an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

irreducible representations of nongraded witt type lie algebras abstract from his classification of quadratic conformal algebras corresponding to certain hamiltonian pairs in integrable systems xu gave an explicit construction of seven types of nongraded infinite dimensional simple lie algebra related to a finite set of locally finite derivations on certain commutative associative algebras in this paper we construct a family of irreducible generalized weight modules for the nongraded witt type lie algebras based on finite dimensional irreducible modules of general linear lie algebras our results are nongraded generalizations of rao s work on irreducible representations of the derivation lie algebra of the algebra of laurent polynomials in several variables

new generalized simple lie algebras of cartan type over a field with characteristic 0 abstract we construct four new series of generalized simple lie algebras of cartan type using the mixtures of grading operators and down grading operators our results in this paper are further generalizations of those in osborn s work j algebra 185 1996 820 835

multiplicity one representations of divergence free lie algebras abstract divergence free lie algebras also known as the special lie algebras of cartan type are lie algebras of volume preserving transformation groups they are simple in generic case dokovic and zhao found a certain graded generalization of them in this paper we classify all the irreducible and indecomposable multiplicity one modules of the simple generalized divergence free lie algebras

identification and nonparametric estimation of a transformed additively separable model let r x z be a function that along with its derivatives can be consistently estimated nonparametrically this paper discusses the identification and consistent estimation of the unknown functions h m g and f where r x z h m x z m x z g x f z and h is strictly monotonic an estimation algorithm is proposed for each of the model s unknown components when r x z represents a conditional mean function the resulting estimators use marginal integration to separate the components g and f our estimators are shown to have a limiting normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives their small sample performance is studied in a monte carlo experiment we apply our results to estimate generalized homothetic production functions for four industries in the chinese economy

estimation of additive regression models with known links summary we consider estimation of an additive nonparametric regression model with known link function the asymptotic distribution of this regression estimate is given the practical performance is investigated via an application to the study of migration between east and west germany

local partitioned regression in this paper we introduce a kernel based estimation principle for nonparametric models named local partitioned regression lpr this principle is a nonparametric generalization of the familiar partition regression in linear models it has several key advantages first it generates estimators for a very large class of semi and nonparametric models a number of examples that are particularly relevant for economic applications will be discussed in this paper this class contains the additive partially linear and varying coefficient models as well as several other models that have not been discussed in the literature second lpr based estimators achieve optimality criteria they have optimal speed of convergence and are oracle efficient moreover they are simple in structure widely applicable and computationally inexpensive a monte carlo simulation highlights these advantages

some representations of nongraded lie algebras of generalized witt type abstract in a recent paper by xu some simple lie algebras of generalized cartan type were constructed using the mixtures of grading operators and down grading operators among them are the simple lie algebras of generalized witt type which are in general nongraded and have no torus in this paper some representations of these simple lie algebras of generalized witt type are presented

structure of a new class of non graded infinite dimensional simple lie algebras abstract a new class of infinite dimensional simple lie algebras over a field with characteristic 0 are constructed these are examples of non graded lie algebras the isomorphism classes of these lie algebras are determined the structure space of these algebras is given explicitly

non parametric estimation of the odds ratios for continuous exposures using generalized additive models with an unknown link function the generalized additive model gam is a powerful and widely used tool that allows researchers to fit non parametrically the effect of continuous predictors on a transformation of the mean response variable such a transformation is given by a so called link function and in gams this link function is assumed to be known nevertheless if an incorrect choice is made for the link the resulting gam is misspecified and the results obtained may be misleading in this paper we propose a modified version of the local scoring algorithm that allows for the non parametric estimation of the link function by using local linear kernel smoothers to better understand the effect that each covariate produces on the outcome results are expressed in terms of the non parametric odds ratio or curves bootstrap techniques were used to correct the bias in the or estimation and to construct point wise confidence intervals a simulation study was carried out to assess the behaviour of the resulting estimates the proposed methodology was illustrated using data from the aids register of galicia nw spain with a view to assessing the effect of the cd4 lymphocyte count on the probability of being aids diagnosed via tuberculosis tb this application shows how the link s flexibility makes it possible to obtain or curve estimates that are less sensitive to the presence of outliers and unusual values that are often present in the extremes of the covariate distributions

direct semiparametric estimation of single index models with discrete covariates abstract others have developed average derivative estimators of the parameter in the model e y x x g x where g is an unknown function and x is a random vector these estimators are noniterative and easy to compute but require that x be continuously distributed this article develops a noniterative easily computed estimator of for models in which some components of x are discrete the estimator is n consistent and asymptotically normal an application to data on product innovation by german manufacturers illustrates the estimator s usefulness

efficiency of weighted average derivative estimators and index models weighted average derivatives are useful parameters for semiparametric index models and nonparametric demand analysis this paper gives efficiency results for average derivative estimators including formulating estimators that have high efficiency our analysis is carried out in three steps first we derive the efficiency bound for weighted average derivatives of conditional location functionals such as the conditional mean and median second we derive the efficiency bound for semiparametric index models where the location measure depends only on indices or linear combinations of the regressors third we compare the bound for index models with the asymptotic variance of weighted average derivative estimators of the index coefficients we characterize the form of the optimal weight function when the distribution of the regressors is elliptically symmetric in more general cases we discuss how to combine estimators with different weight functions to achieve efficiency we derive a general condition for approximate efficiency of pooled minimum chi square estimators for index model coefficients based on weighted average derivatives finally we discuss ways of selecting the type and number of weighting functions to achieve high efficiency

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

simple lie algebras of witt type abstract letkbe a field letabe an associative commutativek algebra and let be a nonzerok vector space of commutingk derivations ofa then with a rather natural definition a k a becomes a lie algebra and we obtain necessary and sufficient conditions here for this lie algebra to be simple with one minor exception in characteristic 2 simplicity occurs if and only ifais simple anda a acts faithfully as derivations ona

classification of simple novikov algebras and their irreducible modules of characteristic 0 abstract in this paper we first present a classification theorem of simple infinite dimensional novikov algebras over an algebraically closed field of characteristic 0 then we classify all the irreducible modules of certain infinite dimensional simple novikov algebras with an idempotent element whose left action is locally finite

identification of a competing risks model with unknown transformations of latent failure times this paper is concerned with identification of a competing risks model with unknown transformations of latent failure times the model includes as special cases competing risks versions of proportional hazards mixed proportional hazards and accelerated failure time models it is shown that covariate effects on latent failure times cause specific link functions and the joint survivor function of the disturbance terms can be identified without relying on modelling the dependence between latent failure times parametrically nor using an exclusion restriction among covariates as a result the paper provides an identification result about the joint survivor function of the latent failure times conditional on covariates

estimation of a nonparametric censored regression model with an application to unemployment insurance spells in this paper we consider identification and estimation of a censored nonparametric location scale model we first show that in the case where the location function is strictly less than the fixed censoring point for all values in the support of the explanatory variables then the location function is not identified anywhere in contrast if the location function is greater or equal to the censoring point with positive probability then the location function is identified on the entire support including the region where the location function is below the censoring point in the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for three distinct quantiles the new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution a small scale simulation study indicates that the proposed estimation procedure performs well in finite samples we also present an empirical application to unemployment insurance duration using administrative level data from new jersey jel classification c14 c24 j64 j65

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

smooth optimum kernel estimators of densities regression curves and modes several criteria concerning the choice of kernels for the nonparametric estimation of functions and their derivatives are discussed a specific optimality criterion is described which applies to kernels of compact support and of different orders of smoothness the solutions of the corresponding variational problems are explicitly given many kernels discussed previously are obtained as special cases

generalized varying coefficient models with unknown link function summary we propose a new estimation method for generalized varying coefficient models where the link function is specified up to some smoothness conditions consistency and asymptotic normality of the estimated varying coefficient functions are established simulation results and a real data application demonstrate the usefulness of the new method

complex analytic quotients of algebraic g varieties it is shown that any compact semistable quotient of a normal variety by a complex reductive lie group g in the sense of heinzner and snow is a good quotient this reduces the investigation and classification of such complex analytic quotients to the corresponding questions in the algebraic category as a consequence of our main result we show that every compact space in nemirovski s class fancyscript q g has a realisation as a good quotient and that every complete algebraic variety in fancyscript q g is unirational with finitely generated cox ring and at worst rational singularities in particular every compact space in class fancyscript q t where t is an algebraic torus is a toric variety

cross validation and the estimation of conditional probability densities many practical problems especially some connected with forecasting require nonparametric estimation of conditional densities from mixed data for example given an explanatory data vector x for a prospective customer with components that could include the customer s salary occupation age sex marital status and address a company might wish to estimate the density of the expenditure y that could be made by that person basing the inference on observations of x y for previous clients choosing appropriate smoothing parameters for this problem can be tricky not in the least because plug in rules take a particularly complex form in the case of mixed data an obvious difficulty is that there exists no general formula for the optimal smoothing parameters more insidiously and more seriously it can be difficult to determine which components of x are relevant to the problem of conditional inference for example if the jth component of x is independent of y then that component is irrelevant to es

local polynomial estimation of nonparametric simultaneous equations models abstract we define a new procedure for consistent estimation of nonparametric simultaneous equations models under the conditional mean independence restriction of newey et al 1999 nonparametric estimation of triangular simultaneous equation models econometrica 67 565 603 it is based upon local polynomial regression and marginal integration techniques we establish the asymptotic distribution of our estimator under weak data dependence conditions simulation evidence suggests that our estimator may significantly outperform the estimators of pinkse 2000 nonparametric two step regression estimation when regressors and errors are dependent canadian journal of statistics 28 289 300 and newey and powell 2003 instrumental variable estimation of nonparametric models econometrica 71 1565 1578

nonparametric estimation of homothetic and homothetically separable functions for vectors x and w let r x w be a function that can be nonparametrically estimated consistently and asymptotically normally we provide consistent asymptotically normal estimators for the functions g and h where r x w h g x w g is linearly homogeneous and h is monotonic in g this framework encompasses homothetic and homothetically separable functions such models reduce the curse of dimensionality provide a natural generalization of linear index models and are widely used in utility production and cost function applications extensions to related functional forms include a generalized partly linear model with unknown link function we provide simulation evidence on the small sample performance of our estimator and we apply our method to a chinese production dataset

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

a note on jackknifing kernel regression function estimators corresp estimation of the value of a regression function at a point of continuity using a kernel type estimator is considered and improvements by a jackknife technique are discussed it is seen that a so called generalized jackknife estimator asymptotically improves upon an ordinary kernel type estimator however for a fixed sample size the generalized jackknife method may inflate the mean square error

a virtual fundamental class construction for the moduli space of c n equivariant morphisms abstract let x be a smooth projective variety with the action of c n the article describes the moduli space of c n equivariant morphisms from stable toric varieties into x as the inverse limit of the git quotients of x and their flips when these spaces are enhanced with a naturally associated deligne mumford stack structure this description is used for constructing a class in the chow group of the moduli space of dimension dim x n which is invariant under equivariant deformations of x

generalized cartan typeslie algebras in characteristic zero generalized witt algebras w s w a t w over a field f of characterw x istic 0 were introduced by n kawamoto 8 about 10 years ago and have w x been studied by several authors since that time see 2 6 7 9 12 let us just mention here that a is a torsion free abelian group t a vector space over f and w t a a f a map which is linear in the first variable and additive in the second one as a vector space w s fa m t where fa is f the group algebra of a over f with basis t x g a we write t instead of t x m for x g a and g t for the definition of the lie bracket see the next section the lie algebra w is a graded with homogeneous components w s t t x g a x for simplicity we shall assume in this introduction that the lie algebra w is simple i e that w is nondegenerate in the sense defined in the next w x section in our previous paper 2 we have determined the derivation algebra der w of w we have constructed all isomorphisms w a w9 between two simple generalized witt algebras and we have computed the 2 second cohomology group h w f one can introduce several classes of simple lie subalgebras of w one such class so called algebras of generalized cartan type w has been w x introduced and investigated in our recent paper 4 in the present paper we introduce yet another class to which we refer as the algebras of

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

quasi likelihood estimation in semiparametric models abstract suppose the expected value of a response variable y may be written h x t where x and t are covariates each of which may be vector valued is an unknown parameter vector is an unknown smooth function and h is a known function in this article we outline a method for estimating the parameter of this type of semiparametric model using a quasi likelihood function algorithms for computing the estimates are given and the asymptotic distribution theory for the estimators is developed the generalization of this approach to the case in which y is a multivariate response is also considered the methodology is illustrated on two data sets and the results of a small monte carlo study are presented

weak and strong uniform consistency of kernel regression estimates we study the estimation of a regression function by the kernel method under mild conditions on the window the bandwidth and the underlying distribution of the bivariate observations x i y i we obtain the weak and strong uniform convergence rates on a bounded interval these results parallel those of silverman 1978 on density estimation and extend those of schuster and yakowitz 1979 and collomb 1979 on regression estimation

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

consistent model selection for marginal generalized additive model for correlated data we consider the generalized additive model when responses from the same cluster are correlated incorporating correlation in the estimation of nonparametric components for the generalized additive model is important because it improves estimation efficiency and increases statistical power for model selection in our setting there is no specified likelihood function for the generalized additive model because the outcomes could be nonnormal and discrete which makes estimation and model selection very challenging problems we propose consistent estimation and model selection that incorporate the correlation structure we establish an asymptotic property with l2 norm consistency for the nonparametric components which achieves the optimal rate of convergence in addition the proposed model selection strategy is able to select the correct generalized additive model consistently that is with probability approaching to 1 the estimators for the zero function components converge to 0 almost surely we illus

nonparametric matching and efficient estimators of homothetically separable functions for vectors z and w and scalar v let r v z w be a function that can be non parametrically estimated consistently and asymptotically normally such as a distribution density or conditional mean regression function we provide consistent asymptotically normal nonparametric estimators for the functions g and h where r v z w h vg z w and some related models this framework encompasses homothetic and homothetically separable functions and transformed partly additive models r v z w h v g z w for unknown functions g and h such models reduce the curse of dimensionality provide a natural generalization of linear index models and are widely used in utility production and cost function applications we also provide an estimator of g that is oracle efficient achieving the same performance as an estimator based on local least squares when h is known

simulation and the asymptotics of optimization estimators on demontre un theoreme de limite centrale general pour des estimateurs definis par minimisation de la longueur d une fonction de critere aleatoire a valeurs vectorielles aucune hypothese de regularite suffisante n est imposee sur la fonction de critere pour que les resultats puissent etre appliques a une classe d estimlateurs de simulation assez large des analyses completes de deux estimateurs de simulation l un introduit par pakes l autre par mcfadden illustrent l application des theoremes generaux

on kolmogorov s representation of functions of several variables by functions of one variable abstract this paper proposes a multivariate nonparametric regression estimator motivated by kolmogorov doklady 114 1957 679 we consider functions of the form k 1 t g k k 1 k x 1 k d k x d 1 t

structure of divergence free lie algebras abstract one of the four well known series of simple lie algebras of cartan type is the series of lie algebras of special type which are divergence free lie algebras associated with polynomial algebras and the operators of taking partial derivatives connected with volume preserving diffeomorphisms in this paper we determine the structure space of the divergence free lie algebras associated with pairs of a commutative associative algebra with an identity element and its finite dimensional commutative locally finite derivation subalgebra such that the commutative associative algebra is derivation simple with respect to the derivation subalgebra

derivation simple algebras and the structures of lie algebras of witt type abstract we classify all the pairs of a commutative associative algebra with an identity element and its finite dimensional locally finite abelian derivation subalgebra such that the commutative associative algebra is derivation simple with respect to the derivation subalgebra over an algebraically closed field with characteristic 0 such pairs are the fundamental ingredients for constructing simple lie algebras of cartan type moreover we determine the isomorphism classes of the simple lie algebras of witt type the structure space of these algebras is given explicitly

classification of derivation simple color algebras related to locally finite derivations we classify the pairs a d consisting of an e color commutative associative algebra a with an identity element over an algebraically closed field f of characteristic zero and a finite dimensional subspace d of e color commutative locally finite color derivations of a such that a is graded d simple and the eigenspaces for elements of d are graded such pairs are the important ingredients in constructing some simple lie color algebras which are in general not finitely graded as some applications using such pairs we construct new explicit simple lie color algebras of generalized witt type weyl type

rate optimal estimation for a general class of nonparametric regression models with unknown link functions this paper discusses a nonparametric regression model that naturally generalizes neural network models the model is based on a finite number of one dimensional transformations and can be estimated with a one dimensional rate of convergence the model contains the generalized additive model with unknown link function as a special case for this case it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion

semiparametric estimation of a panel data proportional hazards model with fixed effects this paper considers a panel duration model that has a proportional hazards specification with fixed effects the paper shows how to estimate the baseline and integrated baseline hazard functions without assuming that they belong to known finite dimensional families of functions existing estimators assume that the baseline hazard function belongs to a known parametric family therefore the estimators presented here are more general than existing ones this paper also presents a method for estimating the parametric part of the proportional hazards model with dependent right censoring under which the partial likelihood estimator is inconsistent the paper presents some monte carlo evidence on the small sample performance of the new estimators

derivations isomorphisms and second cohomology of generalized witt algebras generalized witt algebras over a field f of characteristic 0 were defined by kawamoto about 12 years ago using different notations from kawamoto s we give an essentially equivalent definition of generalized witt algebras w w a t over f where the ingredients are an abelian group a a vector space t over f and a map t a k which is linear in the first variable and additive in the second one in this paper the derivations of any generalized witt algebra w w a t with the right kernel of being 0 are explicitly described the isomorphisms between any two simple generalized witt algebras are completely determined and the second cohomology group h2 w f for any simple generalized witt algebra is computed the derivations the automorphisms and the second cohomology groups of some special generalized witt algebras have been studied by several other authors as indicated in the references

gradient based smoothing parameter selection for nonparametric regression estimation abstract estimating gradients is of crucial importance across a broad range of applied economic domains here we consider data driven bandwidth selection based on the gradient of an unknown regression function this is a difficult problem given that direct observation of the value of the gradient is typically not observed the procedure developed here delivers bandwidths which behave asymptotically as though they were selected knowing the true gradient simulated examples showcase the finite sample attraction of this new mechanism and confirm the theoretical predictions

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field

nonparametric estimation of a generalized additive model with an unknown link function mean of a random scalar y conditional on a random vector x e rd let h x e yix x denote the conditional mean function this paper is concerned with estimating h under weak assumptions about its functional form when x is a multidimensional continuous random variable the paper describes a model that nests single index additive and multiplicative models and that can be estimated with a faster rate of convergence in probability than can a fully nonparametric model nonparametric estimation of h is usually unattractive when x is multidimensional the rate of convergence of nonparametric estimators decreases rapidly as the dimension of x increases and nonparametric estimates can be very imprecise with samples of practical size when x is multidimensional the curse of dimensionality this problem can be overcome through the use of dimension reduction methods they reduce the effective dimension of the estimation problem by making assumptions about the functional form of h that are stronger than those of a fully nonparametric estimator but weaker than those of a finite dimensional parametric model one method of dimension reduction is semiparametric single index modeling the best known and most easily estimated semiparametric single index model assumes that 1 1 h x g 3 x where 3 is an unknown d x 1 vector and g is an unknown function the vector 3 can be estimated with an n 1 2 rate of convergence in probability which is the rate that would be obtained if g were known han 1987 hardle and stoker 1989 horowitz and hardle 1996 ichimura 1993 klein and spady 1993 newey and stoker 1993 powell stock and stoker 1989 sherman 1993 stoker 1991 g can be estimated with the rate of convergence n r 2r 1 where r is an integer that depends on the smoothness of g but not on d dimension reduction can also be achieved by using a nonparametric generalized additive model in such a model