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

efficient semiparametric estimation via moment restrictions conditional moment restrictions can be combined through gmm estimation to construct more efficient semiparametric estimators this paper is about attainable efficiency for such estimators we define and use a moment tangent set the directions of departure from the truth allowed by the moments to characterize when the semiparametric efficiency bound can be attained the efficiency condition is that the moment tangent set equals the model tangent set we apply these results to transformed censored and truncated regression models e g finding that the conditional moment restrictions from powell s 1986 censored regression quantile estimators can be combined to approximate efficiency when the disturbance is independent of regressors

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

approximation methods for common fixed points for a countable family of nonexpansive mappings abstract let e l p or l p space 1 p let k be a closed convex and nonempty subset of e let t i i 1 be a family of nonexpansive self mappings of k for arbitrary fixed 0 1 define a family of nonexpansive maps s i i 1 by s i 1 i t i where i is the identity map of k let f i 1 f t i 0 it is proved that the iterative sequence x n defined by x 0 k x n 1 n u i 1 i t n s i x n n 0 converges strongly to a common fixed point of the family t i i 1 where n and i t n are sequences in 0 1 satisfying appropriate conditions in each of the following cases a e l p 1 p and b e l p 1 p and at least one of the maps t i s is demicompact our theorems extend the results of p mainge approximation methods for common fixed points of nonexpansive mappings in hilbert space j math anal appl 325 2007 469 479 from hilbert spaces to l p spaces 1 p

indirect inference for dynamic panel models maximum likelihood ml estimation of the autoregressive parameter of a dynamic panel data model with fixed effects is inconsistent under fixed time series sample size and large cross section sample size asymptotics this paper proposes a general computationally inexpensive method of bias reduction that is based on indirect inference shows unbiasedness and analyzes efficiency monte carlo studies show that our procedure achieves substantial bias reductions with only mild increases in variance thereby substantially reducing root mean square errors the method is compared with certain consistent estimators and is shown to have superior finite sample properties to the generalized method of moment gmm and the bias corrected ml estimator

a hybrid algorithm for pseudo contractive mappings abstract in this paper we suggest and analyze a hybrid algorithm for pseudo contractive mappings in hilbert spaces further we prove the strong convergence of the proposed iterative algorithm for lipschitz pseudo contractive mappings in hilbert spaces

a general iterative method for nonexpansive mappings in hilbert spaces let h be a real hilbert space consider on h a nonexpansive mapping t with a fixed point a contraction f with coefficient 0 0 let 0

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

a general iterative method for addressing mixed equilibrium problems and optimization problems abstract in this paper we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem mep the set of fixed points of an infinite family of nonexpansive mappings t n n 1 and the set of solutions of variational inequalities for a inverse strongly monotone mapping in hilbert spaces furthermore we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems our results extend and improve the recent results of yao et al y yao m a noor s zainab y c liou mixed equilibrium problems and optimization problems j math anal appl 354 2009 319 329 y yao m a noor y c liou on iterative methods for equilibrium problems nonlinear anal 70 1 2009 479 509 and many others

asymptotically efficient estimation in the presence of heteroskedasticity of unknown form in a multiple regression model the residual variance is an unknown function of the explanatory variables and estimated by nearest neighbor nonparametric regression the resulting weighted least squares estimator of the regression coefficients is shown to be adaptive in the sense of having the same asymptotic distribution to first order as estimators based on knowledge of the actual variance function or a finite parameterization of it a similar result was established by carroll 1982 using kernel estimation and under substantially more restrictive conditions on the data generating process than ours extensions to various other models seem to be possible

gmm redundancy results for general missing data problems we consider questions of efficiency and redundancy in the gmm estimation problem in which we have two sets of moment conditions where two sets of parameters enter into one set of moment conditions while only one set of parameters enters into the other we then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest and the second set of moment conditions is for the selection process we use these results to explain the counterintuitive result in the literature that under an ignorability assumption that justifies gmm with weighted moment conditions weighting using estimated probabilities of selection is better than weighting using the true probabilities we also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid and we show that when weighting is not needed for consistency it is also not useful for efficiency

on relaxed viscosity iterative methods for variational inequalities in banach spaces in this paper we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self mappings defined on a nonempty closed convex subset of a reflexive banach space we prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method the results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature

common fixed points of strict pseudocontractions by iterative algorithms in this paper we present iteration schemes to weakly and strongly approximate common fixed points of a finite family of a class of strict pseudocontractions

best nonlinear three stage least squares estimation of certain econometric models a method is presented for estimating nonlinear simultaneous equations and transformation models in the presence of disturbance distribution of unknown form it asymptotically achieves the lower variance bound for instrumental variables estimates the author avoids smoothed nonparametric estimation his instruments averaging over the unsmoothed empirical distribution of preliminary residuals he allows for stationary serial dependence in various settings estimates are proposed and large sample inference rules justified these being unaffected if the optimal instruments use only an arbitrarily small vanishing fraction of the residuals the author investigates theoretically the effect of such computational savings on the goodness of the normal approximation copyright 1991 by the econometric society

strong convergence of an iterative method for nonexpansive mappings with new control conditions abstract the purpose of this paper is to study the convergence problem of an iterative method for nonexpansive mappings in banach spaces under some new control conditions on parameters

an iterative method for finding common solutions of equilibrium and fixed point problems we introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem

long difference instrumental variables estimation for dynamic panel models with fixed effects this paper proposes a new instrumental variables estimator for a dynamic panel model with fixed effects with good bias and mean squared error properties even when identification of the model becomes weak near the unit circle we adopt a weak instrument asymptotic approximation to study the behavior of various estimators near the unit circle we show that an estimator based on long differencing the model is much less biased than conventional implementations of the gmm estimator for the dynamic panel model we also show that under the weak instrument approximation conventional gmm estimators are dominated in terms of mean squared error by an estimator with far less moment conditions the long difference ld estimator mimics the infeasible optimal procedure through its reliance on a small set of moment conditions

iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings abstract we introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem our results extend for example the recent result of v colao g marino h k xu an iterative method for finding common solutions of equilibrium and fixed point problems j math anal appl 344 2008 340 352 to systems of equilibrium problems

another look at the instrumental variable estimation of error components models this article develops a framework for efficient iv estimators of random effects models with information in levels which can accommodate predetermined variables our formulation clarifies the relationship between the existing estimators and the role of transformations in panel data models we characterize the valid transformations for relevant models and show that optimal estimators are invariant to the transformation used to remove individual effects we present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors finally we consider models with predetermined variables that have constant correlation with the effects and illustrate their importance with simulations

efficient estimation of panel data models with sequential moment restrictions abstract this paper considers asymptotically efficient estimation of the panel data models with sequential moment restrictions in an environment with i i d observations it is shown that the gmm estimator with an increasing set of instruments attains the semiparametric efficiency bound of the model the estimator considered here allows for the heteroscedasticity of the unknown form

strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings let c be a nonempty closed convex subset of a real strictly convex and reflexive banach space e which has a uniformly g teaux differentiable norm let f c c be a given contractive mapping and tn n 1 c c be an infinite family of nonexpansive mappings such that the common fixed point sets f n 1 f tn let n and n be two real sequences in 0 1 for given x0 c arbitrarily let the sequence xn be generated iteratively by xn 1 nf xn nxn 1 n n wnxn wherewn is the w mapping generated by the mappings tn tn 1 t1 and n n 1 1 suppose the iterative parameters n and n satisfy the following control conditions c1 limn n 0 c2 n 0 n b5 limsupn n 1 then the sequence xn converges strongly to p f where p is the unique solution in f to the following variational inequality i f p j p x 0for allx f

viscosity methods for common solutions of equilibrium and variational inequality problems via multi step iterative algorithms and common fixed points abstract in this paper we present a new multi step iterative method we prove the strong convergence of the method to a common fixed point of a finite number of nonexpansive mappings that also solves a suitable equilibrium problem

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

strong convergence theorems of a general iterative process for a finite family of λi strict pseudo contractions in q uniformly smooth banach spaces in this paper we study a general iterative process to have strong convergence for a finite family of l i strict pseudo contractive non self mappings in the framework of q uniformly smooth banach spaces our results improve and extend the corresponding results announced by many others

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

gmm inference when the number of moment conditions is large abstract asymptotic theory typically presumes that the dimensionality of econometric models is independent of the sample size even though this presumption is often quite unrealistic in gmm estimation whenever optimal instruments are not available it can frequently be shown that adding over identifying restrictions moment conditions will increase asymptotic precision however the conventional asymptotics which underlies this view insists that the number of moment conditions remain finite even though the number of available moment conditions may grow without bound we consider the explicit dependence of the number of moment conditions or instruments q n on the sample size n and establish that under conventional regularity conditions for the estimation of a linear model with general heteroskedasticity q n 3 n 0 is a sufficient condition for the validity of conventional asymptotic inference about the gmm estimator

a general iterative method for a finite family of nonexpansive mappings abstract we study the approximation of common fixed points of a finite family of nonexpansive mappings and suggest a modification of the iterative algorithm without the assumption of any type of commutativity also we show that the convergence of the proposed algorithm can be proved under some types of control conditions

dentability indices with respect to measures of non compactness abstract we study the relationships between the ordinal indices of set derivations associated to several measures of non compactness we obtain applications to the szlenk index improving a result of lancien and lur renorming providing a non probabilistic proof of a result of troyanski

viscosity approximation methods for fixed points problems the aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed point of a given nonexpansive self mapping

estimating systems of equations with different instruments for different equations abstract for applications where different instruments are required for different equations this paper offers a relatively primitive set of assumptions under which the nonlinear three stage least squares estimator is the asymptotically efficient generalized method of moments estimator these conditions can be verified for a general class of panel data models under reasonable assumptions about the dynamics in the model on the other hand the 3sls estimator is necessarily inefficient for models such as hedonic price systems and for certain simultaneous equations models with measurement error or omitted variables in some equations

efficient instrumental variables estimation of nonlinear models this paper considers asymptotically efficient instrumental variables estimation of nonlinear models in an i i d environment the class of models includes nonlinear simultaneous equations models and other models of interest a problem in constructing efficient instrumental variables estimators for such models is that the optimal instruments involve a conditional expectation calculation of which can require functional form assumptions for the conditional distribution of endogenous variables as well as integration nonparametric methods provide a way of avoiding this difficulty here it is shown that nonparametric estimates of the optimal instruments can give asymptotically efficient instrumental variables estimators also ways of choosing the nonparametric estimate in applications are discussed two types of nonparametric estimates of the optimal instruments are considered each involves nonparametric regression one by nearest neighbor and the other by series approximation the finite sample properties of the estimators are considered in a small sampling experiment involving an endogenous dummy variable model

iterative methods for common fixed points for a countable family of nonexpansive mappings in uniformly convex spaces abstract let e be a uniformly convex real banach space with a uniformly g teaux differentiable norm let k be a closed convex and nonempty subset of e let t i i 1 be a family of nonexpansive self mappings of k for arbitrary fixed 0 1 define a family of nonexpansive maps s i n 1 by s i 1 i t i where i is the identity map of k let f i 1 f t i 0 it is proved that an iterative sequence x n defined by x 0 k x n 1 n u i 1 i t n s i x n n 0 converges strongly to a common fixed point of the family t i i 1 where n and i t n are sequences in 0 1 satisfying appropriate conditions in each of the following cases a e l p 1 p and b at least one of the t i s is demicompact

strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings abstract let h be a hilbert space consider on h a sequence of nonexpansive mappings t n with common fixed points an equilibrium function g a contraction f with coefficient 0 1 and a strongly positive linear bounded operator a with coefficient 0 let 0 we define a suitable mann type algorithm which strongly converges to the unique solution of the minimization problem min x c 1 2 a x x h x where h is a potential function for f and c is the intersection of the equilibrium points and the common fixed points of the sequence t n

gmm estimation of linear panel data models with time varying individual effects abstract this paper considers models for panel data in which the individual effects vary over time the temporal pattern of variation is arbitrary but it is the same for all individuals the model thus allows one to control for time varying unobservables that are faced by all individuals e g macro economic events and to which individuals may respond differently a generalized within estimator is consistent under strong assumptions on the errors but it is dominated by a generalized method of moments estimator this is perhaps surprising because the generalized within estimator is the mle under normality the efficiency gains from imposing second moment error assumptions are evaluated they are substantial when the regressors and effects are weakly correlated

convergence theorems of shrinking projection methods for equilibrium problem variational inequality problem and a finite family of relatively quasi nonexpansive mappings we introduce a w mapping for a finite family of relatively quasi nonexpansive mappings and construct an iterative scheme for finding a common element of the solution set of equilibrium problem the solution set of the variational inequality problem for an inverse strongly monotone operator and set of common fixed points of a finite family of relatively quasi nonexpansive mappings strong convergence theorems are presented in a 2 uniformly convex and uniformly smooth banach space our results generalize and extend relative results

efficient estimation of models for dynamic panel data abstract in this paper we consider a dynamic model for panel data we show that under standard assumptions there are more moment conditions than are currently exploited in the literature some of these are linear but others are quadratic so that nonlinear gmm is required we also show that exogenous regressors generate a larger number of relevant moment conditions in a dynamic model than they would in a static model

strong convergence theorems on an iterative method for a family of finite nonexpansive mappings in reflexive banach spaces in this paper by using some new analysis techniques we study the approximation problems of common fixed points of halpern s iterative sequence for a class of finite nonexpansive mappings in strictly convex and reflexive banach spaces by using banach s limit the main results presented in this paper generalize extend and improve the corresponding results of bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert spaces j math anal appl 202 1996 150 159 halpern fixed points of nonexpansive maps bull am math soc 73 1967 957 961 shioji and takahashi strong convergence of approximated sequences for nonexpansive mappings in banach spaces proc am math soc 125 1997 3641 3645 takahashi et al approximation of common fixed points of a family of finite nonexpansive mappings in banach spaces sci math jpn 56 2002 475 480 wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 xu another control condition in an iterative method for nonexpansive mappings bull austral math soc 65 2002 109 113 remarks on an iterative method for nonexpansive mappings commun appl nonlinear anal 10 2003 67 75 and others

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

on the convergence of han s method for convex programming with quadratic objective we present an iterative method for minimizing strictly convex quadratic functions over the intersection of a finite number of convex sets the method consists in computing projections onto the individual sets simultaneously and the new iterate is a convex combination of those projections we give convergence proofs even for the inconsistent case i e when the intersection of the sets is empty

how informative is the initial condition in the dynamic panel model with fixed effects abstract i consider estimation of the autoregressive panel model with fixed effects yit ci yi t 1 eit i investigate the estimation method developed by blundell and bond 1998 which makes use of the stationarity of the initial levels i do it by numerically comparing the semiparametric information bounds for the case that incorporates the stationarity of the initial condition and for the case that does not it is found that the efficiency gain can be substantial

the approximation of fixed points of compositions of nonexpansive mappings in hilbert space determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences an algorithm for finding common fixed points of nonexpansive mappings in hilbert space essentially due to halpern is analyzed the main theorem extends wittmann s recent work and partially generalizes a result by lions algorithms of this kind have been applied to the convex feasibility problem

an implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings abstract let h be a hilbert space consider on h a sequence of nonexpansive mappings t n with common fixed points a finite family of equilibrium functions g i i 1 k a contraction f with coefficient 0 1 and a strongly positive linear bounded operator a with coefficient 0 let 0 assuming there are common equilibrium points of the family g i i 1 k which are also fixed points for t n we define a suitable sequence which strongly converges to the unique such point which also satisfies the variational inequality a f x x x 0 for all the x in the intersection of the equilibrium points and the common fixed points of the sequence t n

on general systems of variational inequalities in this paper we present a new relaxed viscosity approximation method and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a suitable equilibrium problem and a general system of variational inequalities