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

semiparametric estimation of censored selection models with a nonparametric selection mechanism abstract in this paper estimation of the coefficients in a single index selectivity bias model is considered under the assumption that the selection correction function depends on the conditional mean of some observable selection variable the estimation method follows a familiar two step strategy the first step uses a nonparametric regression estimator for the selection variable while the second step uses a weighted instrumental variables estimator for the coefficients in the equation of interest the paper gives conditions under which the proposed estimator is root n consistent and asymptotically normal the proposed method is applied to data on labor supply

a fixed point formula and harish chandra s character formula the main result in this paper is a fixed point formula for equivariant indices of elliptic differential operators for proper actions by connected semisimple lie groups on possibly noncompact manifolds with compact quotients for compact groups and manifolds this reduces to the atiyah segal singer fixed point formula other special cases include an index theorem by connes and moscovici for homogeneous spaces and an earlier index theorem by the second author both in cases where the group acting is connected and semisimple as an application of this fixed point formula we give a new proof of harish chandra s character formula for discrete series representations

combining panel data sets with attrition and refreshment samples tistical models that allow for more complex relationships than can be inferred using only cross sectional data panel i e longitudinal data in which the same units are observed repeatedly at different points in time can often provide the richer data needed for such models e g chamberlain 1984 hsiao 1986 baltagi 1995 arellano and honore forthcoming missing data problems however can be more severe in panels because even those units that respond in initial waves of the panel may drop out of the sample in subsequent waves e g hausman and wise 1979 robins and west 1986 ridder 1990 verbeek and nijman 1992 abowd crepon kramarz and trognon 1995 fitzgerald gottschalk and moffitt 1998 and vella 1998 sometimes in the hope of mitigating the effects of such attrition panel data sets are augmented by replacing the units that have dropped out with new units randomly sampled from the original population following ridder 1992 who used such replacement units to test alternative models for attrition we call such additional samples refreshment samples here we explore the benefits of refreshment samples for inference in the presence of attrition two general approaches are often used to deal with attrition in panel data sets when refreshment samples are not available one model based on the missing at random assumption mar rubin 1976 little and rubin 1987 allows the probability of attrition to depend on lagged but not on contemporaneous variables that have missing values the other model denoted by hw in the remainder of the paper given the similarity to a model developed by hausman and wise 1979 allows the probability of attrition to depend on such contemporaneous but not on lagged variables both sets of models have some theoretical plausibility but they rely on fundamentally different restrictions on the

application of statistical mechanics to np complete problems in combinatorial optimisation recently developed techniques of the statistical mechanics of random systems are applied to the graph partitioning problem the averaged cost function is calculated and agrees well with numerical results the problem bears close resemblance to that of spin glasses the authors find a spin glass transition in the system and the low temperature phase space has an ultrametric structure this sheds light on the nature of hard computation problems

dirac operator and its cohomology for the quantum group uq x1d598 x1d591 x1d7d0 we introduce a dirac operator d for the quantum group uq x1d530 x1d529 2 as an element of the tensor product of uq x1d530 x1d529 2 with the clifford algebra on two generators we study the properties of d including an analogue of vogan s conjecture we compute the cohomology of d acting on various uq x1d530 x1d529 2 modules

classification of aq λ modules by their dirac cohomology for type d g2 and sp 2n r abstract let g be a connected real reductive group with maximal compact subgroup k of the same rank as g in the recent paper of huang pand ic and vogan it was shown that the admissible stable parabolic subalgebras q of g are in one to one correspondence with the faces of w intersecting the k dominant weyl chamber and that a q 0 modules can be classified by their dirac cohomology in geometric terms they described in detail the cases when g 0 is of type a b f and c except for g 0 sp 2 n r we will describe faces corresponding to a q 0 modules for g 0 sp 2 n r and for g 0 of type d and g 2

dirac series for some real exceptional lie groups abstract up to equivalence this paper classifies all the irreducible unitary representations with non zero dirac cohomology for the following simple real exceptional lie groups ei e 6 6 eiv e 6 26 fi f 4 4 fii f 4 20 along the way we find an irreducible unitary representation of f 4 4 whose dirac index vanishes while its dirac cohomology is non zero this disproves a conjecture raised in 2015 asserting that there should be no cancellation between the even part and the odd part of the dirac cohomology

towards the solution of the graph bipartitioning problem the author presents the replica symmetric solution of the graph bipartitioning problem he points out the possibility of many solutions even with the replica symmetry assumption he also comments on the possibility of constructing a model with an arbitrary finite number of transition temperatures

panel data discrete choice models with lagged dependent variables in this paper we consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables lags of the endogenous dependent variable as well as unobservable individual specific effects for the binary logit model with the dependent variable lagged only once chamberlain 1993 gave conditions under which the model is not identified we present a stronger set of conditions under which the parameters of the model are identified the identification result suggests estimators of the model and we show that these are consistent and asymptotically normal although their rate of convergence is slower than the inverse of the square root of the sample size we also consider identification in the semiparametric case where the logit assumption is relaxed we propose an estimator in the spirit of the conditional maximum score estimator manski 1987 and we show that it is consistent in addition we discuss an extension of the identification result to multinomial discrete choice models and to the case where the dependent variable is lagged twice finally we present some monte carlo evidence on the small sample performance of the proposed estimators for the binary response model

symmetric subalgebras noncohomologous to zero in a complex semisimple lie algebra and restrictions of symmetric invariants abstract let g be a semisimple involutory lie algebra and g k the corresponding symmetric pair let h be a fundamental cartan subalgebra of g containing a cartan subalgebra t of k the semisimple involutory lie algebras g with the symmetric subalgebra k noncohomologous to zero in g are completely classified by showing that k is noncohomologous to zero in g if and only if the spin representation of g is primary based on this result we then determine the image of the restriction map s h w g h s t w k t where w g h and w k t are the respective weyl groups

dirac cohomology and geometric quantization let g be a connected real semisimple lie group having a finite center and a compact cartan subgroup t with lie algebra t0 let be a g t invariant symplectic form on xdg t0 we incorporate dirac cohomology into the geometric quantization of x and study the resulting multiplicity free unitary g t representation on a hilbert space h x we also perform symplectic reduction of x and show that our quantiza tion method satisfies the principle quantization commutes with reduction as an application we construct various models of discrete series

conditions for identification in nonparametric and parametric models on presente une definition formelle de l identification dans un contexte non parametrique sur la base des travaux de koopmans et reiersol 1950

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

induction functor in noncommutative equivariant cohomology and dirac cohomology abstract the aim of this paper is to put some recent results of huang and pandzic conjectured by vogan and kostant on dirac cohomology in a broader perspective this is achieved by introducing an induction functor in the noncommutative equivariant cohomology in this context the results of huang pandzic and kostant are interpreted as special cases corresponding to the manifold being a point of more general results on noncommutative equivariant cohomology introduced by alekseev and meinrenken

dirac cohomology unitary representations and a proof of a conjecture of vogan u radu je dokazana slutnja d vogana koja odredjuje infinitesimalni karakter ireducibilnog g k modula koji ima diracovu kohomologiju razlicitu od nula infinitesimalni karakter je dan kao rho translat najvece tezine k tipa u diracovoj kohomologiji diracova kohomologija se definira kao ker d im d cap ker d gdje d oznacava diracov operator na zadanom g k modulu tenzoriranom sa spin modulom

dirac cohomology and translation functors abstract we study the relationship between the dirac cohomology of a g k module x and the dirac cohomology of a jantzen zuckerman translate of x more precisely we show that if x is unitary and if some submodule x of a translate of x has nonzero dirac cohomology then x has nonzero dirac cohomology we also show that the space of harmonic spinors i e the kernel of the dirac operator related to x embeds into a certain product of harmonic spinors for x and harmonic spinors for the finite dimensional module used to define the translation this generalizes with a simpler proof results of mehdi and parthasarathy 2008 mp1 and mehdi and parthasarathy 2010 mp2

principal series representations and harmonic spinors abstract let g be a real reductive lie group and g h a reductive homogeneous space we consider kostant s cubic dirac operator d on g h twisted with a finite dimensional representation of h under the assumption that g and h have the same complex rank we construct a nonzero intertwining operator from principal series representations of g into the kernel of d the langlands parameters of these principal series are described explicitly in particular we obtain an explicit integral formula for certain solutions of the cubic dirac equation d 0 on g h

dirac cohomology k characters and branching laws inspired by work of enright and willenbring ew we prove a generalized littlewood s restriction formula in terms of dirac cohomology our approach is to use a character formula of irreducible unitary lowest weight modules instead of the bernstein gelfand gelfand resolution and the proof is much simpler we also show that our branching formula is equivalent to the formula of enright and willenbring in terms of nilpotent lie algebra cohomology this follows from the close relationship between the dirac cohomology and the corresponding nilpotent lie algebra cohomology for unitary representations of semisimple lie groups of hermitian type which was established in hpr

replica symmetric solutions of the graph bipartitioning problem with fixed finite valence using the replica method the author presents the replica symmetric solutions of the graph bipartitioning problem with fixed finite valence with the constraint sigma ni 1 si 0 strictly enforced the author is able to find another solution which gives a lower cost function than that given by the spin glass solution

simple estimators for nonparametric panel data models with sample attrition abstract this paper considers a multiperiod random effects panel model with attrition of observations over the panel allowing for flexible regressions unknown distributions and attrition in one period to be followed by reappearance in a future period in each time period the regression in the retained data is additive in the function of interest and a time varying correction term that depends on the contemporaneous probability of retention in the sample these retention probabilities themselves depend on a regressor vector that grows with time in particular for the t th and t s th periods these vectors differ by exactly s terms the paper gives two step estimators that correct for attrition bias by including estimates of these retention probabilities one for each period that experiences attrition asymptotic normality for a class of functionals of the model is derived also including as special cases the linear and partially linear versions of the model

multiplets of representations twisted dirac operators and vogan s conjecture in affine setting abstract we extend classical results of kostant et al on multiplets of representations of finite dimensional lie algebras and on the cubic dirac operator to the setting of affine lie algebras and twisted affine cubic dirac operator we prove in this setting an analogue of vogan s conjecture on infinitesimal characters of harish chandra modules in terms of dirac cohomology for our calculations we use the machinery of lie conformal and vertex algebras

inference in panel data models under attrition caused by unobservables this paper concerns identification and estimation of a finite dimensional parameter in a panel data model under nonignorable sample attrition attrition can depend on second period variables which are unobserved for the attritors but an independent refreshment sample from the marginal distribution of the second period values is available this paper shows that under a quasi separability assumption the model implies a set of conditional moment restrictions where the moments contain the attrition function as an unknown parameter this formulation leads to i a simple proof of identification under strictly weaker conditions than those in the existing literature and more importantly ii a sieve based root n consistent estimate of the finite dimensional parameter of interest these methods are applicable to both linear and nonlinear panel data models with endogenous attrition and analogous methods are applicable to situations of endogenously missing data in a single cross section the theory is illustrated with a simulation exercise using current population survey data where a panel structure is introduced by the rotation group feature of the sampling process

the non commutative weil algebra for any compact lie group g together with an invariant inner product on its lie algebra g we define the non commutative well algebra w g as a tensor product of the universal enveloping algebra u g and the clifford algebra cl 8 just like the usual we

selection corrections for panel data models under conditional mean independence assumptions some new methods for testing and correcting for sample selection bias in panel data models are proposed the assumptions allow the unobserved effects in both the regression and selection equations to be correlated with the observed variables the error distribution in the regression equation is unspecified arbitrary serial dependence in the idiosyncratic errors of both equations is allowed and all idiosyncratic errors can be heterogeneously distributed compared with maximum likelihood and other estimators derived under fully parametric assumptions the new estimators are much more robust and have significant computational advantages

dirac index and associated cycles of harish chandra modules abstract let g r be a simple real linear lie group with maximal compact subgroup k r and assume that rank g r rank k r for any representation x of gelfand kirillov dimension 1 2 dim g r k r we consider the polynomial on the dual of a compact cartan subalgebra given by the dimension of the dirac index of members of the coherent family containing x under a technical condition involving the springer correspondence we establish an explicit relationship between this polynomial and the multiplicities of the irreducible components occurring in the associated cycle of x this relationship was conjectured in 12

varying coefficient panel data model in the presence of endogenous selectivity and fixed effects this paper considers a exible panel data sample selection model in which i the outcome equation is permitted to take a semiparametric varying coecient form to capture potential parameter heterogeneity in the relationship of interest ii both the outcome and parametric selection equations contain unobserved xed eects and iii selection is generalized to a polychotomous case we propose a two stage estimator given consistent parameter estimates from the selection equation obtained in the rst stage we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time the selection bias term is then asymptotically removed from the equation along with xed eects using kernel based weights the proposed estimator is consistent and asymptotically normal we rst investigate the nite sample properties of the estimator in a small monte carlo study and then apply it to study production technologies of u s retail credit unions from 2002 to 2006

heterogeneity and selection in dynamic panel data abstract the data generating process dgp for generic dynamic panel data consists of a law of state dynamics g a selection or attrition rule h and an initial condition f i study nonparametric identifiability of this complete dgp g h f using short unbalanced panel data allowing for nonseparability between observed states and unobserved heterogeneity in each of g h and f for t 3 the dgp is identified by using a proxy variable for t 6 the three additional periods construct a proxy and thus the dgp is identified without an auxiliary variable

on the dirac series of u p q this paper computes the dirac index of all the weakly fair a mathfrak q lambda modules of u p q we find counter examples to a conjecture of vogan on the unitary dual of u p q which was phrased by trapa in 2001 however we still believe that any irreducible unitary representation of u p q with non zero dirac cohomology must be a weakly fair a mathfrak q lambda module

estimation of a panel data sample selection model we consider the problem of estimation in a panel data sample selection model where both the selection and the regression equation of interest contain unobservable individual specific effects we propose a two step estimation procedure which differences out both the sample selection effect and the unobservable individual effect from the equation of interest in the first step the unknown coefficients of the selection equation are consistently estimated the estimates are then used to estimate the regression equation of interest the estimator proposed in this paper is consistent and asymptotically normal with a rate of convergence that can be made arbitrarily close to n 1 2 depending on the strength of certain smoothness assumptions the finite sample properties of the estimator are investigated in a small monte carlo simulation

corrigendum to dirac cohomology and translation functors j algebra 375 2013 328 336 abstract the statements of theorem 1 3 lemma 3 2 and proposition 5 2 in 4 are incorrect we give counterexamples to these statements and we offer a replacement for theorem 1 3 under stronger assumptions

translation principle for dirac index let g be a finite cover of a closed connected transpose stable subgroup of rm gl n bbb r with complexified lie algebra frak g let k be a maximal compact subgroup of g and assume that g and k have equal rank we prove a translation principle for the dirac index of virtual frak g k modules as a byproduct to each coherent family of such modules we attach a polynomial on the dual of the compact cartan subalgebra of frak g this index polynomial generates an irreducible representation of the weyl group contained in the coherent continuation representation we show that the index polynomial is the exact analogue on the compact cartan subgroup of king s character polynomial the character polynomial was defined by king on the maximally split cartan subgroup and it was shown to be equal to the goldie rank polynomial up to a scalar multiple in the case of representations of gelfand kirillov dimension at most half the dimension of g k we also conjecture an explicit relationship between our index polynomial and the multiplicities of the irreducible components occurring in the associated cycle of the corresponding coherent family

identification and sequential estimation of panel data models with insufficient exclusion restrictions abstract this paper presents estimators for nonparametric panel data models with additive fixed effects we analyze a model in which the entire regressor vector consisting of time varying as well as time invariant regressors is correlated with the individual fixed effect but there are insufficient exclusion restrictions to permit direct instrumental variables estimation of the model it is shown that when the model satisfies the additive interactive regression air representation of andrews and whang economic theory 6 1990 466 480 a sequential estimator consistently estimates the model the limiting distribution of scalar nonlinear functionals of the model is shown to be standard normal finite sample properties of the estimator are considered in a monte carlo simulation study and used to estimate the returns to education in a cohort of mature men from the national longitudinal survey

dirac cohomology of cohomologically induced modules for reductive lie groups we extend the setting and a proof of the vogan s conjecture on dirac cohomology to a possibly disconnected real reductive lie group g in the harish chandra class we show that the dirac cohomology of cohomologically induced module mathcal l s z is completely determined by the dirac cohomology of the inducing module z more precisely we prove that if z is weakly good then the dirac cohomology h d mathcal l s z is equal to mathcal l widetilde k s h d z otimes bbb c rho frak p cap frak u an immediate application is a classification of tempered irreducible unitary representations with nonzero dirac cohomology

jacquet modules and dirac cohomology abstract we show that dirac cohomology of the jacquet module of a harish chandra module is a harish chandra module for the corresponding levi subgroup we obtain an explicit formula of dirac cohomology of the jacquet module for most of the principal series based on our determination of dirac cohomology of irreducible generalized verma modules with regular infinitesimal characters

a vanishing theorem for dirac cohomology of standard modules abstract this paper studies the dirac cohomology of standard modules in the setting of graded hecke algebras with geometric parameters we prove that the dirac cohomology of a standard module vanishes if and only if the module is not twisted elliptic tempered the proof makes use of two deep results one is some structural information from the generalized springer correspondence obtained by s kato and lusztig another one is a computation of the dirac cohomology of tempered modules by barbasch ciubotaru trapa and ciubotaru we apply our result to compute the dirac cohomology of ladder representations for type a n for each of such representations with non zero dirac cohomology we associate to a canonical weyl group representation we use the dirac cohomology to conclude that such representations appear with multiplicity one