semi parametric single index panel data models with interactive fixed effects theory and practice abstract in this paper we propose a single index panel data model with unobserved multiple interactive fixed effects this model has the advantages of being flexible and of being able to allow for common shocks and their heterogeneous impacts on cross sections thus making it suitable for the investigation of many economic issues the asymptotic theories are established accordingly our monte carlo simulations show that our methodology works well for large n and t cases in our empirical application we illustrate our model by analysing the returns to scale of large commercial banks in the u s

adaptive fuzzy neural network control for a dsp based permanent magnet linear synchronous motor servo drive an adaptive fuzzy neural network afnn control system is proposed to control the position of the mover of a field oriented control permanent magnet linear synchronous motor pmlsm servo drive system to track periodic reference trajectories in this paper in the proposed afnn control system an fnn with accurate approximation capability is employed to approximate the unknown dynamics of the pmlsm and a robust compensator is proposed to confront the inevitable approximation errors due to finite number of membership functions and disturbances including the friction force the adaptive learning algorithm that can learn the parameters of the fnn on line is derived using lyapunov stability theorem moreover to relax the requirement for the value of lumped uncertainty in the robust compensator which comprises a minimum approximation error optimal parameter vectors higher order terms in taylor series and friction force an adaptive lumped uncertainty estimation law is investigated furthermore all the control algorithms are implemented in a tms320c32 dsp based control computer the simulated and experimental results due to periodic reference trajectories show that the dynamic behaviors of the proposed control systems are robust with regard to uncertainties

recursive estimation in large panel data models theory and practice abstract bai 2009 proposes recursive estimation for panel data models with interactive effects we study the behaviours of this recursive estimator the recursive formula is established that shows the behaviours of recursive estimators depend on the initial estimator the population structure and the iterative steps under some general scenarios we find that the recursive estimator becomes consistent after the first iteration from any initials we also obtain the optimal number of iterative steps under some prescribed conditions the central limit theorem of the recursive estimator is established when the initial estimator is ols various simulations are conducted to support our theoretical findings

existence of solutions for first order ordinary differential equations with nonlinear boundary conditions we present an existence theorem for nonlinear ordinary differential equations of first order with nonlinear boundary conditions the result includes for instance the initial value problem the final value problem and the antiperiodic boundary value problem the main novelty of the method lies in that it unifies different techniques for initial or boundary conditions

periodic boundary value problems for first order impulsive integro differential equations of mixed type this paper investigates the existence of minimal and maximal solutions of periodic boundary value problem for first order impulsive integro differential equations of mixed type by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique

periodic boundary value problem for first order impulsive ordinary differential equations this paper investigates the existence of minimal and maximal solutions of the periodic boundary value problem for first order impulsive differential equations by establishing two comparison results and using the method of upper and lower solutions and the monotone iterative technique

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

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

first order impulsive ordinary differential equations with anti periodic and nonlinear boundary conditions the monotone iterative technique is a powerful method that have been used to approximate the extremal solutions of several problems 1 2 on the other hand impulsive differential equations are a basic tool to study some problems of biology medicine engineering and physics 3 in this paper we deal with the following nonlinear boundary value problem for first order differential equation with impulses at fixed points

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

nagumo type existence results of sturm liouville bvp for impulsive differential equations abstract in this paper the method of upper and lower solutions and the schauder degree theory are employed in the study of sturm liouville boundary value problems for second order impulsive differential equations we obtain the existence of at least three solutions to the problem under the assumption that the nonlinear term f satisfies a nagumo condition with respect to the first order derivative

online adaptive fuzzy neural identification and control of a class of mimo nonlinear systems this paper presents a robust adaptive fuzzy neural controller afnc suitable for identification and control of a class of uncertain multiple input multiple output mimo nonlinear systems the proposed controller has the following salient features 1 self organizing fuzzy neural structure i e fuzzy control rules can be generated or deleted automatically 2 online learning ability of uncertain mimo nonlinear systems 3 fast learning speed 4 fast convergence of tracking errors 5 adaptive control where structure and parameters of the afnc can be self adaptive in the presence of disturbances to maintain high control performance 6 robust control where global stability of the system is established using the lyapunov approach simulation studies on an inverted pendulum and a two link robot manipulator show that the performance of the proposed controller is superior

a nonparametric test for poolability using panel data this paper derives a nonparametric procedure for testing poolability in a panel data framework this is contrasted with alternative parametric tests which are not robust to functional misspecification this test is illustrated with an earning equation using data from the panel study of income dynamics psid

specification test for panel data models with interactive fixed effects abstract in this paper we propose a consistent nonparametric test for linearity in a large dimensional panel data model with interactive fixed effects both lagged dependent variables and conditional heteroskedasticity of unknown form are allowed in the model we estimate the model under the null hypothesis of linearity to obtain the restricted residuals which are then used to construct the test statistic we show that after being appropriately centered and standardized the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of pitman local alternatives by using the concept of conditional strong mixing that was recently introduced by prakasa rao 2009 to improve the finite sample performance we propose a bootstrap procedure to obtain the bootstrap p value a small set of monte carlo simulations illustrates that our test performs well in finite samples an application to an economic growth panel dataset indicates significant nonlinear relationships between economic growth initial income level and capital accumulation

stability criteria of impulsive differential systems the notion of eventual stability has been recently discussed we extend this notion to impulsive systems of differential equations our technique depends on liapunov s direct method

shrinkage estimation of dynamic panel data models with interactive fixed effects abstract we consider the problem of determining the number of factors and selecting the proper regressors in linear dynamic panel data models with interactive fixed effects based on the preliminary estimates of the slope parameters and factors a la bai 2009 and moon and weidner 2015 we propose a method for simultaneous selection of regressors and factors and estimation through the method of adaptive group lasso least absolute shrinkage and selection operator we show that with probability approaching one our method can correctly select all relevant regressors and factors and shrink the coefficients of irrelevant regressors and redundant factors to zero further we demonstrate that our shrinkage estimators of the nonzero slope parameters exhibit some oracle property we conduct monte carlo simulations to demonstrate the superb finite sample performance of the proposed method we apply our method to study the determinants of economic growth and find that in addition to three common unobserved factors selected by our method government consumption share has negative effects whereas investment share and lagged economic growth have positive effects on economic growth

a generalization of the method of upper and lower solutions for discontinuous first order problems with nonlinear boundary conditions in this paper we prove the existence of extremal solutions for a discontinuous bvp between a lower and an upper solution which may be discontinuous in a finite set of points furthermore we present a monotone method with which we can explicitly construct a pair of sequences that converge to the extremal solutions despite the discontinuities of the right hand side of the equation

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

extremal solutions of periodic boundary value problems for first order integro differential equations of mixed type this paper investigates the maximal and minimal solutions of periodic boundary value problems for first order nonlinear integro differential equations of mixed type by establishing a comparison result and using the monotone iterative technique

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

monotone method for a system of nonlinear mixed type implicit impulsive integro differential equations in banach spaces in this paper by using a monotone iterative technique in the presence of lower and upper solutions we discuss the existence of solutions for a new system of nonlinear mixed type implicit impulsive integro differential equations in banach spaces under wide monotonicity conditions and the noncompactness measure conditions we also obtain the existence of extremal solutions and a unique solution between lower and upper solutions

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

quasilinearization of a boundary value problem for impulsive differential equations in this paper we study the existence and approximation of solution for nonlinear impulsive differential equations with fixed moments of impulsive perturbations using quasilinearization technique we obtain a monotone sequence of approximate solutions that converges quadratically to a solution

nonlinear boundary problem of first order impulsive integro differential equations this paper focuses on first order impulsive integro differential equations with nonlinear boundary the lower and upper solutions combined with monotone iterative techniques are used to obtain the existence of extremal solutions of the problem numerical examples are given to prove its validity

periodic boundary value problem for first order impulsive functional differential equations in this paper by means of the method of upper and lower solutions and the monotone iterative technique the existence of minimal and maximal solutions of the periodic boundary value problem for first order impulsive functional differential equations is considered

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

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

monotone iterative technique for impulsive integro differential equations with periodic boundary conditions this paper investigates the existence of minimal and maximal solutions of impulsive integro differential equations with periodic boundary conditions by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique

monotone and numerical analytic methods for differential equations abstract the method of lower and upper solutions combined with monotone iterative techniques is used for ordinary differential equations with integral boundary conditions showing the existence of extremal solutions some existence results are also formulated using the numerical analytic method sufficient conditions for existence are given

boundary value problems for first order functional differential equations with impulsive integral conditions in this paper by using the method of lower and upper solutions coupled with the monotone iterative technique we give conditions for existence of extreme solutions for first order functional differential equations with a new impulsive integral condition some comparison results are also formulated

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

adaptive fuzzy control with guaranteed convergence of optimal approximation error with no a priori knowledge of plant boundary functions a novel direct adaptive fuzzy controller afc for a class of single input single output siso uncertain affine nonlinear systems is developed in this paper based on the theory of fuzzy logic systems flss with variable universes of discourse uds sufficient conditions that guarantee that the optimal fuzzy approximation error fae is locally convergent are given by the use of the output tracking error and its derivatives as input variables and by the selection of suitable adjusting parameters a variable ud fls with an optimal fae local convergence is constructed and its parameter adaptive law is derived by virtue of the lyapunov stability theorem under the assumption that the optimal fae is bounded it is proved that the closed loop system is asymptotically stable in the sense that all variables are uniformly ultimately bounded and that the tracking errors converge to zero the proposed approach eliminates the influence of the fae on the tracking errors by means of the inherent mechanism of the variable ud fls thus it has the potential to achieve high control performance without additional compensation under only a few fuzzy rules simulation studies demonstrate the superiority of the proposed afc in terms of the settling time tracking accuracy smoothness of the control input and robustness against external disturbances and parameter variations

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

bias in dynamic panel estimation with fixed effects incidental trends and cross section dependence abstract explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size n the results extend earlier work by nickell 1981 biases in dynamic models with fixed effects econometrica 49 1417 1426 and later authors in several directions that are relevant for practical work including models with unit roots deterministic trends predetermined and exogenous regressors and errors that may be cross sectionally dependent the asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient another finding of interest is that when there is cross section error dependence the probability limit of the dynamic panel regression estimator is a random variable rather than a constant which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where n is very large some proposals for bias correction are suggested and finite sample performance is analyzed in simulations

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

an evolving construction scheme for fuzzy systems this paper proposes an evolving construction scheme for fuzzy systems ecsfs ecsfs begins with a simple fuzzy system and evolves its structure by adding more fuzzy terms and rules to achieve a better accuracy in a greedy way an interesting feature of ecsfs is that it is able to automatically locate mathematically meaningful points such as the extremum and inflexion points of the approximated function one by one and then adds fuzzy terms based on these points fuzzy systems with such extreme points like their fuzzy terms are more efficient than other fuzzy systems by using the same number of fuzzy rules as a result ecsfs often achieves a better accuracy for fuzzy system identification compared with the previous methods when using the same number of fuzzy rules a number of simulation results are given to illustrate the advantages of the proposed scheme

impulsive anti periodic boundary value problem of first order integro differential equations this paper is concerned with the anti periodic boundary value problem of first order nonlinear impulsive integro differential equations we first establish a new comparison principle and then obtain the existence of extremal solutions by upper lower solution and monotone iterative techniques some examples are presented to illustrate the main results

generalized likelihood ratio statistics and wilks phenomenon likelihood ratio theory has had tremendous success in parametric inference due to the fundamental theory of wilks yet there is no general applicable approach for nonparametric inferences based on function estimation maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting even if they exist they are hard to find and can not be optimal as shown in this paper we introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics a new s wilks phenomenon is unveiled we demonstrate that a class of the generalized likelihood statistics based on some appropriate nonparametric estimators are asymptotically distribution free and follow chi 2 distributions under null hypotheses for a number of useful hypotheses and a variety of useful models including gaussian white noise models nonparametric regression models varying coefficient models and generalized varying coefficient models we further demonstrate that generalized likelihood ratio statistics are asymptotically optimal in the sense that they achieve optimal rates of convergence given by ingster they can even be adaptively optimal in the sense of spokoiny by using a simple choice of adaptive smoothing parameter our work indicates that the generalized likelihood ratio statistics are indeed general and powerful for nonparametric testing problems based on function estimation

robust control of an lusm based x hbox y hbox theta motion control stage using an adaptive interval type 2 fuzzy neural network the robust control of a linear ultrasonic motor based x y thetas motion control stage to track various contours is achieved by using an adaptive interval type 2 fuzzy neural network ait2fnn control system in this study in the proposed ait2fnn control system an it2fnn which combines the merits of an interval type 2 fuzzy logic system and a neural network is developed to approximate an unknown dynamic function moreover adaptive learning algorithms are derived using the lyapunov stability theorem to train the parameters of the it2fnn online furthermore a robust compensator is proposed to confront the uncertainties including the approximation error optimal parameter vectors and higher order terms in taylor series to relax the requirement for the value of lumped uncertainty in the robust compensator an adaptive lumped uncertainty estimation law is also investigated in addition the circle and butterfly contours are planned using a nonuniform rational b spline curve interpolator the experimental results show that the contour tracking performance of the proposed ait2fnn is significantly improved compared with the adaptive type 1 fnn additionally the robustness to parameter variations external disturbances cross coupled interference and frictional force can also be obtained using the proposed ait2fnn

a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems abstract an adaptive observer for a class of single input single output siso nonlinear systems is proposed using a generalized dynamic recurrent neural network drnn the neural network nn weights are tuned on line with no off line learning required no exact knowledge of non linearities in the observed system is required furthermore no linearity with respect to unknown system parameters is assumed the drnn observer does not assume that nonlinearities in the system are restricted to the system output only the overall adaptive observer scheme is shown to be uniformly ultimately bounded simulation results have verified the performance of the drnn observer

panel threshold regressions with latent group structures abstract in this paper we consider the least squares estimation of a panel structure threshold regression pstr model where both the slope coefficients and threshold parameters may exhibit latent group structures we study the asymptotic properties of the estimators of the latent group structure and the slope and threshold coefficients we show that we can estimate the latent group structure correctly with probability approaching 1 and the estimators of the slope and threshold coefficients are asymptotically equivalent to the infeasible estimators that are obtained as if the true group structures were known we study likelihood ratio based inferences on the group specific threshold parameters under the shrinking threshold effect framework we also propose two specification tests one tests whether the threshold parameters are homogeneous across groups and the other tests whether the threshold effects are present when the number of latent groups is unknown we propose a bic type information criterion to determine the number of groups in the data simulations demonstrate that our estimators and tests perform reasonably well in finite samples we apply our model to revisit the relationship between capital market imperfection and the investment behavior of firms and to examine the impact of bank deregulation on income inequality we document a large degree of heterogeneous effects in both applications that cannot be captured by conventional panel threshold regressions

periodic boundary value problems of second order impulsive differential equations abstract this paper discusses periodic boundary value problems of second order impulsive differential equations by using schaeffer s fixed point theorem and monotone iterative technique some existence results are obtained

boundary value problems for first order differential equations of mixed type abstract we apply the monotone iterative method to formulate existence results for integro differential equations with nonlinear boundary conditions some results for integro differential inequalities are also given examples illustrate obtained results

periodic boundary value problems for a class of second order impulsive integro differential equations in banach spaces abstract this paper investigates periodic boundary value problems for a class of second order nonlinear impulsive integro differential equations of mixed type in a banach space by establishing a comparison result criteria on the existence of maximal and minimal solutions are obtained

consistent specification tests for semiparametric nonparametric models based on series estimation methods abstract this paper considers the problem of consistent model specification tests using series estimation methods the null models we consider in this paper all contain some nonparametric components a leading case we consider is to test for an additive partially linear model the null distribution of the test statistic is derived using a central limit theorem for hilbert valued random arrays the test statistic is shown to be able to detect local alternatives that approach the null models at the order of op n 1 2 we show that the wild bootstrap method can be used to approximate the null distribution of the test statistic a small monte carlo simulation is reported to examine the finite sample performance of the proposed test we also show that the proposed test can be easily modified to obtain series based consistent tests for other semiparametric nonparametric models

qml estimation of dynamic panel data models with spatial errors abstract we propose quasi maximum likelihood qml estimation of dynamic panel models with spatial errors when the cross sectional dimension n is large and the time dimension t is fixed we consider both the random effects and fixed effects models and prove consistency and derive the limiting distributions of the qml estimators under different assumptions on the initial observations we propose a residual based bootstrap method for estimating the standard errors of the qml estimators monte carlo simulation shows that both the qml estimators and the bootstrap standard errors perform well in finite samples under a correct assumption on initial observations but may perform poorly when this assumption is not met

advanced differential equations with nonlinear boundary conditions we investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions sufficient conditions when the problem has extremal solutions or a unique solution are formulated linear advanced differential inequalities are also discussed

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

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

periodic boundary value problems for first order functional differential equations with impulse by applying the well known fixed point theorem of cone expansion and compression this paper investigates the existence of multiple positive solutions of periodic boundary value problems for first order functional differential equations with impulse meanwhile four examples are worked out to demonstrate the main results

kernel estimation of hazard functions when observations have dependent and common covariates abstract we propose a hazard model where dependence between events is achieved by assuming dependence between covariates this model allows for correlated variables specific to observations as well as macro variables which all observations share this setup better fits many economic and financial applications where events are not independent nonparametric estimation of the hazard function is then studied kernel estimators proposed in nielsen and linton 1995 and linton et al 2003 are shown to have similar asymptotic properties compared with the i i d case mixing conditions ensure the asymptotic results follow these results depend on adjustments to bandwidth conditions simulations are conducted which verify the impact of dependence on estimators bandwidth selection accounting for dependence is shown to improve performance in an empirical application trade intensity in high frequency financial data is estimated

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

stability criteria of impulsive differential systems this paper discusses the uniform eventual lipschitz stability and uniform eventual asymptotic stability of impulsive differential system some criteria of such stability for impulsive differential system are given compared with the existing result the condition is less conservative our technique depends on lyapunov s direct method and comparison principle

testing capital asset pricing models using functional coefficient panel data models with cross sectional dependence abstract this paper proposes a functional coefficient panel data model with cross sectional dependence motivated by re examining the empirical performance of conditional capital asset pricing model in order to characterize the time varying property of assets betas and alpha our proposed model allows the betas to be unknown functions of some macroeconomic and financial instruments moreover a common factor structure is introduced to characterize cross sectional dependence which is an attractive feature under a panel data regression setting as different assets or portfolios may be affected by same unobserved shocks compared to the existing studies such as the classic fama macbeth two step procedure our model can achieve substantial efficiency gains for inference by adopting a one step procedure using the entire sample rather than a single cross sectional regression at each time point we propose a local linear common correlated effects estimator for estimating time varying betas by pooling the data the consistency and asymptotic normality of the proposed estimators are established another methodological and empirical challenge in asset pricing is how to test the constancy of conditional betas and the significance of pricing errors we echo this challenge by constructing an l 2 norm statistic for functional coefficient panel data models allowing for cross sectional dependence we show that the new test statistic has a limiting standard normal distribution under the null hypothesis finally the method is applied to test the model in fama and french 1993 using fama french 25 and 100 portfolios sorted by size and book to market ratio respectively dated from july 1963 to july 2018

inferential theory for factor models of large dimensions this paper develops an inferential theory for factor models of large dimensions the principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator if normality is assumed we derive the rate of convergence and the limiting distributions of the estimated factors factor loadings and common components the theory is developed within the framework of large cross sections n and a large time dimension t to which classical factor analysis does not apply we show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of n and t the estimated factors and their loadings are generally normal although not always so the convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components these results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic a necessary and sufficient condition for consistency is derived for large n but fixed t

nonparametric estimation and testing of fixed effects panel data models in this paper we consider the problem of estimating nonparametric panel data models with fixed effects we introduce an iterative nonparametric kernel estimator we also extend the estimation method to the case of a semiparametric partially linear fixed effects model to determine whether a parametric semiparametric or nonparametric model is appropriate we propose test statistics to test between the three alternatives in practice we further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model simulations are used to examine the finite sample performance of the proposed estimators and the test statistics

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