reachability and minimal times for state constrained nonlinear problems without any controllability assumption we consider a target problem for a nonlinear system under state constraints we give a new continuous level set approach for characterizing the optimal times and the backward reachability sets this approach leads to a characterization via a hamilton jacobi equation without assuming any controllability assumption we also treat the case of time dependent state constraints as well as a target problem for a two player game with state constraints our method gives a good framework for numerical approximations and some numerical illustrations are included in the paper

simple diagonal locally finite lie algebras the ground field f is an algebraically closed field of zero characteristic and bbb n is the set of natural numbers let l be a locally finite dimensional or em locally finite for brevity lie algebra assume for simplicity that l has countable dimension then one can choose finite dimensional subalgebras l i i in bbb n of l in such a way that l i subset l i 1 for all i and l bigcup i in bbb n l i the set l i mid i in bbb n is called a em local system of l assume that l is simple then all l i can be chosen to be perfect that is l i l i l i we shall call such local systems em perfect let s i s i 1 oplus ldots oplus s i n i be a levi subalgebra of l i where s i 1 ldots s i n i are simple components of s i and let v i k be the standard s i k module since l i is perfect for every k there exists a unique irreducible l i module cal v i k such that the restriction cal v i k downarrow s i k is isomorphic to v i k an embedding l i to l i 1 is called em diagonal if for each l any non trivial composition factor of the restriction cal v i 1 l downarrow l i is isomorphic to cal v i k or its dual cal v i k for some k we prove that a simple locally finite lie algebra l can be embedded into a locally finite associative algebra if and only if there exists a perfect local system l i i in bbb n of l such that all embeddings l i to l i 1 are diagonal note that this result can be considered as a version of ado s theorem for simple locally finite lie algebras let v be a vector space an element x in frak gl v is called em finitary if dim xv infty the finitary transformations of v form an ideal frak fgl v of frak gl v and any subalgebra of frak fgl v is called a em finitary lie algebra we classify all finitary simple lie algebras of countable dimension it turns out that there are only three frak sl infty f frak so infty f and frak sp infty f the author has classified all finitary simple lie algebras and will describe this in a subsequent paper the analogous problem in group theory has been recently solved by j i hall he classified simple locally finite groups of finitary linear transformations 1991 mathematics subject classification 17b35 17b65

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

nonparametric quantile estimations for dynamic smooth coefficient models in this article quantile regression methods are suggested for a class of smooth coefficient time series models we use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework we establish the asymptotic properties of both the local polynomial and local constant estimators for mixing time series also a bandwidth selector based on the nonparametric version of the akaike information criterion is suggested together with a consistent estimate of the asymptotic covariance matrix furthermore the asymptotic behaviors of the estimators at boundaries are examined a comparison of the local polynomial quantile estimator with the local constant estimator is presented a simulation study is carried out to illustrate the performance of estimates an empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures

a bott borel weil theory for direct limits of algebraic groups we develop a bott borel weil theory for direct limits of algebraic groups some of our results apply to locally reductive ind groups g in general i e to arbitrary direct limits of connected reductive linear algebraic groups our most explicit results concern root reductive ind groups g the locally reductive ind groups whose lie algebras admit root decomposition given a parabolic subgroup p of g and a rational irreducible p module we consider the irreducible g sheaves inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i and their duals inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i these sheaves are locally free in general of infinite rank we prove a general analog of the bott borel weil theorem for inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i namely that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i is nonzero for at most one index q q 0 and that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i is isomorphic to the dual of a rational irreducible g module v for q 0 0 we show that in contrast to the finite dimensional case v need not admit an irreducible p submodule there however one has a larger parabolic subgroup w p p constructed from p and a weyl group element w of length q 0 such that v is generated by an irreducible w p submodule consequently certain g modules v can appear only for q 0 0 never for q 0 0 for inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 06i we show that there is no analog of bott s vanishing theorem more precisely that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 07i can have arbitrarily many nonzero cohomology groups finally we give an explicit criterion for the projectivity of the ind variety g p showing that g p is in general not projective

unitary highest weight modules of inductive limit lie algebras and groups abstract representations of inductive limits of finite dimensional lie groups and algebras am our main objects of study such representations can be constructed by taking inductive limits of the representations of the finite dimensional groups or algebras for finite dimensional lie groups and algebras of hermitian symmetric type enright howe wallach classified those highest weight representations which are unitarizable in this paper we consider the limits of the algebras u p n so 2n and sp n r the limits of the corresponding maximal compact subgroup and the limits of the corresponding generalized verma modules we give necessary and sufficient conditions for the inductive limit representation to be unitarizable in all three cases we show that a necessary condition for unitarizability is that the highest weight is eventually constant we also give sufficient conditions depending on the constant which will ensure that the limit is unitarizable

functional coefficient instrumental variables models we consider estimation of nonparametric structural models under a functional coefficient representation for the regression function under this representation models are linear in the endogenous components with coefficients given by unknown functions of the predetermined variables a nonparametric generalization of random coefficient models the functional coefficient restriction is an intermediate approach between fully nonparametric structural models that are ill posed when endogenous variables are continuously distributed and partially linear models over which they have appreciable flexibility we propose two step estimators that use local linear approximations in both steps the first step is to estimate a vector of reduced forms of regression models and the second step is local linear regression using the estimated reduced forms as regressors our large sample results include consistency and asymptotic normality of the proposed estimators the high practical power of estimators is illustrated via both a monte carlo simulation study and an application to returns to education

discontinuous differential games and control systems with supremum cost abstract this paper concerns with the existence of a value for a zero sum two player differential game with supremum cost of the form c t 0 x 0 u v sup t 0 t h x t 0 x 0 u v under isaacs condition we characterize the value function as the unique solution in a suitable sense to a pde namely the hamilton jacobi isaacs equation as a byproduct we obtain a pde characterization of the value function for control system

a semiparametric quantile panel data model with an application to estimating the growth effect of fdi abstract this paper estimates the impact of foreign direct investment on economic growth by proposing a new semiparametric quantile panel data model with correlated random effects in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant a three stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated a simple and easily implemented procedure for making inferences is proposed monte carlo simulation is conducted to examine the finite sample performance of the proposed estimators finally using the cross country panel data we find a strong empirical evidence of the existence of the absorptive capacity hypothesis together with another new finding that fdi has much stronger growth effects for countries with fast economic growth than for those with slow economic growth

quantile regression under misspecification with an application to the u s wage structure quantile regression qr fits a linear model for conditional quantiles just as ordinary least squares ols fits a linear model for conditional means an attractive feature of ols is that it gives the minimum mean squared error linear approximation to the conditional expectation function even when the linear model is misspecified empirical research using quantile regression with discrete covariates suggests that qr may have a similar property but the exact nature of the linear approximation has remained elusive in this paper we show that qr minimizes a weighted mean squared error loss function for specification error the weighting function is an average density of the dependent variable near the true conditional quantile the weighted least squares interpretation of qr is used to derive an omitted variables bias formula and a partial quantile regression concept similar to the relationship between partial regression and ols we also present asymptotic theory for the qr process under misspecification of the conditional quantile function the approximation properties of qr are illustrated using wage data from the u s census these results point to major changes in inequality from 1990 to 2000

the bott borel weil theorem for direct limit groups we show how highest weight representations of certain infinite dimensional lie groups can be realized on cohomology spaces of holomorphic vector bundles this extends the classical bott borel weil theorem for finite dimensional compact and complex lie groups our approach is geometric in nature in the spirit of bott s original generalization of the borel weil theorem the groups for which we prove this theorem are strict direct limits of compact lie groups or their complexifications we previously proved that such groups have an analytic structure our result applies to most of the familiar examples of direct limits of classical groups we also introduce new examples involving iterated embeddings of the classical groups and see exactly how our results hold in those cases one of the technical problems here is that in general the limit lie algebras will have root systems but need not have root spaces so we need to develop machinery to handle this somewhat delicate situation

the pontry agin maximum principle for minimax problems of optimal control the subject of this paper is the pontryagin maximum principle for the minimax problem of optimal control that is we will derive the necessary conditions which a control must satisfy in order to be optimal for the problem in which the cost is measured pointwise in time by the essential supremum over t of some function of time the state and the control it is desired to use controls to minimize this cost

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

hamilton jacobi equations in infinite dimensions i uniqueness of viscosity solutions soient un espace de banach v son dual v et des solutions d une equation h x u du 0 dans etablies dans un sous ensemble de v h v r v r est continue on demontre que des solutions classiques sont determinees de facon unique par leurs valeurs limites on montre que l extension de la notion de solutions viscosite aux espaces de banach reussit dans des espaces munis de la propriete de radon nikodym

geometric representation theory for unitary groups of operator algebras geometric realizations for the restrictions of gns representations to unitary groups of c algebras are constructed these geometric realizations use an appropriate concept of reproducing kernels on vector bundles to build such realizations in spaces of holomorphic sections a class of complex coadjoint orbits of the corresponding real banach lie groups are described and some homogeneous holomorphic hermitian vector bundles that are naturally associated with the coadjoint orbits are constructed

infinite horizon stochastic optimal control problems with running maximum cost an infinite horizon stochastic optimal control problem with running maximum cost is considered the value function is characterized as the viscosity solution of a second order hjb equation with mixed boundary condition a general numerical scheme is proposed and convergence is established under the assumptions of consistency monotonicity and stability of the scheme a convergent semi lagrangian scheme is presented in detail

adaptive varying coefficient linear models varying coefficient linear models arise from multivariate nonparametric regression nonlinear time series modelling and forecasting functional data analysis longitudinal data analysis and others it has been a common practice to assume that the vary coefficients are functions of a given variable which is often called an index a frequently asked question is which variable should be used as the index in this paper we explore the class of the varying coefficient linear models in which the index is unknown and is estimated as a linear combination of regression and or other variables this will enlarge the modelling capacity substantially we search for the index such that the derived varying coefficient model provides the best approximation to the underlying unknown multi dimensional regression function in the least square sense the search is implemented through the newly proposed hybrid backfitting algorithm the core of the algorithm is the alternative iteration between estimating the index through a one step scheme and estimating coefficient functions through a one dimensional local linear smoothing the generalised cross validation method for choosing bandwidth is efficiently incorporated into the algorithm the locally significant variables are selected in terms of the combined use of t statistic and akaike information criterion we further extend the algorithm for the models with two indices simulation shows that the proposed methodology has appreciable flexibility to model complex multivariate nonlinear structure and is practically feasible with average modern computers the methods are further illustrated through the canadian mink muskrat data in 1925 1994 and the pound dollar exchange rates in 1974 1983

discontinuous control problems for non convex dynamics and near viability for singularly perturbed control systems abstract the aim of this paper is to study two classes of discontinuous control problems without any convexity assumption on the dynamics in the first part we characterize the value function for the mayer problem and the supremum cost problem using viscosity tools and the notion of e viability near viability these value functions are given with respect to discontinuous cost functionals in the second part we obtain results describing the e viability near viability of singularly perturbed control systems

multivariate regression models for panel data abstract the paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x the relationship is very strong when x is continuous weaker when x is discrete and non existent as the order of the distributed lag becomes infinite the individual specific random variables introduce nonlinearity and heteroskedasticity so the paper provides an appropriate framework for the estimation of multivariate linear predictors restrictions are imposed using a minimum distance estimator it is generally more efficient than the conventional estimators such as quasi maximum likelihood there are computationally simple generalizations of two and three stage least squares that achieve this efficiency gain some of these ideas are illustrated using the sample of young men in the national longitudinal survey the paper reports regressions on the leads and lags of variables measuring union coverage smsa and region the results indicate that the leads and lags could have been generated just by a random intercept this gives some support for analysis of covariance type estimates these estimates indicate a substantial heterogeneity bias in the union smsa and region coefficients

remarks on hamilton jacobi equations with measurable time dependent hamiltonians on considere les equations de hamilton jacobi de la forme suivante u t h x t u u 0 dans r n 0 t ou h x t s p est continu en x s p et mesurable en t on considere une extension de la notion de solution viscosite au cas de h mesurable dependant du temps

on reachability and minimum cost optimal control questions of reachability for continuous and hybrid systems can be formulated as optimal control or game theory problems whose solution can be characterized using variants of the hamilton jacobi bellman or isaacs partial differential equations the formal link between the solution to the partial differential equation and the reachability problem is usually established in the framework of viscosity solutions this paper establishes such a link between reachability viability and invariance problems and viscosity solutions of a special form of the hamilton jacobi equation this equation is developed to address optimal control problems where the cost function is the minimum of a function of the state over a specified horizon the main advantage of the proposed approach is that the properties of the value function uniform continuity and the form of the partial differential equation standard hamilton jacobi form continuity of the hamiltonian and simple boundary conditions make the numerical solution of the problem much simpler than other approaches proposed in the literature this fact is demonstrated by applying our approach to a reachability problem that arises in flight control and using numerical tools to compute the solution

on additive conditional quantiles with high dimensional covariates we investigate the estimation of the conditional quantile when many covariates are involved in particular we model the conditional quantile of a response as a nonlinear additive function of relevant covariates for this setup we propose a nonparametric smoother to estimate the unknown functions the estimator provides direct computation of the nonlinear functions because it does not require any iteration the estimator allows fast and routine data analysis on the theoretical front we also show asymptotic properties of the estimator including mean squared error and limiting distribution the theory confirms that for moderate dimension of the covariates the estimator escapes the curse of dimensionality problem both simulated and real data examples are provided to illustrate the methodology

growth and convergence a profile of distribution dynamics and mobility in this paper we focus primarily on the dynamic evolution of the world distribution of growth rates in per capita gdp we propose new concepts and measures of convergence or divergence that are based on entropy distances and dominance relations between groups of countries over time we update the sample period to include the most recent decade of data available and we offer traditional parametric and new nonparametric estimates of the most widely used growth regressions for two important subgroups of countries oecd and non oecd traditional parametric models are rejected by the data however using robust nonparametric methods we find strong evidence in favor of polarization and within group mobility

worst case analysis of nonlinear systems the authors work out a framework for evaluating the performance of a continuous time nonlinear system when this is quantified as the maximal value at an output port under bounded disturbances the disturbance problem this is useful in computing gain functions and l sub spl infin induced norms which are often used to characterize performance and robustness of feedback systems the approach is variational and relies on the theory of viscosity solutions of hamilton jacobi equations convergence of euler approximation schemes via discrete dynamic programming is established the authors also provide an algorithm to compute upper bounds for value functions differences between the disturbance problem and the optimal control problem are noted and a proof of convergence of approximation schemes for the control problem is given case studies are presented which assess the robustness of a feedback system and the quality of trajectory tracking in the presence of structured uncertainty

semiparametric quantile regression estimation in dynamic models with partially varying coefficients national science foundation of china 71131008 70871003 70971113 university of north carolina at charlotte chinese ministry of education minjiang scholarship from fujian province china xiamen university boston college

l1 limit solutions for control systems abstract for a control cauchy problem x f t x u v 1 m g x u x a x on an interval a b we propose a notion of limit solution x verifying the following properties i x is defined for l 1 impulsive inputs u and for standard bounded measurable controls v ii in the commutative case i e when g g 0 for all 1 m x coincides with the solution one can obtain via a change of coordinates that makes the g simultaneously constant iii x subsumes former concepts of solution valid for the generic noncommutative case in particular when u has bounded variation we investigate the relation between limit solutions and single valued graph completion solutions furthermore we prove consistency with the classical caratheodory solution when u and x are absolutely continuous even though some specific problems are better addressed by means of special representations of the solutions we believe that various theoretical issues call for a unified notion of trajectory for instance this is the case of optimal control problems possibly with state and endpoint constraints for which no extra assumptions like e g coercivity bounded variation commutativity are made in advance

hilbert schmidt groups as infinite dimensional lie groups and their riemannian geometry abstract we describe the exponential map from an infinite dimensional lie algebra to an infinite dimensional group of operators on a hilbert space notions of differential geometry are introduced for these groups in particular the ricci curvature which is understood as the limit of the ricci curvature of finite dimensional groups is calculated we show that for some of these groups the ricci curvature is

a max plus based algorithm for a hamilton jacobi bellman equation of nonlinear filtering the hamilton jacobi bellman hjb equation associated with the robust hinfty filter as well as the mortensen filter is considered these filters employ a model where the disturbances have finite power the hjb equation for the filter information state is a first order equation with a term that is quadratic in the gradient yet the solution operator is linear in the max plus algebra this property is exploited by the development of a numerical algorithm where the effect of the solution operator on a set of basis functions is computed off line the precomputed solutions are stored as vectors of coefficients of the basis functions these coefficients are then used directly in the real time computations

generalized viscosity solutions for hamilton jacobi equations with time measurable hamiltonians the objective of this paper is to extend the idea of viscosity solution for nonlinear first order hamilton jacobi equations u h t x d u 0 with time continuous h to time measurable hamiltonians we are primarily motivated by the fact that control problems for which the value function is the viscosity solution of a hamilton jacobi equation should not be restric ted to continuity in time in barron and jensen 1 we were confronted with a linear hamilton jacobi equation arising in the proof of the pon tryagin which had time measurable coeflicients the existing theory of viscosity solutions did not apply to even this case moreover important models of controlled first order hamiltonjacobi equations require time measurable controls for example models of controlled traffic flow or queueing processes might be of this type we are about then to extend the definition of viscosity solution to generalized viscosity solution applying to time measurable hamiltonians in this paper we give the definition and derive the corresponding uni queness result with an implicit domain of dependence consequent the fun damental technique used in the proof is the so called blow up method which has also been used elsewhere s although not in the generality discussed here this method effectively freezes the point to x0 under consideration and essentially removes it from the problem of course t is

nonparametric estimation of an additive quantile regression model this article is concerned with estimating the additive components of a nonparametric additive quantile regression model we develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n r 2r 1 when the additive components are r times continuously differentiable for some r 2 this result holds regardless of the dimension of the covariates and thus the new estimator has no curse of dimensionality in addition the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function the numerical performance and usefulness of the estimator are illustrated by monte carlo experiments and an empirical example

hamilton jacobi equations in infinite dimensions ii existence of viscosity solutions on demontre des resultats d existence generaux pour 2 problemes 1 le probleme de cauchy u t h x t u du 0 dans v 0 t u x 0 x dans v et 2 le probleme stationnaire u h x u du 0 dans v ou h et sont donnees

viscosity solutions of isaacs equations and differential games with lipschitz controls abstract it is demonstrated that the upper and lower values of a two person zero sum differential game solve the respective upper and lower isaacs equations in the viscosity sense introduced by crandall and lions trans amer math soc 277 1983 1 42 since such solutions are unique this yields a fairly simple proof that the game has value should the minimax condition hold as a further application of viscosity techniques a new and simpler proof that the upper and lower values can be approximated by the values of certain games with lipschitz controls is given

sample splitting and threshold estimation threshold models have a wide variety of applications in economics direct applications include models of separating and multiple equilibria other applications include empirical sample splitting when the sample split is based on a continuously distributed variable such as firm size in addition threshold models may be used as a parsimonious strategy for nonparametric function estimation for example the threshold autoregressive model tar is popular in the nonlinear time series literature threshold models also emerge as special cases of more complex statistical frameworks such as mixture models switching models markov switching models and smooth transition threshold models it may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures despite the large number of potential applications the statistical theory of threshold estimation is undeveloped it is known that threshold estimates are super consistent but a distribution theory useful for testing and inference has yet to be provided this paper develops a statistical theory for threshold estimation in the regression context we allow for either cross section or time series observations least squares estimation of the regression parameters is considered an asymptotic distribution theory for the regression estimates the threshold and the regression slopes is developed it is found that the distribution of the threshold estimate is nonstandard a method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic it is shown that this yields asymptotically conservative confidence regions monte carlo simulations are presented to assess the accuracy of the asymptotic approximations the empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of durlauf and johnson 1995

hamilton jacobi formulation for reach avoid differential games a new framework for formulating reachability problems with competing inputs nonlinear dynamics and state constraints as optimal control problems is developed such reach avoid problems arise in among others the study of safety problems in hybrid systems earlier approaches to reach avoid computations are either restricted to linear systems or face numerical difficulties due to possible discontinuities in the hamiltonian of the optimal control problem the main advantage of the approach proposed in this paper is that it can be applied to a general class of target hitting continuous dynamic games with nonlinear dynamics and has very good properties in terms of its numerical solution since the value function and the hamiltonian of the system are both continuous the performance of the proposed method is demonstrated by applying it to a case study which involves the target hitting problem of an underactuated underwater vehicle in the presence of obstacles

lie group structures on quotient groups and universal complexifications for infinite dimensional lie groups we characterize the existence of lie group structures on quotient groups and the existence of universal complexifications for the class of baker campbell hausdorff bch lie groups which subsumes all banach lie groups and linear direct limit lie groups as well as the mapping groups ckr m g cr m g m k 1 for every bch lie group g second countable finite dimensional smooth manifold m compact subset k of m and 0 r also the corresponding test function groups dr m g kckr m g are bch lie groups

iwasawa decompositions of some infinite dimensional lie groups we set up an abstract framework that allows the investigation of iwasawa decompositions for involutive infinite dimensional lie groups modeled on banach spaces this provides a method to construct iwasawa decompositions for classical real or complex banach lie groups associated with the schatten ideals o p h on a complex separable hilbert space h if 1 p

homogenization in l abstract homogenization of deterministic control problems with l running cost is studied by viscosity solutions techniques it is proved that the value function of an l problem in a medium with a periodic micro structure converges uniformly on the compact sets to the value function of the homogenized problem as the period shrinks to 0 our main convergence result extends that of ishii stochastic analysis control optimization and applications pp 305 324 birkhauser boston boston ma 1999 to the case of a discontinuous hamiltonian the cell problem is solved but as non uniqueness occurs the effective hamiltonian must be selected in a careful way the paper also provides a representation formula for the effective hamiltonian and gives illustrations to calculus of variations averaging and one dimensional problems

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

commutator structure of operator ideals commutator structure of operator ideals ken dykema 1 tadeusz figiel gary weiss and mariusz wodzicki department of mathematics texas a m university college station tx 77843 3368 usa b instytut matematyczny polskiej akademii nauk 81 825 sopot poland department of mathematical sciences university of cincinnati cincinnati oh 45221 0025 usa department of mathematics university of california berkeley ca 94720 3840 usa

on existence and uniqueness of solutions of hamilton jacobi equations abstract the theory of scalar first order nonlinear partial differential equations has been enjoying a rapid development in the last few years this development occurred because the authors established uniqueness criteria for generalized solutions called viscosity solutions which correctly identify the solutions sought in areas of application including control theory differential games and the calculus of variations the concept of viscosity solutions is relatively easy to work with and many formally heuristic or difficult proofs have been made rigorous or simple using this concept a feedback process has begun and the experience recently gained in working with viscosity solution has suggested new existence and uniqueness results the current paper continues this interaction by establishing new existence ane uniqueness results in a natural generality suggested by earlier proofs it is also felt that the presentation of the comparison results which imply uniqueness continuous dependence and are used to estimate moduli of continuity has something to offer over earlier presentations in special cases author

instrumental quantile regression inference for structural and treatment effect models we introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference these methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes we describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it we focus our discussion of inference on tests of distributional equality constancy of effects conditional dominance and exogeneity we apply the procedures to characterize the returns to schooling in the u s

robust penalized quantile regression estimation for panel data this paper investigates a class of penalized quantile regression estimators for panel data the penalty serves to shrink a vector of individual specific effects toward a common value the degree of this shrinkage is controlled by a tuning parameter it is shown that the class of estimators is asymptotically unbiased and gaussian when the individual effects are drawn from a class of zero median distribution functions the tuning parameter can thus be selected to minimize estimated asymptotic variance monte carlo evidence reveals that the estimator can significantly reduce the variability of the fixed effect version of the estimator without introducing bias

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

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

bivariate quantile smoothing splines it has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample we introduce bivariate quantile smoothing splines which belong to the space of bilinear tensor product splines as nonparametric estimators for the conditional quantile functions in a two dimensional design space the estimators can be computed by using standard linear programming techniques and can further be used as building blocks for conditional quantile estimations in higher dimensions for moderately large data sets we recommend penalized bivariate b splines as approximate solutions we use real and simulated data to illustrate the methodology proposed

conical representations for direct limits of symmetric spaces we extend the definition of conical representations for riemannian symmetric spaces to a certain class of infinite dimensional riemannian symmetric spaces using a certain infinite dimensional version of weyl s unitary trick we show that there is a correspondence between smooth representations of infinite dimensional noncompact type riemannian symmetric spaces and smooth representations of infinite dimensional compact type symmetric spaces we classify all smooth conical representations which are unitary on the compact type side finally a new class of non smooth unitary conical representations appears on the compact type side which has no analogue in the finite dimensional case we classify these representations and show how to decompose them into direct integrals of irreducible conical representations

quantile regression for dynamic panel data with fixed effects abstract this paper studies a quantile regression dynamic panel model with fixed effects panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors to reduce the dynamic bias we suggest the use of the instrumental variables quantile regression method of chernozhukov and hansen 2006 along with lagged regressors as instruments in addition we describe how to employ the estimated models for prediction monte carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias and the empirical levels for prediction intervals are very close to nominal levels finally we illustrate the procedures with an application to forecasting output growth rates for 18 oecd countries