identification theory for high dimensional static and dynamic factor models abstract high dimensional factor models can involve thousands of parameters the jacobian matrix for identification is of a large dimension it can be difficult and numerically inaccurate to evaluate the rank of such a jacobian matrix we reduce the identification problem to a small rank problem which is easy to check the identification conditions allow both linear and nonlinear restrictions under reasonable assumptions for high dimensional factor models the small rank conditions are shown to be necessary and sufficient for local identification

tests for stability in linear structural equation systems interpretations regarding the effects of exogenous and endogenous variables on endogenous variables in linear structural equation systems depend upon the convergence of a matrix power series convergence depends upon the eigenvalues of the structural coefficient matrix the test for convergence developed by joreskog and sorbom is shown to be only sufficient not necessary and sufficient

identification in restricted factor models and the evaluation of rank conditions abstract this paper presents a rank condition for the local identification in restricted factor analysis models and it provides a method for the computation of the exact rank in the condition the method can be applied to evaluate the rank of rather general jacobian matrices

generalized canonical transformations for time dependent systems we introduce the concept of generalized canonical transformations as symplectomorphisms of the extended phase space we prove that any such transformation factorizes in a standard canonical transformation times another one that changes only the time variable the theory of generating functions as well as that of hamilton jacobi is developed some further applications are developed

bayesian stochastic search for var model restrictions we propose a bayesian stochastic search approach to selecting restrictions for vector autoregressive var models for this purpose we develop a markov chain monte carlo mcmc algorithm that visits high posterior probability restrictions on the elements of both the var regression coefficients and the error variance matrix numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance to illustrate the potential of our approach we apply our stochastic search to var modeling of inflation transmission from producer price index ppi components to the consumer price index cpi

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

a theory of miyawaki liftings the hilbert siegel case the miyawaki liftings are defined by the pullbacks of ikeda liftings recently ikeda and yamana extended the theory of ikeda liftings to hilbert siegel modular forms in this paper using their results we establish a theory of miyawaki liftings both locally and globally in the local theory we describe the miyawaki liftings for almost tempered unitary representations explicitly in the global theory we discuss the non vanishing of the miyawaki liftings using seesaw identities and the global gan gross prasad conjecture as an application of local miyawaki liftings we prove a new case of the local gan gross prasad conjecture

equivalent lagrangians multidimensional case we generalize a theorem known for one dimensional nonsingular equivalent lagrangians l and to the multidimensional case in particular we prove that the matrix which relates the left hand sides of the euler lagrange equations obtained from l and is such that the trace of all its integer powers are constants of the motion we construct several multidimensional examples in which the elements of are functions of position velocity and time and prove that in some cases equivalence prevails even if det 0

identification of linear stochastic models with covariance restrictions abstract the purpose of this paper is to provide a systematic treatment of the problem of identification in systems of linear structural equations where some of the disturbances are uncorrelated

generic representations of metaplectic groups and their theta lifts in this paper we give the description of generic representations of metaplectic groups over p adic fields in terms of their langlands parameters and calculate their theta lifts on all levels for any tower of odd orthogonal groups we also describe precisely all the occurrences of the failure of the standard module conjecture for metaplectic groups

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

error bands for impulse responses we show how correctly to extend known methods for generating error bands in reduced form var s to overidentified models we argue that the conventional pointwise bands common in the literature should be supplemented with measures of shape uncertainty and we show how to generate such measures we focus on bands that characterize the shape of the likelihood such bands are not classical confidence regions we explain that classical confidence regions mix information about parameter location with information about model fit and hence can be misleading as summaries of the implications of the data for the location of parameters because classical confidence regions also present conceptual and computational problems in multivariate time series models we suggest that likelihood based bands rather than approximate confidence bands based on asymptotic theory be standard in reporting results for this type of model

local theta correspondence of tempered representations and langlands parameters in this paper we give an explicit determination of the theta lifting for symplectic orthogonal and unitary dual pairs over a nonarchimedean field f of characteristic 0 we determine when theta lifts of tempered representations are nonzero and determine the theta lifts in terms of the local langlands correspondence

equivalent models in covariance structure analysis defining equivalent models as those that reproduce the same set of covariance matrices necessary and sufficient conditions are stated for the local equivalence of two expanded identified modelsm1 andm2 when fitting the more restricted modelm0 assuming several regularity conditions the rank deficiency of the jacobian matrix composed of derivatives of the covariance elements with respect to the union of the free parameters ofm1 andm2 which characterizes modelm12 is a necessary and sufficient condition for the local equivalence ofm1 andm2 this condition is satisfied in practice when the analysis dealing with the fitting ofm0 predicts that the decreases in the chi square goodness of fit statistic for the fitting ofm1 orm2 orm12 are all equal for any set of sample data except on differences due to rounding errors

the gross prasad conjecture and local theta correspondence we establish the fourier jacobi case of the local gross prasad conjecture for unitary groups by using local theta correspondence to relate the fourier jacobi case with the bessel case established by beuzart plessis to achieve this we prove two conjectures of prasad on the precise description of the local theta correspondence for almost equal rank unitary dual pairs in terms of the local langlands correspondence the proof uses arthur s multiplicity formula and thus is one of the first examples of a concrete application of this global reciprocity law

identification in linear simultaneous equations models with covariance restrictions an instrumental variables interpretation necessary and sufficient conditions for identification with linear coefficient and covari ance restrictions are developed in a limited information context for the limited informa tion case covariance restrictions aid identification if and only if they imply that a set of endogenous variables is predetermined in the equation of interest generalizing the idea of recursiveness under full information covariance restrictions imply that residuals from other equations are predetermined in a particular equation and under certain conditions can aid in identification sufficient conditions for identification are obtained for the hierarchical system in which the identification of a particular equation does not depend upon the identifiability of higher numbered equations in the general case the fiml first order conditions show that if the system of equations is identifiable as a whole covariance restrictions cause residuals to behave as instruments in both limited and full information settings the link between identification and estimation is worked out restrictions useful for identification yield instruments required for estimation

blow up regularization of singular lagrangians we propose a method for regularizing singular lagrangians by adding new degrees of freedom we illustrate this regularization method with some particular examples this procedure is shown to be very useful when the lagrangian is homogeneous of degree one in the velocities giving rise to an identically vanishing hamiltonian

theta dichotomy for unitary groups some recent work of gross and prasad 14 suggests that the root numbers attached to certain symplectic representations of the weil deligne group of a local field f control certain branching rules for representations of orthogonal groups over f on a global level this local phenomenon should have implications for the structure of the value at the center of symmetry for certain l functions of arithmetic interest 12 this conjectural picture is based to some extent on the now classic work of tunnell 47 and waldspurger 49 as well as on the case of the triple product l function 13 34 17 in all of these examples the local root number detects the existence of a certain type of invariant linear functional it is possible to set up analogous conjectures for the isometry groups of hermitian or quaternion hermitian forms it turns out that root numbers also play a role in the local and global theta correspondence roughly speaking certain local root numbers should control the occurrence of representations in the local theta correspondence between groups of the same size e g for dual pairs of the form sp n o 2n 1 and u n u n as will be seen the theta correspondence for such pairs is connected with a certain induced representation in s at the point s 0 on the unitary axis by contrast the correspondence for the pairs sp n o 2n and sp n o 2n 2 discussed by prasad 35 is connected to the behavior of a similar induced representation at the points 12 in which case no epsilon factor arises in this paper we consider the local theta correspondence for unitary groups in the non archimedean case let f be a non archimedean local field of characteristic not equal to 2 and let e be a quadratic extension of f for further notation see the notation section at the end of this introduction let v and w be e vector spaces of dimensions m and n equipped respectively with a hermitian form v v e and a skew hermitian form w w e then the isometry groups g v and g w of the spaces v and w form a dual reductive pair in the symplectic group sp w where w v e w viewed as an f vector space of dimension 2mn and equipped with the symplectic form

transcending classical invariant theory let sp2 r sp2 sp be the real symplectic group of rank n let sp denote the two fold cover of sp there is a unitary representation constructed by shale sh and weil wa of sp that is of considerable interest in the theory of automorphic forms we denote this representation by co and call it the oscillator representation the purpose of this paper is to establish about c a fact that should be useful for clarifying the structure of spaces of automorphic forms constructed using co we begin by formulating the result let e be a reductive subgroup of sp and let e denote the inverse image of e in sp denote by r e the set of infinitesimal equivalence classes of continuous irreducible admissible representations of e on locally convex spaces let co be the smooth representation of sp associated to co let co be realized on a hilbert space and let the subspace of smooth vectors on which space co is defined be written denote by r9 e co the set of elements of e which are realized as quotients by co e invariant closed subspaces of t g consider a reductive dual pair g g c sp h2 it is not hard to show that g and g commute with one another hence we may regard co i g g as a representation of gx g it is well known f that r gx g s9 g xr9 g the identification associates to p e r g and p e i g the tensor product p x p we note that p x p is not defined as a topological vector space nevertheless the infinitesimal equivalence class of p op is well defined select p x p e g x g suppose that in fact p p e 9 g g c then clearly p e r g c and p e 9 g c hence g co defines the graph of a correspondence between certain subsets of r9 g cv and j g co in fact the situation is quite precise

theta lifts and distinction for regular supercuspidal representations this article has a twofold purpose first by recent works of kaletha and loke ma we give an explicit description of the local theta correspondence between regular supercuspidal representations in the equal rank symplectic orthogonal case second based on this description we show that the local theta correspondence preserves distinction with respect to unramified galois involutions

the local langlands correspondence for gln over p adic fields we extend our methods from scholze invent math 2012 doi 10 1007 s00222 012 0419 y to reprove the local langlands correspondence for gl n over p adic fields as well as the existence of l adic galois representations attached to most regular algebraic conjugate self dual cuspidal automorphic representations for which we prove a local global compatibility statement as in the book of harris taylor the geometry and cohomology of some simple shimura varieties 2001 in contrast to the proofs of the local langlands correspondence given by henniart invent math 139 2 439 455 2000 and harris taylor the geometry and cohomology of some simple shimura varieties 2001 our proof completely by passes the numerical local langlands correspondence of henniart ann sci ec norm super 21 4 497 544 1988 instead we make use of a previous result from scholze invent math 2012 doi 10 1007 s00222 012 0419 y describing the inertia invariant nearby cycles in certain regular situations

a note on the identification of restricted factor loading matrices it is shown that problems of rotational equivalence of restricted factor loading matrices in orthogonal factor analysis are equivalent to problems of identification in simultaneous equations systems with covariance restrictions a necessary under a regularity assumption and sufficient condition for local uniqueness is given and a counterexample is provided to a theorem by j algina concerning necessary and sufficient conditions for global uniqueness

on the non vanishing of theta liftings of tempered representations of u p q abstract in this paper we give an explicit determination of the non vanishing of the theta liftings of tempered representations for unitary dual pairs u p q u r s for arbitrary non negative integers p q r s for discrete series representations in terms of harish chandra parameters we give a complete criterion when the theta lifts are nonzero for tempered representations we determine the non vanishing in terms of the local langlands correspondence assuming the local gan gross prasad conjecture

the local theta correspondence and the local gan gross prasad conjecture for the symplectic metaplectic case we prove the local gan gross prasad conjecture for the symplectic metaplectic case under some assumptions this is the last case of the local gan gross prasad conjectures which has not been established we also prove two of prasad s conjectures on the local theta correspondence in the almost equal rank case

le lemme fondamental pondere ii enonces cohomologiques dans cet article on etudie la cohomologie de la fibration de hitchin tronquee introduite dans un article precedent on etend les principaux theoremes de ngo sur la cohomologie de la partie elliptique de la fibration de hitchin comme consequence on obtient une demonstration du lemme fondamental pondere d arthur in this paper we study the cohomology of the truncated hitchin fibration which was introduced in a previous paper we extend ngo s main theorems on the cohomology of the elliptic part of the hitchin fibration as a consequence we get a proof of arthur s weighted fundamental lemma