asymptotic upper curvature bounds in coarse geometry we define a notion of an asymptotic upper curvature bound for gromov hyperbolic metric spaces that is invariant under rough isometries and examine the basic properties of this concept

robust gmm tests for structural breaks we propose a class of new robust generalized method of moments gmm tests for endogenous structural breaks the tests are based on supremum average and exponential functionals derived from robust gmm estimators with bounded influence function we study the theoretical local robustness properties of the new tests and show that they imply a uniformly bounded asymptotic sensitivity of size and power under general local deviations from a reference model we then analyze the finite sample performance of the new robust tests via monte carlo simulations and compare it with that of classical gmm tests for structural breaks in large samples we find that the performance of classical asymptotic gmm tests can be quite unstable under slight departures from some given reference distribution in particular the loss in power can be substantial in some models robust asymptotic tests for structural breaks yield important power improvements both in exactly identified and overidentified model settings in small samples bootstrapped versions of the classical and the robust gmm tests provide accurate and stable empirical levels also for quite small sample sizes however bootstrapped robust gmm tests are found to provide again a higher finite sample efficiency

testing for structural change in dynamic models the well known cusum test for structural change is investigated whe n there are lagged dependent variables among the regressors in a linear model the authors show that both a modified cusum test suggested b y j m dufour 1982 and the straightforward cusum test retain their asymptotic significance levels in dynamic models and find that the power depends crucially on the angle between the mean regressor and the structural shift copyright 1988 by the econometric society

from constant mean curvature hypersurfaces to the gradient theory of phase transitions given a nondegenerate minimal hypersurface in a riemannian manifold we prove that for all e small enough there exists ue a critical point of the allen cahn energy ee u e2 u 2 1 u2 2 whose nodal set converges to as e tends to 0 moreover if is a volume nondegenerate constant mean curvature hypersurface then the same conclusion holds with the function ue being a critical point of ee under some volume constraint

second order estimate on transition layers abstract in this paper we establish a uniform c 2 estimate for level sets of stable solutions to the singularly perturbed allen cahn equation in dimensions n 10 which is optimal the proof combines two ingredients one is a reverse application of the infinite dimensional lyapunov schmidt reduction method which enables us to reduce the c 2 estimate for these level sets to a corresponding one on solutions of toda system the other one uses a small regularity theorem on stable solutions of toda system to establish various decay estimates which gives a lower bound on distances between different sheets of solutions to toda system or level sets of solutions to allen cahn equation

compensated compactness and the heisenberg group jacobians of maps on the heisenberg group are shown to map suitable group sobolev spaces into the group hardy space h1 from this result and a weak convergence theorem for the hardy space h1 of the heisenberg group a compensated compactness property for these jacobians is obtained 0 introduction we investigate compensated compactness properties of jacobians of maps on the heisenberg group and we prove results analogous to those for the jacobians of maps on r let h c r be the lie group with multiplicative structure z t z t z z t t 2 im z z where z z1 zn z z 1 z n and z z n j 1 zj z j this is the n order heisenberg group it can be shown that the group operation is c on the manifold c r and hence h is a locally compact lie group let z1 zn t be coordinates on h write zj xj iyj and define the vector fields xj xj 2yj t yj yj 2xj t t t it turns out that the xj yj and t form a basis for the left invariant vector fields on h they satisfy the commutation relations xj yj 4t j 1 n and all other work partially supported by the national science foundation work partially supported by nsf grant dms 9007491 mathematics subject classification 1991 42 typeset by ams tex 1 commutators vanish the group h is equipped with a natural dilation structure r z t rz rt r 0 which is consistent with the group multiplication the associated norm z t z 4 t is homogeneous of degree 1 with respect to this group of dilations we denote by br u0 the heisenberg group ball u h u 1u0 0 f u where u 2n 2 1u if 2n 2 2n 3 the hardy space h h h is the set of all f such that f l h an alternative definition of h h can be given via the atomic decomposition see fos or cw for details given a c map f f1 fn from h into r define 0 3 jac f det l1f1 l1f2 l1fn l2f1 l2f2 l2fn lnf1 lnf2 lnfn where lj is either xj or yj we would like to show that jac f maps a product of suitable group sobolev spaces into the spaces h h for 1 2n 2 2n 3 the analogous result for the vector fields xj 1 j n on r n has been proved by p l lions and y meyer when 1 and extended by clms for 1 n n 1 note that the lower bound for in both cases is d d 1 where d is the homogeneous dimension of the group our first result is theorem 1 let n 2 and for 1 j n let 1 0 that depends only on n and on the pj s such that for every map f f1 fn on h we have 0 4 jac f h c n

geometric properties of heisenberg type groups on montre qu il y a une certaine metrique riemannienne contravariante qui induit une longueur d arc

optimal mass transportation in the heisenberg group in this paper we consider the problem of optimal transportation of absolutely continuous masses in the heisenberg group hn in the case when the cost function is either the square of the carnot caratheodory distance or the square of the koranyi norm in both cases we show existence and uniqueness of an optimal transport map in the former case the proof requires a delicate analysis of minimizing geodesics of the group and of the differentiability properties of the squared distance function in the latter case the proof requires some fine properties of bv functions in the heisenberg group

groups quasi isometric to complex hyperbolic space we show that any finitely generated group quasi isometric to complex hyperbolic space is a finite extension of a properly discontinuous cocompact subgroup of the isometry group

are consumption based intertemporal capital asset pricing models structural abstract hansen and singleton 1982 and dunn and singleton 1986 have found supporting evidence for the overidentifying restrictions of two empirical consumption based asset pricing models when estimated with a particular set of single asset returns in this paper we submit these models to further scrutiny by testing whether they exhibit structural stability a series of tests recently developed by ghysels and hall 1990 are applied and a test for structuralinvariance is introduced based on the likelihood ratio type test procedure of eichenbaum hansen and singleton 1988 there are a number of reasons why structural stability tests are particularly appropriate for diagnostic testing of euler equation models namely 1 the lucas econometric policy evaluation critique 2 euler equations are only a partial description of the data generating process and parameter stability is one of the few assumptions imposed in their estimation via the generalized method of moments and finally 3 it is demonstrated that hansen s overidentifying restrictions test has no power against a class of local alternatives characterized by a parameter drift

area stationary surfaces in the heisenberg group h1 we consider area stationary surfaces perhaps with a volume constraint in the heisenberg group h1 endowed with its carnot caratheodory distance by analyzing the first variation of area we characterize c2 area stationary surfaces as those with mean curvature zero or constant if a volume preserving condition is assumed and such that the characteristic curves meet orthogonally the singular curves moreover a minkowski type formula relating the area the mean curvature and the volume is obtained for volume preserving area stationary surfaces enclosing a given region as a consequence of the characterization of area stationary surfaces we refine the bernstein type theorem given in jih hsin cheng jenn fang hwang andrea malchiodi paul yang minimal surfaces in pseudohermitian geometry ann sc norm super pisa cl sci 5 4 1 2005 129 177 mr 2165405 and nicola garofalo scott pauls the bernstein problem in the heisenberg group arxiv math dg 0209065 to describe all c2 entire area stationary graphs over the xy plane in a calibration argument shows that these graphs are globally area minimizing finally by using the description of the singular set in jih hsin cheng jenn fang hwang andrea malchiodi paul yang minimal surfaces in pseudohermitian geometry ann sc norm super pisa cl sci 5 4 1 2005 129 177 mr 2165405 the characterization of area stationary surfaces and the ruling property of constant mean curvature surfaces we prove our main results where we classify area stationary surfaces in with or without a volume constraint and non empty singular set in particular we deduce the following counterpart to alexandrov uniqueness theorem in euclidean space any compact connected c2 surface in area stationary under a volume constraint must be congruent to a rotationally symmetric sphere obtained as the union of all the geodesics of the same curvature joining two points as a consequence we solve the isoperimetric problem in assuming c2 smoothness of the solutions 13 completely reducible hypersurfaces in a pencil pages 672 688 j v pereira s yuzvinsky preview pdf 324 k related articles 14 modules over motivic cohomology pages 689 727 oliver rondigs paul arne ostvaer preview pdf 303 k related articles 15 the fundamental group of period domains over finite fields pages 728 741 sascha orlik preview pdf 154 k related articles articles 1 15

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

h type groups and iwasawa decompositions since their introduction by a kaplan kpl some ten years ago generalised heisenberg groups also known as groups of heisenberg type or h type groups have provided a framework in which to construct interesting examples in geometry and analysis see for instance c2 kp2 kp3 kpr k2 rl r2 tl tv the iwasawa n groups associated to all the real rank one simple lie groups are h type so one has a convenient vehicle for studying these in a unified way many problems on these simple lie groups can be reduced to a problem on h type groups via the so called noncompact picture and often problems on h type groups can be solved on all the groups of the family in one fell swoop as in for example ch ck dr out of this approach to studying simple lie groups several problems arise such as why only some h type groups correspond to simple lie groups of real rank one in this paper we discuss various features of iwasawa n groups which distinguish them in the class of all h type groups we shall show that all h type groups which possess certain geometric properties clearly possessed by iwasawa n groups satisfy a lie algebraic condition implicit in the work of b kostant kt2 that we shall call the j condition we shall also use elementary clifford algebra to classify the

admissibility of the likelihood ratio test when a nuisance parameter is present only under the alternative this paper establishes the asymptotic admissibility of the likelihood ratio lr test for a general class of testing problems in which a nuisance parameter is present only under the alternative hypothesis the paper also establishes the finite sample admissibility of the lr test for testing problems of this sort that arise in gaussian linear regression models with known variance

the geometry of the eisenstein picard modular group the eisenstein picard modular group rm pu 2 1 mathbb z omega is defined to be the subgroup of rm pu 2 1 whose entries lie in the ring mathbb z omega where omega is a cube root of unity this group acts isometrically and properly discontinuously on bf h 2 mathbb c that is on the unit ball in mathbb c 2 with the bergman metric we construct a fundamental domain for the action of rm pu 2 1 mathbb z omega on bf h 2 mathbb c which is a 4 simplex with one ideal vertex as a consequence we elicit a presentation of the group see theorem 5 9 this seems to be the simplest fundamental domain for a finite covolume subgroup of rm pu 2 1

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

some examples of quasiisometries of nilpotent lie groups we construct quasiisometries of nilpotent lie groups in particular for any simply connected nilpotent lie group n we construct quasiisometries from n to itself that is not at finite distance from any map that is a composition of left translations and automorphisms we also construct bilipschitz maps of the heisenberg groups that send vertical lines to curves that are not vertical lines

inference and prediction in a multiple structural break model this paper develops a new bayesian approach to structural break modeling the focuses of the approach are the modeling of in sample structural breaks and forecasting time series allowing out of sample breaks the model has several desirable features first the number of regimes is not fixed but is treated as a random variable second the model adopts a hierarchical prior for regime coefficients which allows for the coefficients of one regime to contain information about coefficients of other regimes third the regime coefficients can be integrated analytically in the posterior density as a consequence the posterior simulator is fast and reliable an application to us real gdp quarterly growth rates links groups of regimes to specific historical periods and provides forecasts of future growth rates

abnormal minimizers this paper constructs the first example of a singular abnormal minimizer for the lagrange problem with linear velocity constraints and quadratic definite lagrangian or equivalently for an optimal control system of linear controls with k controls n states and a running cost function that is quadratic positive definite in the controls in the example k 2 n 3 and the system is completely controllable the example is stable if both the control law and cost are perturbed the singular minimizer persists its importance is due in part to the fact that it is a counterexample to a theorem that has appeared several times in the differential geometry literature there the problem is called the problem of finding minimizing sub riemannian geodesics and it has been claimed that all minimizers are normal pontryagin extremals the mathematical theory of optimal processes wiley interscience new york 1962 if the number of states equals the number of controls then the problem is that of finding riemannian geodesics the main difficulty is proving minimality to do this the length cost of the abnormal is compared with all competing normal extremals a detailed asymptotic analysis of the differential equations governing the normals shows that they are all longer

moser trudinger and beckner onofri s inequalities on the cr sphere we derive sharp moser trudinger inequalities on the cr sphere the rst type is in the adams form for powers of the sublaplacian and for general spectrally dened operators on the space of cr pluriharmonic functions we will then obtain the sharp beckner onofri inequality for crpluriharmonic functions on the sphere and as a consequence a sharp logarithmic hardy littlewood sobolev inequality in the form given by carlen and loss

end of sample instability tests this paper considers tests for structural instability of short duration such as at the end of the sample the key feature of the testing problem is that the number m of observations in the period of potential change is relatively small possibly as small as one the well known f test of chow 1960 for this problem only applies in a linear regression model with normally distributed iid errors and strictly exogenous regressors even when the total number of observations n m is large we generalize the f test to cover regression models with much more general error processes regressors that are not strictly exogenous and estimation by instrumental variables as well as least squares in addition we extend the f test to nonlinear models estimated by generalized method of moments and maximum likelihood asymptotic critical values that are valid as n with m fixed are provided using a subsampling like method the results apply quite generally to processes that are strictly stationary and ergodic under the null hypothesis of no structural instability

quasiconformal mappings on the heisenberg group on etudie les applications conformes et quasi conformes sur le groupe de heisenberg la metrique invariante a gauche naturelle sur cet espace est non isotrope sous des dilatations et ne peut se decrire par une metrique de riemann ceci engendre de nouveaux phenomenes

the effect of a singular perturbation on nonconvex variational problems we study the effect of a singular perturbation on certain nonconvex variational problems the goal is to characterize the limit of minimizers as some perturbation parameter 0 the technique utilizes the notion of convergence of variational problems developed by de giorgi the essential idea is to identify the first nontrivial term in an asymptotic expansion for the energy of the perturbed problem in so doing one characterizes the limit of minimizers as the solution of a new variational problem for the cases considered here these new problems have a simple geometric nature involving minimal surfaces and geodesics

eigenforms of the laplacian on real and complex hyperbolic spaces on decrit l espace total des solutions de l equation c ou est une p forme sur un espace x hyperbolique reel ou complexe a n dimensions et c une constante complexe

ideal triangle groups dented tori and numerical analysis we prove the goldman parker conjecture a complex hyperbolic ideal triangle group is discretely embedded in pu 2 1 if and only if the product of its three standard generators is not elliptic we also prove that such a group is indiscrete if the product of its three standard generators is elliptic a novel feature of this paper is that it uses a rigorous computer assisted proof to deal with difficult geometric estimates

on the convergence of stable phase transitions we consider the local behavior of critical points of the functional as e 0 here w is a double well potential and u is a regular domain in n n 2 assuming that ue e 0 is stable for n 2 and locally energy minimizing for n 3 we show that the level sets of solutions converge in an average sense to a stationary n 1 rectifiable varifold our study is based on estimates derived from the second variation formula and is entirely local 1998 john wiley sons inc

symmetry algebra for multi contact structures given by 2n vector fields on mathbb r 2n 1 the notion of multicontact structures has been introduced in 2 as the geometry of manifolds with several distinguished mutually transversal subbundles of the tangent bundle such structures appear naturally as secondary structures in parabolic geometry more precisely let g be a semi simple lie group and p a parabolic subgroup then the nilpotent factor n in the iwasawa decomposition g kan naturally gives rise to mutually transversal subbundles

singular solutions homogeneous norms and quasiconformal mappings in carnot groups in any carnot nilpotent stratified lie group g of homogeneous dimension q green s function u for the q laplace equation exists and is unique we prove that there exists a constant gamma gamma g so that n e gamma u is a homogeneous norm in g then the extremal lengths of spherical ring domains measured with respect to n can be computed and used to give estimates for the extremal lengths of ring domains measured with respect to the carnot caratheodory metric applications include regularity properties of quasiconformal mappings and a geometric characterization of bi lipschitz mappings

hardy space estimates of hausdorff operators on the heisenberg group abstract this is a continuation of a series of works about hausdorff operator on hardy spaces in the setting of the heisenberg group in this paper we obtain the boundedness from lebesgue spaces to hardy spaces for fractional hausdorff operators and their compositions with riesz transforms we also establish the boundedness for two kinds of special hausdorff operators the hausdorff poisson operator and the hausdorff gauss operator on hardy spaces

quasiregular mappings of the heisenberg group the condition 1 1 means that for all d g the coordinate functions o f f belong to the sobolev space w d of functions in l d whose distributional first order partial derivatives are also l integrable in d in the above definition f x is the formal derivative of f a t x defined by means of the partial derivatives i f x l is the operator norm of f x and ji x is the jacobian determinant of f a t x these are uniquely defined almost everywhere by 1 1 it turns out that quasiregular mappings are differentiable almost everywhere and a nonconstant quasiregular map is discrete open and sense preserving for these and other basic properties of qr maps we refer to books re by reshetnyak vu by vuorinen and also to a forthcoming book r6 by the second author the definition extends immediately to the case f m n where m and n are connected oriented riemannian n manifolds we say that a continuous map f m n is quasiregular if it has a local representation at each point of m which is quasiregular in the above sense and if there exists k 1 k oe such that

a notable family of entire intrinsic minimal graphs in the heisenberg group which are not perimeter minimizing one of the main objectives of this paper is to unravel a new interesting phenomenon of the sub riemannian bernstein problem with respect to its euclidean ancestor with the purpose of also indicating a possible line of attack toward its solution we show that the global intrinsic graphs 1 2 are unstable critical points of the horizontal perimeter as a consequence of this fact the study of the stability acquires a central position in the problem itself

structural change tests for simulated method of moments simulation based estimation methods have become more widely used in recent years we propose a set of tests for structural change in models estimated via simulated method of moments see duffe and singleton econometrica 61 1993 929 these tests extend the work of andrews econometrica 61 1993 821 ghysels et al j econom 82 1997 209 and sowell econometrica 64 1996 1085 tests for violation of moment conditions manuscript graduate school of industrial administration carnegie mellon university which covered generalized method of moments estimators not involving simulation we derive the asymptotic distributions of various tests we show that the number of simulations does not affect the asymptotic distribution under the null but adversely influences local asymptotic power a monte carlo investigation of the finite sample size and power reveals that a relatively small number of simulations suffices to obtain tests with desirable small sample size and power properties

quasiconformal maps in metric spaces with controlled geometry this paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry the principal message is that such a theory is both relevant and viable the first main issue is the problem of definition which we next describe quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount this requirement makes sense in every metric space given a homeomorphism f from a metric space x to a metric space y then for x x and r 0 set

sub riemannian calculus and monotonicity of the perimeter for graphical strips we consider the class of minimal surfaces given by the graphical strips mathcal s in the heisenberg group mathbb h 1 and we prove that for points p along the center of mathbb h 1 the quantity frac sigma h mathcal s cap b p r r q 1 is monotone increasing here q is the homogeneous dimension of mathbb h 1 we also prove that these minimal surfaces have maximum volume growth at infinity

predictive tests for structural change with unknown breakpoint abstract this paper considers predictive tests for structural change in models estimated via generalized method of moments our analysis extends earlier work by ghysels and hall 1990a by allowing for the instability to occur at an unknown point in the sample we analyse various statistics based on continuous mappings of the sequence of predictive test calculated for a set of possible breakpoints in the sample the limiting distribution of these statistics is derived under both the null hypothesis and local alternatives percentiles are reported for the distribution under the null a sideproduct of our analysis is that we can illuminate the power properties of the predictive test and also compare its properties to those of the wald lr and lm tests for parameter variation we study those power properties both via local asymptotic analysis and monte carlo

segmenting mean nonstationary time series via trending regressions abstract in this paper we provide a segmentation procedure for mean nonstationary time series the segmentation is obtained by casting the problem into the framework of detecting structural breaks in trending regression models in which the regressors are generated by suitably smooth functions as test statistics we propose to use the maximally selected likelihood ratio statistics and a related statistics based on partial sums of weighted residuals the main theoretical contribution of the paper establishes the extreme value distribution of these statistics and their consistency to circumvent the slow convergence to the extreme value limit we propose to employ a version of the circular bootstrap this procedure is completely data driven and does not require knowledge of the time series structure in an empirical part we show in a simulation study and applications to air carrier traffic and s p 500 data that the finite sample performance is very satisfactory