some characterizations of almost sure bounds for weighted multidimensional empirical distributions and a glivenko cantelli theorem for sample quantiles characterizations of almost sure bounds and a glivenko cantelli theorem are obtained for certain weighted m dimensional empirical distributions these results constitute generalizations and extensions of the work of shorack and wellner 1978 and wellner 1977 1978 also as an example of the potential use of the techniques developed in this paper a glivenko cantelli type theorem is proven for sample quantiles

transversality conditions for infinite horizon optimality higher order differential problems abstract michel p michel some clarifications on the transversality condition econometrica 58 1990 705 723 and ekeland and scheinkman i ekeland j a scheinkman transversality conditions for some infinite horizon discrete time optimization problems mathematics of operations research 11 1986 216 229 presented the transversality condition for the first order differential problems max x 0 v x t x t t d t which may have unbounded objective functions kamihigashi t kamihigashi necessity of transversality conditions for infinite horizon problems econometrica 69 2001 995 1012 showed a generalization of their transversality condition that does not assume concavity using the variational approach this paper deals with higher order differential problems max x 0 v x t x t x t x n t t d t we derive two conditions euler s condition and the transversality condition for such problems in a simple manner they are imperative for solving variational problems furthermore two assumptions are necessary to induce the two conditions we construct a counterexample in which the transversality condition is not satisfied without the two assumptions

gaussian approximation of local empirical processes indexed by functions an extended notion of a local empirical process indexed by functions is introduced which includes kernel density and regression function estimators and the conditional empirical process as special cases under suitable regularity conditions a central limit theorem and a strong approximation by a sequence of gaussian processes are established for such processes a compact law of the iterated logarithm lil is then inferred from the corresponding lil for the approximating sequence of gaussian processes a number of statistical applications of our results are indicated

necessity of transversality conditions for infinite horizon problems this paper studies necessity of transversality conditions for the continuous time reduced form model by generalizing benveniste and scheinkman s 1982 envelope condition and michel s 1990 version of the squeezing argument we show a generalization of michel s 1990 theorem 1 necessity result that does not assume concavity the generalization enables us to generalize ekeland and scheinkman s 1986 result as well as to establish a new result that does not require the objective functional to be finite the new result implies that homogeneity of the return function alone is sufficient for the necessity of the most standard transversality condition our results are also applied to a nonstationary version of the one sector growth model it is shown that bubbles never arise in an equilibrium asset pricing model with a nonlinear constraint

picard lefschetz theory for the coadjoint quotient of a semisimple lie algebra the paper develops a picard lefschetz theory for the coadjoint quotient of a semisimple lie algebra and analyzes the resulting monodromy representation of the weyl group

green functions and character sheaves purely combinatorial way using earlier ideas of p hall in the general case they were introduced 3 in terms of l adic cohomology as values of certain virtual representations of r o t is a maximal torus defined over fq at unipotent elements the characters of rg 0 at arbitrary elements were then expressible in a simple form in terms of green functions of g and of smaller groups one drawback of the definition of 3 was that it did not allow one to compute the green functions except in some simple cases another definition of green functions was proposed by springer first in terms of trigonometric sums on the lie algebra and later in geometrical terms 17 this definition was applicable only in large characteristic and in that case it was identified with the definition in 3 by springer 17 and kazhdan 10 in 12 i observed that green functions for gln can be redefined in terms of intersection cohomology this led me to a new definition of green functions

inference on endogenously censored regression models using conditional moment inequalities under a quantile restriction randomly censored regression models can be written in terms of conditional moment inequalities we study the identified features of these moment inequalities with respect to the regression parameters where we allow for covariate dependent censoring endogenous censoring and endogenous regressors these inequalities restrict the parameters to a set we show regular point identification can be achieved under a set of interpretable sufficient conditions we then provide a simple way to convert conditional moment inequalities into unconditional ones while preserving the informational content our method obviates the need for nonparametric estimation which would require the selection of smoothing parameters and trimming procedures without the point identification conditions our objective function can be used to do inference on the partially identified parameter maintaining the point identification conditions we propose a quantile minimum distance estimator which converges at the parametric rate to the parameter vector of interest and has an asymptotically normal distribution a small scale simulation study and an application using drug relapse data demonstrate satisfactory finite sample performance

some clarifications on the transversality condition in this paper the authors study a general concave discrete time infinite horizon optimal control problem they establish necessary and sufficient conditions for optimality in the weak sense of w a brock and for optimality in the strong sense of d gale the corresponding transversality conditions are general exhaustion properties of the limit value of the optimal state variables these properties cover and extend the well known results obtained in special cases copyright 1990 by the econometric society

on a resource allocation model with infinite horizon in this paper we treat a resource allocation model defined on an infinite interval we show that the solution of the corresponding problem with finite horizon cannot be extended to a solution of the infinite horizon problem since the resource allocation problem in the unmodified setting does not have a solution on an unbounded interval to change this situation we bring an additional state constraint into the model which contains a weight function the new problem called now the adapted resource allocation problem has an optimal solution which will be identified by means of the duality concept of klotzler

pontryagin type maximum principle for budget constrained infinite horizon optimal control problems with linear dynamics abstract in this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint also interpreted as a budget constraint is considered herein a linear both in the state and in the control dynamic is allowed the problem setting includes a weighted sobolev space as the state space for this class of problems we establish the necessary optimality conditions in form of a pontryagin type maximum principle including a transversality condition the proved theoretical result is applied to a linear quadratic regulator problem

nonparametric efficiency analysis a multivariate conditional quantile approach this paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup multiple inputs and multiple outputs it introduces quantile efficiency scores a nonparametric estimator is proposed achieving strong consistency and asymptotic normality then if increases to one as a function of the sample size we recover the properties of the fdh estimator but our estimator is more robust to the perturbations in data since it attains a finite gross error sensitivity environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed numerical examples illustrate the usefulness of the approach

conditional empirical processes consider a sequence i xi yi i 1 of independent d 1 random vectors with common d f h text h left text x y right mathbb p left text x x y y right text left text x y right in mathbb r text d 1

transversality conditions for some infinite horizon discrete time optimization problems this paper considers a class of discrete time infinite horizon optimization problems arising in economics necessary optimality conditions for such problems consist of an euler equation and a transversality condition at infinity our concern here is with the latter condition previous results for this type of problem have required such restrictions as concavity and boundedness of the utility functions whose sum is being maximized here we derive a transversality condition that remains valid under considerably more general hypotheses in doing so we introduce methods that may also be applicable to other situations such as optimization in continuous time

the pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons this paper suggests some further developments in the theory of first order necessary optimality conditions for problems of optimal control with infinite time horizons we describe an approximation technique involving auxiliary finite horizon optimal control problems and use it to prove new versions of the pontryagin maximum principle special attention is paid to the behavior of the adjoint variables and the hamiltonian typical cases in which standard transversality conditions hold at infinity are described several significant earlier results are generalized

shadow prices in infinite horizon optimal control problems with dominating discounts we consider a nonlinear optimal control problem in which an integrated discounted utility index is maximized over an infinite time interval the problem statement is motivated by various optimization problems arising in economics assuming that the discount parameter dominates the growth rates in the state variables and in the gradient of the current utility we develop a version of the pontryagin maximum principle providing a complete set of necessary optimality conditions and also suggesting an analytic expression for the values of the adjoint variables often viewed as shadow prices in the economic literature we illustrate the proposed methodology by applying it to the problem of optimal capital accumulation for a stylized model of an enterprise

optimal control problems with mixed control state constraints noindent we consider control problems governed by semilinear parabolic equations in the presence of pointwise mixed control state constraints we obtain optimality conditions with finitely additive measures as multipliers associated to the mixed constraints we study the regularity of the multipliers for different problems in particular when a monotonicity or a separation condition is satisfied we prove that multipliers are bounded measurable functions

weighted functional spaces approach in infinite horizon optimal control problems a systematic analysis of hidden opportunities and advantages abstract this paper constitutes the advantages of using the weighted sobolev and weighted lebesgue spaces in optimal control problems defined on an infinite time interval based on numerous examples it demonstrates how the introduction of certain weight or density functions into the problem statement may influence the existence of an optimal solution and the optimality of a chosen candidate the positive effects of the proper relation between the state and the co state functional spaces for the necessary optimality conditions as well as for the development of numerical schemes are discussed this paper is based on over one decade of research in this field and summarizes the main findings concerning the use of weight functions in optimal control problems

higher order infinite horizon variational problems in discrete quantum calculus we obtain necessary optimality conditions for higher order infinite horizon problems of the calculus of variations via discrete quantum operators

inference in censored models with endogenous regressors this paper analyzes the linear regression model y x with a conditional median assumption med e z 0 where z is a vector of exogenous instrument random variables we study inference on the parameter when y is censored and x is endogenous we treat the censored model as a model with interval observation on an outcome thus obtaining an incomplete model with inequality restrictions on conditional median regressions we analyze the identified features of the model and provide sufficient conditions for point identification of the parameter we use a minimum distance estimator to consistently estimate the identified features of the model we show that under point identification conditions and additional regularity conditions the estimator based on inequality restrictions is n normal and we derive its asymptotic variance one can use our setup to treat the identification and estimation of endogenous linear median regression models with no censoring a monte carlo analysis illustrates our estimator in the censored and the uncensored case

stationary bubble equilibria in rational expectation models abstract a linear rational expectation model with current expectations admits a unique linear stationary dynamic equilibrium only under specific restrictions on the parameter values this paper shows that in general there is a multiplicity of stationary dynamic equilibria due to the existence of nonlinear stationary equilibria these nonlinear stationary equilibria are consistent with the self fulfilling prophecies that characterize the rational expectation equilibria and can display speculative bubbles volatility induced mean reversion and or stochastic autoregressive patterns they are also compatible with the transversality conditions when the model involves intertemporal optimization the stationary nonlinear dynamic equilibria are economically relevant their analysis requires revised methods of identification for the stationary equilibrium impulse response analysis and estimation techniques which are presented in this paper standard econometric and economic methods which ignore the nonlinear stationary solutions provide misleading outcomes which may affect the validity of an economic policy or portfolio strategy

an existence result for optimal economic growth problems abstract an existence result for optimal control problems of lagrange type with unbounded time domain is derived very directly from a corresponding result for problems with bounded time domain this subsumes the main existence result of r f baum j optim theory appl 19 1976 89 116 and has the existence results for optimal economic growth problems of s i takekuma j math econom 7 1980 193 208 and m j p magill econometrica 49 1981 679 711 j math anal appl 82 1981 66 74 as simple corollaries in addition a new notion of uniform integrability is used which coincides with the classical notion if the time domain is bounded

uniform in bandwidth consistency of kernel type function estimators we introduce a general method to prove uniform in bandwidth consistency of kernel type function estimators examples include the kernel density estimator the nadaraya watson regression estimator and the conditional empirical process our results may be useful to establish uniform consistency of data driven bandwidth kernel type function estimators

testing for stochastic monotonicity we propose a test of the hypothesis of stochastic monotonicity this hypothesis is of interest in many applications in economics our test is based on the supremum of a rescaled u statistic we show that its asymptotic distribution is gumbel the proof is difficult because the approximating gaussian stochastic process contains both a stationary and a nonstationary part and so we have to extend existing results that only apply to either one or the other case we also propose a refinement to the asymptotic approximation that we show works much better in finite samples we apply our test to the study of intergenerational income mobility

brief paper pseudospectral methods for solving infinite horizon optimal control problems an important aspect of numerically approximating the solution of an infinite horizon optimal control problem is the manner in which the horizon is treated generally an infinite horizon optimal control problem is approximated with a finite horizon problem in such cases regardless of the finite duration of the approximation the final time lies an infinite duration from the actual horizon at t in this paper we describe two new direct pseudospectral methods using legendre gauss lg and legendre gauss radau lgr collocation for solving infinite horizon optimal control problems numerically a smooth strictly monotonic transformation is used to map the infinite time domain t 0 onto a half open interval t 1 1 the resulting problem on the finite interval is transcribed to a nonlinear programming problem using collocation the proposed methods yield approximations to the state and the costate on the entire horizon including approximations at t these pseudospectral methods can be written equivalently in either a differential or an implicit integral form in numerical experiments the discrete solution exhibits exponential convergence as a function of the number of collocation points it is shown that the map f 1 1 0 can be tuned to improve the quality of the discrete approximation

on almost sure convergence of conditional empirical distribution functions on etudie la convergence presque sure d une distribution empirique conditionnelle de type noyau a la fois en norme sup et en norme sup ponderee

different interpretations of the improper integral objective in an infinite horizon control problem abstract we provide an example of a convex infinite horizon problem with a linear objective functional where the different interpretations of the improper integral 0 f t x t u t d t in either lebesgue or riemann sense lead to different but finite optimal values

optimal solutions to the infinite horizon problems constructing the optimum as the limit of the solutions for the finite horizon problems abstract the limit of the solutions for the finite horizon problems is not always optimal for the infinite horizon problems in this paper we provide some special conditions that ensure its validity it can be applied to constructing the optimal solutions for the undiscounted infinite horizon optimization problems we also demonstrate a simple example to explain this structure

orbits invariants and representations associated to involutions of reductive groups by an involution of an algebraic group or lie algebra we mean an automorphism 0 such that 0 2 is the identity automorphism let 0 be an involution of a complex reductive lie algebra q and let p denote the 1 eigenspace of 0 on q get g be the adjoint group of q and let k g glog go kostant and rallis 10 have made a detailed study of the action of k on p in particular they obtain very precise information concerning the orbits of k on p and the representation of k on c p the algebra of polynomial functions on p in this paper we consider a global analogue of the problem studied by kostant and rallis let g be a reductive affine algebraic group over an algebraically closed field k of characteristic 2 let 0 be an involution of g and let k gegi0 g g if g is semisimple and the base field is c then g k is the complexification of a riemannian symmetric space we study the action of k and of groups closely related to k by left translation on the coset space g k for technical reasons it is convenient to study a slightly different but equivalent problem let r g g be defined by r g g0 g i then z g p is a closed subvariety of g furthermore z is constant on left cosets of g modulo k and induces an isomorphism o g k p we have o k g k k o g k for k e k and geg thus p is stable under conjugation by k and a is a k isomorphism of affine k varieties we consider the action of k on p by conjugation let x e g have jordan decomposition x x x then we show that x e p if and only if both x and x are in p thus we have a jordan decomposition for elements of p this will play a key role in our results a torus s of g is o anisotropic if o s s 1 for every ses it is known that any two maximal 0 anisotropic tori of g are k let a be a maximal 0 anisotropic torus of g the following result characterizes semisimple elements of p

brief on a sufficient transversality condition for infinite horizon optimal control problems we prove that for a class of optimal control problems with infinite horizon convergence to zero for the co state variable when time goes to infinity is a sufficient transversality condition