias and variance of the newly proposed distribution function estimator and show that it is more efficient than the traditional non parametric kernel distribution estimator we also derive the asymptotic bias and variance of our new roc curve estimator and show that it is more efficient than the smooth non parametric roc curve estimator proposed by zou et al stat med 1997 16 2143 2156 and lloyd j am stat assoc 1998 93 1356 1364 for our proposed estimators we derive data based methods for bandwidth selection in addition we present some results on the analysis of two real data sets finally a simulation study is presented to show that our estimators are better than the non parametric counterparts in terms of bias standard error and mean square error

semiparametric roc surfaces for continuous diagnostic tests based on two test measurements we propose a semiparametric method for estimating roc surfaces for continuous diagnostic tests based on two test measurements such a three class diagnostic problem based on two test measurements arises naturally from some dna amplification related diagnostic scenarios simulation results show that our proposed semiparametric roc surface estimator is more efficient than the nonparametric counterpart and is quite comparable with the parametric counterpart when model assumption of the data is correctly specified for the parametric method moreover when the parametric model assumption is not true our proposed semiparametric method is superior to both nonparametric and parametric methods some discussions and a simulated example along with r programs for implementation of the proposed method are also provided

panel data models with interactive fixed effects this paper considers large n and large t panel data models with unobservable multiple interactive eects these models are useful for both micro and macro econometric modelings in earnings studies for example workers motivation persistence and diligence combined to influence the earnings in addition to the usual argument of innate ability in macroeconomics the interactive eects represent unobservable common shocks and their heterogeneous responses over cross sections since the interactive eects are allowed to be correlated with the regressors they are treated as fixed eects parameters to be estimated along with the common slope coecients the model is estimated by the least squares method which provides the interactive eect s counterpart of the within estimator we first consider model identification and then derive the rate of convergence and the limiting distribution of the interactive eect s estimator of the common slope coecients the estimator is shown to be p nt consistent this rate is valid even in the presence of correlations and heteroskedasticities in both dimensions a striking contrast with fixed t framework in which serial correlation and heteroskedasticity imply unidentification the asymptotic distribution is not necessarily centered at zero biased corrected estimators are derived we also derive the constrained estimator and its limiting distribution imposing additivity coupled with interactive eects the problem of testing additive versus interactive eects is also studied we also derive identification conditions for models with grand mean time invariant regressors and common regressors it is shown that there exists a set of necessary and sucient identification conditions for those models given identification the rate of convergence and limiting results continue to hold

on the convergence of volterra series of finite dimensional quadratic mimo systems in this paper the volterra series decomposition of a class of quadratic time invariant single input finite dimensional systems is analyzed the kernels are given by a recursive sequence of linear pdes in the time domain and an equivalent algebraic recursion in the laplace domain this is used to prove the convergence of the volterra series to a possibly weak trajectory of the system to provide a practicable value for the radius of convergence of the input in l and to compute a guaranteed error bound in l for the truncated series the result is then extended to mimo systems a numerical simulation is performed on an academic siso example to illustrate how easily the truncated volterra series can be implemented

initial conditions and moment restrictions in dynamic panel data models estimation of the dynamic error components model is considered using two alternative linear estimators that are designed to improve the properties of the standard first differenced gmm estimator both estimators require restrictions on the initial conditions process asymptotic efficiency comparisons and monte carlo simulations for the simple ar 1 model demonstrate the dramatic improvement in performance of the proposed estimators compared to the usual first differenced gmm estimator and compared to non linear gmm the importance of these results is illustrated in an application to the estimation of a labour demand model using company panel data

asymptotic theory for nonparametric regression with spatial data nonparametric regression with spatial or spatio temporal data is considered the conditional mean of a dependent variable given explanatory ones is a nonparametric function while the conditional covariance reflects spatial correlation conditional heteroscedasticity is also allowed as well as non identically distributed observations instead of mixing conditions a possibly non stationary linear process is assumed for disturbances allowing for long range as well as short range dependence while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities a basic triangular array setting is employed with the aim of covering various patterns of spatial observation sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates when the cross sectional dependence is sufficiently mild the asymptotic variance in the central limit theorem is the same as when observations are independent otherwise the rate of convergence is slower we discuss the application of our conditions to spatial autoregressive models and models defined on a regular lattice

flexible functional forms and global curvature conditions empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions lau and gallant and golub have worked out methods for imposing the appropriate curvature conditions locally but those local techniques frequently fail to yield satisfactory results we develop two methods for imposing curvature conditions globally in the context of cost function estimation the first method adopts lau s technique to a generalization of a functional form first proposed by mcfadden using this generalized mcfadden functional form it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally the second method adopts a technique used by mcfadden and barnett which is based on the fact that a non negative sum of concave functions will be concave our various suggested techniques are illustrated using the u s manufacturing data utilized by berndt and khaled

a goodness of fit test for logistic regression models based on case control data summary we test the logistic regression assumption under a case control sampling plan after reparameterisation the assumed logistic regression model is equivalent to a two sample semiparametric model in which the log ratio of two density functions is linear in data by identifying this model with a biased sampling model we propose a kolmogorov smirnovtype statistic to test the validity of the logistic link function moreover we point out that this test statistic can also be used in mixture sampling we present a bootstrap procedure along with some results on simulation and on analysis of two real datasets

large panels with common factors and spatial correlation this paper considers the statistical analysis of large panel data sets where even after condi tioning on common observed eects the cross section units might remain dependently distrib uted this could arise when the cross section units are subject to unobserved common eects and or if there are spill over eects due to spatial or other forms of local dependencies the paper provides an overview of the literature on cross section dependence introduces the con cepts of time speci c weak and strong cross section dependence and shows that the commonly used spatial models are examples of weak cross section dependence it is then established that the common correlated eects cce estimator of panel data model with a multifactor error structure recently advanced by pesaran 2006 continues to provide consistent estimates of the slope coe cient even in the presence of spatial error processes small sample properties of the cce estimator under various patterns of cross section dependence including spatial forms are investigated by monte carlo experiments results show that the cce approach works well in the presence of weak and or strong cross sectionally correlated errors we also explore the role of certain characteristics of spatial processes in determining the performance of cce estimators such as the form and intensity of spatial dependence and the sparseness of the spatial weight