heat flow on alexandrov spaces we prove that on compact alexandrov spaces with curvature bounded below the gradient flow of the dirichlet energy in the space produces the same evolution as the gradient flow of the relative entropy in the wasserstein space this means that the heat flow is well defined by either one of the two gradient flows combining properties of these flows we are able to deduce the lipschitz continuity of the heat kernel as well as bakry emery gradient estimates and the condition our identification is established by purely metric means unlike preceding results relying on pde techniques our approach generalizes to the case of heat flow with drift 2012 wiley periodicals inc

matrix orthogonal polynomials on the unit circle the properties of matrix orthogonal polynomials on the unit circle are investigated beginning with their recurrence formulas the techniques of scattering theory and banach algebras are used in the investigation a matrix generalization of a theorem of baxter is proved

li yau and harnack type inequalities in rcd k n metric measure spaces abstract metric measure spaces satisfying the reduced curvature dimension condition cd k n and where the heat flow is linear are called rcd k n spaces this class of non smooth spaces contains gromov hausdorff limits of riemannian manifolds with ricci curvature bounded below by k and dimension bounded above by n we prove that in rcd k n spaces the following properties of the heat flow hold true a li yau type inequality a bakry qian inequality the harnack inequality

some applications of the hermite matrix polynomials series expansions this paper deals with hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of differential systems properties of hermite matrix polynomials such as the three terms recurrence formula permit an efficient computation of matrix functions avoiding important computational drawbacks of other well known methods results are applied to compute accurate approximations of certain differential systems in terms of hermite matrix polynomials

inference and testing breaks in large dynamic panels with strong cross sectional dependence in this paper we provide a new central limit theorem for estimators of the slope papers in large dynamic panel data models where both n and t increase without bound in the presence of possibly strong cross sectional dependence we proceed by providing two related tests for breaks homogeneity in the time dimension the first test is based on the cusum principle the second test is based on a hausman durbin wu approach some of the key features of the tests are that they have nontrivial power when the number of individuals for which the slope parameters may differ is a negligible fraction or when the break happens to be towards the end of the sample and do not suffer from the incidental parameter problem we provide a simple bootstrap algorithm to obtain asymptotic valid critical values for our statistics an important feature of the bootstrap is that there is no need to know the underlying model of the cross sectional dependence a monte carlo simulation analysis sheds some light on the small sample behaviour of the tests and their bootstrap analogues we implement our test to some real economic data

matrix polynomial solutions of tangential lagrange sylvester interpolation conditions of low mcmillan degree abstract a matrix polynomial of mcmillan degree n 1 which satisfies n tangential lagrange interpolation conditions is constructed explicitly in realization form analogous results are given for more general bitangential lagrange sylvester interpolation conditions a corollary is a type of euclidean algorithm for matrix polynomials and mcmillan degree the main tool is the recent parametrization of all matrix polynomial solutions of a set of lagrange sylvester interpolation conditions due to ball gohberg and rodman

weak curvature conditions and functional inequalities we give sufficient conditions for a measured length space x d to admit local and global poincare inequalities along with a sobolev inequality we first introduce a condition dm on x d d ef ined in terms of transport of measures we show that dm together with a doubling condition on implies a scaleinvariant local poincare inequality we show that if x d has nonnegative n ricci curvature and has unique minimizing geodesics between almost all pairs of points then it satisfies dm with constant 2 n t he condition dm is preserved by measured gromov hausdorff limits we then prove a sobolev inequality for measured length spaces with n ricci curvature bounded below by k 0 finally we derive a sharp global poincare inequality

euclidean spaces as weak tangents of infinitesimally hilbertian metric measure spaces with ricci curvature bounded below we show that in any infinitesimally hilbertian cd k n space at almost every point there exists a euclidean weak tangent i e there exists a sequence of dilations of the space that converges to a euclidean space in the pointed measured gromov hausdorff topology the proof follows by considering iterated tangents and the splitting theorem for infinitesimally hilbertian cd 0 n spaces

on the equivalence of the entropic curvature dimension condition and bochner s inequality on metric measure spaces we prove the equivalence of the curvature dimension bounds of lott sturm villani via entropy and optimal transport and of bakry emery via energy and gamma 2 calculus in complete generality for infinitesimally hilbertian metric measure spaces in particular we establish the full bochner inequality on such metric measure spaces moreover we deduce new contraction bounds for the heat flow on riemannian manifolds and on mms in terms of the l 2 wasserstein distance

a laplace approximation to the moments of a ratio of quadratic forms summary the laplace method for approximating integrals is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables the technique utilises the existence of a dominating peak at the boundary point on the range of integration as closed form and tractable formulae do not exist in general this simple approximation which only entails basic algebraic operations has evident practical appeal we exploit the approximation to provide an approximate mean bias function for the least squares estimator of the coefficient of the lag dependent variable in a first order stochastic difference equation

on the hypergeometric matrix function abstract this paper deals with the study of the hypergeometric function with matrix arguments f a b c z conditions for matrices a b c so that the series representation of the hypergeometric function be convergent for z 1 and satisfies a matrix differential equation are given after the study of beta and gamma matrix functions an integral representation of f a b c z is obtained for the case where b c and c b are positive stable matrices with bc cb

orthogonal matrix polynomials and higher order recurrence relations abstract it is well known that orthogonal polynomials on the real line satisfy a three term recurrence relation and conversely every system of polynomials satisfying a three term recurrence relation is orthogonal with respect to some positive borel measure on the real line we extend this result and show that every system of polynomials satisfying some 2 n 1 term recurrence relation can be expressed in terms of orthonormal matrix polynomials for which the coefficients are n n matrices we apply this result to polynomials orthogonal with respect to a discrete sobolev inner product and other inner products in the linear space of polynomials as an application we give a short proof of krein s characterization of orthogonal polynomials with a spectrum having a finite number of accumulation points

estimation of heterogeneous autoregressive parameters with short panel data abstract this paper presents a maximum likelihood approach to estimation of cross sectional distributions of heterogeneous autoregressive ar parameters with short panel data we construct a panel likelihood by integrating the unknown cross sectional density of heterogeneous ar parameters with respect to a known time series data generating kernel the solution to this extremal criterion recovers the unknown density of heterogeneous ar parameters applying our method to a model of employment dynamics with the firm level data of arellano and bond 1991 we find that adjustment rates of employment are significantly heterogeneous across firms

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

the time series and cross section asymptotics of dynamic panel data estimators in this paper we derive the asymptotic properties of within groups wg gmm and liml estimators for an autoregressive model with random effects when both t and n tend to infinity gmm and liml are consistent and asymptotically equivalent to the wg estimator when t n 0 the fixed t results for gmm and liml remain valid but wg although consistent has an asymptotic bias in its asymptotic distribution when t n tends to a positive constant the wg gmm and liml estimators exhibit negative asymptotic biases of order 1 t 1 n and 1 2n t respectively in addition the crude gmm estimator that neglects the autocorrelation in first differenced errors is inconsistent as t n c 0 despite being consistent for fixed t finally we discuss the properties of a random effects pseudo mle with unrestricted initial conditions when both t and n tend to infinity

testing for heteroskedasticity in fixed effects models abstract we derive tests for heteroskedasticity after fixed effects estimation of linear panel models the asymptotic results are based on a large n fixed t framework where the incidental parameters problem is bypassed by utilizing a pseudo likelihood function conditional on the sufficient statistic for these parameters a simple studentization produces distribution free tests that can easily be implemented using an artificial regression based on residuals after fixed effects estimation a monte carlo exploration suggests that the tests perform well in small samples such as those encountered in practice

biorthogonal matrix polynomials related to jacobi matrix polynomials in this paper we define the pair of biorthogonal matrix polynomials suggested by the jacobi matrix polynomials biorthogonality property matrix generating functions and matrix recurrence relations are given

sharp holder continuity of tangent cones for spaces with a lower ricci curvature bound and applications we prove a new estimate on manifolds with a lower ricci bound which asserts that the geometry of balls centered on a minimizing geodesic can change in at most a holder continuous way along the geodesic we give examples that show that the holder exponent along with essentially all the other consequences that follow from this estimate are sharp among the applications is that the regular set is convex for any non collapsed limit of einstein metrics in the general case of a potentially collapsed limit of manifolds with just a lower ricci curvature bound we show that the regular set is weakly convex and a e convex we also show two conjectures of cheeger colding one of these asserts that the isometry group of any even collapsed limit of manifolds with a uniform lower ricci curvature bound is a lie group the other asserts that the dimension of any limit space is the same everywhere

jacobi matrix differential equation polynomial solutions and their properties in this paper jacobi matrix polynomials are introduced starting from the hypergeometric matrix function the differential equation satisfied by them is presented a rodrigues formula orthogonality and a three terms matrix recurrence relationship are then developed for jacobi matrix polynomials

area minimizing discs in metric spaces we solve the classical problem of plateau in the setting of proper metric spaces precisely we prove that among all disc type surfaces with prescribed jordan boundary in a proper metric space there exists an area minimizing disc which moreover has a quasi conformal parametrization if the space supports a local quadratic isoperimetric inequality for curves we prove that such a solution is locally holder continuous in the interior and continuous up to the boundary our results generalize corresponding results of douglas rado and morrey from the setting of euclidean space and riemannian manifolds to that of proper metric spaces

bakry emery curvature dimension condition and riemannian ricci curvature bounds the aim of the present paper is to bridge the gap between the bakry emery and the lott sturm villani approaches to provide synthetic and abstract notions of lower ricci curvature bounds we start from a strongly local dirichlet form mathcal e admitting a carre du champ gamma in a polish measure space x mathfrak m and a canonical distance mathsf d mathcal e that induces the original topology of x we first characterize the distinguished class of riemannian energy measure spaces where mathcal e coincides with the cheeger energy induced by mathsf d mathcal e and where every function f with gamma f le1 admits a continuous representative in such a class we show that if mathcal e satisfies a suitable weak form of the bakry emery curvature dimension condition mathrm be k infty then the metric measure space x mathsf d mathfrak m satisfies the riemannian ricci curvature bound mathrm rcd k infty according to duke math j 163 2014 1405 1490 thus showing the equivalence of the two notions two applications are then proved the tensorization property for riemannian energy spaces satisfying the bakry emery mathrm be k n condition and thus the corresponding one for mathrm rcd k infty spaces without assuming nonbranching and the stability of mathrm be k n with respect to sturm gromov hausdorff convergence

measure rigidity of ricci curvature lower bounds abstract the measure contraction property mcp for short is a weak ricci curvature lower bound conditions for metric measure spaces the goal of this paper is to understand which structural properties such assumption or even weaker modifications implies on the measure on its support and on the geodesics of the space we start our investigation from the euclidean case by proving that if a positive radon measure m over r d is such that r d m verifies a weaker variant of mcp then its support spt m must be convex and m has to be absolutely continuous with respect to the relevant hausdorff measure of spt m this result is then used as a starting point to investigate the rigidity of mcp in the metric framework we introduce the new notion of reference measure for a metric space and prove that if x d m is essentially non branching and verifies mcp and is an essentially non branching mcp reference measure for spt m d then m is absolutely continuous with respect to on the set of points where an inversion plan exists as a consequence an essentially non branching mcp reference measure enjoys a weak type of uniqueness up to densities we also prove a stability property for reference measures under measured gromov hausdorff convergence provided an additional uniform bound holds in the final part we present concrete examples of metric spaces with reference measures both in smooth and non smooth setting the main example will be the hausdorff measure over an alexandrov space then we prove that the following are reference measures over smooth spaces the volume measure of a riemannian manifold the hausdorff measure of an alexandrov space with bounded curvature and the haar measure of the subriemannian heisenberg group

bias assessment and reduction in linear error correction models abstract the small sample bias of the ordinary least squares coefficient estimator for dynamic regression models with innovation errors and lagged dependent and strongly exogenous explanatory variables is approximated through both small disturbance and large sample asymptotics results for the standard armax p 0 k model are obtained and also for such models under linear parameter constraints and variable transformations these approximations are then used to construct corrected estimators for the parameters of interest in higher order dynamic models including the empirically highly relevant linear error correction model by simulating two empirical cases the corrected estimators obtained via large sample asymptotics are shown to have more attractive location and efficiency properties than ordinary least squares

local curvature dimension condition implies measure contraction property abstract we prove that for non branching metric measure spaces the local curvature condition cd loc k n implies the global version of mcp k n the curvature condition cd k n introduced by the second author and also studied by lott and villani is the generalization to metric measure space of lower bounds on ricci curvature together with upper bounds on the dimension this paper is the following step of bacher and sturm 2010 1 where it is shown that cd loc k n is equivalent to a global condition cd k n slightly weaker than the usual cd k n it is worth pointing out that our result implies sharp bishop gromov volume growth inequality and sharp poincare inequality

on time varying factor models estimation and testing abstract conventional factor models assume that factor loadings are fixed over a long horizon of time which appears overly restrictive and unrealistic in applications in this paper we introduce a time varying factor model where factor loadings are allowed to change smoothly over time we propose a local version of the principal component method to estimate the latent factors and time varying factor loadings simultaneously we establish the limiting distributions and uniform convergence of the estimated factors and factor loadings in the standard large n and large t framework we also propose a bic type information criterion to determine the number of factors which can be used in models with either time varying or time invariant factor models based on the comparison between the estimates of the common components under the null hypothesis of no structural changes and those under the alternative we propose a consistent test for structural changes in factor loadings we establish the null distribution the asymptotic local power property and the consistency of our test simulations are conducted to evaluate both our nonparametric estimates and test statistic we also apply our test to investigate stock and watson s 2009 u s macroeconomic data set and find strong evidence of structural changes in the factor loadings

sharp and rigid isoperimetric inequalities in metric measure spaces with lower ricci curvature bounds we prove that if x mathsf d mathfrak m is a metric measure space with mathfrak m x 1 having in a synthetic sense ricci curvature bounded from below by k 0 and dimension bounded above by n in 1 infty then the classic levy gromov isoperimetric inequality together with the recent sharpening counterparts proved in the smooth setting by milman for any k in mathbb r n ge 1 and upper diameter bounds holds i e the isoperimetric profile function of x mathsf d mathfrak m is bounded from below by the isoperimetric profile of the model space moreover if equality is attained for some volume v in 0 1 and k is strictly positive then the space must be a spherical suspension and in this case we completely classify the isoperimetric regions finally we also establish the almost rigidity if the equality is almost attained for some volume v in 0 1 and k is strictly positive then the space must be mgh close to a spherical suspension to our knowledge this is the first result about isoperimetric comparison for non smooth metric measure spaces satisfying ricci curvature lower bounds examples of spaces fitting our assumptions include measured gromov hausdorff limits of riemannian manifolds satisfying ricci curvature lower bounds alexandrov spaces with curvature bounded from below finsler manifolds endowed with a strongly convex norm and satisfying ricci curvature lower bounds the result seems new even in these celebrated classes of spaces

a heteroskedasticity robust breusch pagan test for contemporaneous correlation in dynamic panel data models abstract this paper proposes a heteroskedasticity robust breusch pagan test of the null hypothesis of zero cross section or contemporaneous correlation in linear panel data models without necessarily assuming independence of the cross sections the procedure allows for either fixed strictly exogenous and or lagged dependent regressor variables as well as quite general forms of both non normality and heteroskedasticity in the error distribution the asymptotic validity of the test procedure is predicated on the number of time series observations t being large relative to the number of cross section units n in that either i n is fixed as t or ii n 2 t 0 as both t and n diverge jointly to infinity given this it is not expected that asymptotic theory would necessarily provide an adequate guide to finite sample performance when t n is small because of this we also propose and establish asymptotic validity of a number of wild bootstrap schemes designed to provide improved inference when t n is small across a variety of experimental designs a monte carlo study suggests that the predictions from asymptotic theory do in fact provide a good guide to the finite sample behaviour of the test when t is large relative to n however when t and n are of similar orders of magnitude discrepancies between the nominal and empirical significance levels occur as predicted by the first order asymptotic analysis on the other hand for all the experimental designs the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels when t n is small with a recursive design wild bootstrap scheme performing best in general and providing quite close agreement between the nominal and empirical significance levels of the test even when t and n are of similar size moreover in comparison with the wild bootstrap version of the original breusch pagan test godfrey and yamagata 2011 our experiments indicate that the corresponding version of the heteroskedasticity robust breusch pagan test appears reliable as an illustration the proposed tests are applied to a dynamic growth model for a panel of 20 oecd countries

a joint serial correlation test for linear panel data models abstract this paper proposes a joint error serial correlation test to be applied to linear panel data models after generalised method of moments estimation this new test is an alternative inferential tool to both the m 2 test of arellano m bond s 1991 some tests of specification for panel data monte carlo evidence and an application to employment equations review of economic studies 58 277 297 and the overidentifying restrictions test the proposed test called the m 2 p 2 test involves an examination of the joint significance of estimates of second to p th order first differenced error serial correlations the small sample properties of the m 2 p 2 test are investigated by means of monte carlo experiments the evidence shows that the proposed test mostly outperforms the conventional m 2 test and has high power when the overidentifying restrictions test does not under a variety of alternatives including slope heterogeneity and cross section dependence

riemannian ricci curvature lower bounds in metric measure spaces with finite measure in prior work 4 of the first two authors with savare a new riemannian notion of lower bound for ricci curvature in the class of metric measure spaces x d m was introduced and the corresponding class of spaces denoted by rcd k this notion relates the cd k n theory of sturm and lott villani in the case n to the bakry emery approach in 4 the rcd k property is defined in three equivalent ways and several properties of rcd k spaces including the regularization properties of the heat flow the connections with the theory of dirichlet forms and the stability under tensor products are provided in 4 only finite reference measures m have been considered the goal of this paper is twofold on one side we extend these results to general finite spaces on the other we remove a technical assumption appeared in 4 concerning a strengthening of the cd k condition this more general class of spaces includes euclidean spaces endowed with lebesgue measure complete noncompact riemannian manifolds with bounded geometry and the pointed metric measure limits of manifolds with lower ricci curvature bounds

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

heterogeneous panel data models with cross sectional dependence abstract this paper considers a semiparametric panel data model with heterogeneous coefficients and individual specific trending functions where the random errors are assumed to be serially correlated and cross sectionally dependent we propose mean group estimators for the coefficients and trending functions involved in the model it can be shown that the proposed estimators can achieve an asymptotic consistency with rates of root n t and root n t h respectively as n t where n is allowed to increase faster than t furthermore a statistic for testing homogeneous coefficients is constructed based on the difference between the mean group estimator and a pooled estimator its asymptotic distributions are established under both the null and a sequence of local alternatives even if the difference between these estimators vanishes considerably fast can achieve root n t 2 rate at most under the null and no consistent estimator for the covariance matrix is required the finite sample performance of the proposed estimators together with the size and local power properties of the test are demonstrated by simulated data examples and an empirical application with the oecd health care expenditure dataset is also provided

ricci curvature and volume convergence the purpose of this paper is to give a new integral estimate of distances and angles on manifolds with a given lower ricci curvature bound this will provide us with an integral version of the toponogov comparison triangle theorem for ricci curvature and almost extreme triangles see the earlier works cl and c2 for an analog of this when the manifold has positive ricci curvature using this we prove the anderson cheeger conjecture saying that the volume is a continuous function on the space of all closed n manifolds with ricci curvature greater or equal to n 1 equipped with the gromovhausdorff metric we also prove gromov s conjecture for n 57 3 saying that an almost nonnegatively ricci curved n manifold with first betti number equal to n is a torus further we prove a conjecture of anderson cheeger saying that an open n manifold with nonnegative ricci curvature whose tangent cone at infinity is in is itself in finally we prove a conjecture of fukaya yamaguchi we will now describe these results in more detail let dgh denote the gromov hausdorff distance glp first we have the following result which was conjectured by anderson cheeger

polynomial interpolation and gaussian quadrature for matrix valued functions abstract the techniques for polynomial interpolation and gaussian quadrature are generalized to matrix valued functions it is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the highest degree of precision

testing slope homogeneity in large panels abstract this paper proposes a standardized version of swamy s test of slope homogeneity for panel data models where the cross section dimension n could be large relative to the time series dimension t the proposed test denoted by exploits the cross section dispersion of individual slopes weighted by their relative precision in the case of models with strictly exogenous regressors but with non normally distributed errors the test is shown to have a standard normal distribution as n t j such that n t 2 0 when the errors are normally distributed a mean variance bias adjusted version of the test is shown to be normally distributed irrespective of the relative expansion rates of n and t the test is also applied to stationary dynamic models and shown to be valid asymptotically so long as n t as n t j where 0 using monte carlo experiments it is shown that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of n and t similar results are also obtained for dynamic panels but only if the autoregressive coefficient is not too close to unity and so long as t n

the bias of autoregressive coefficient estimators abstract this article presents simple expressions for the bias of estimators of the coefficients of an autoregressive model of arbitrary but known finite order the results include models both with and without a constant term the effects of overspecification of the model order on the bias are described the emphasis is on least squares and yule walker estimators but the methods extend to other estimators of similar design although only the order t 1 component of the bias is captured where t is the series length this asymptotic approximation is shown to be very accurate for least squares estimators through some numerical simulations the simulations examine fourth order autoregressions chosen to resemble some data series from the literature the order t 1 bias approximations for yule walker estimators need not be accurate especially if the zeros of the associated polynomial have moduli near 1 examples are given where the approximation is accurate and where it is useless the bias expressions are

on a multivariable extension of jacobi matrix polynomials the classical jacobi matrix polynomials only for commutative matrices were first studied by defez et al e defez l jodar a law jacobi matrix differential equation polynomial solutions and their properties comput math appl 48 2004 789 803 the main aim of this paper is to construct a multivariable extension with the help of the classical jacobi matrix polynomials jmps generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived furthermore general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented

on the geometry of metric measure spaces ii we introduce a curvature dimension condition cd k n for metric measure spaces it is more restrictive than the curvature bound underline text curv left m text d m right k introduced in sturm k t 2006 on the geometry of metric measure spaces i acta math 196 65 131 which is recovered as the borderline case cd k the additional real parameter n plays the role of a generalized upper bound for the dimension for riemannian manifolds cd k n is equivalent to text ric m left xi xi right k left xi right 2 and dim m n the curvature dimension condition cd k n is stable under convergence for any triple of real numbers k n l the family of normalized metric measure spaces m d m with cd k n and diameter l is compact condition cd k n implies sharp version of the brunn minkowski inequality of the bishop gromov volume comparison theorem and of the bonnet myers theorem moreover it implies the doubling property and local scale invariant poincare inequalities on balls in particular it allows to construct canonical dirichlet forms with gaussian upper and lower bounds for the corresponding heat kernels

shrinkage estimation of common breaks in panel data models via adaptive group fused lasso abstract in this paper we consider estimation and inference of common breaks in panel data models via adaptive group fused lasso we consider two approaches penalized least squares pls for first differenced models without endogenous regressors and penalized gmm pgmm for first differenced models with endogeneity we show that with probability tending to one both methods can correctly determine the unknown number of breaks and estimate the common break dates consistently we establish the asymptotic distributions of the lasso estimators of the regression coefficients and their post lasso versions we also propose and validate a data driven method to determine the tuning parameter used in the lasso procedure monte carlo simulations demonstrate that both the pls and pgmm estimation methods work well in finite samples we apply our pgmm method to study the effect of foreign direct investment fdi on economic growth using a panel of 88 countries and regions from 1973 to 2012 and find multiple breaks in the model

large manifolds with positive ricci curvature the main purpose of this paper is to show that an n dimensional manifold with ricci curvature greater or equal to n 1 which is close in the gromov hausdor topology to the unit n sphere has volume close to that of the sphere this shows the converse of the theorem in c1 namely together with c1 it shows that an n manifold with ricci curvature greater or equal to n 1 is close to the sphere if and only if the volume is close to that of the sphere in particular by p such a manifold is homeomorphic to a sphere further as an application of this and the result of c1 we prove a radius theorem saying that if an n manifold with ricci curvature greater or equal to n 1 has radius almost equal to then the volume is close to that of the sphere in order to obtain these results we further develop and apply the estimates of c1 whereas the main concern in c1 were with the large scale geometry the main concern of this paper is with the small scale geometry let n be the volume of the round n sphere sn with sectional curvature one

convergence of pointed non compact metric measure spaces and stability of ricci curvature bounds and heat flows aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition we propose various definitions show that all of them are equivalent and that for doubling spaces these are also equivalent to the well known measured gromov hausdorff convergence then we show that the curvature conditions cd k and rcd k are stable under this notion of convergence and that the heat flow passes to the limit as well both in the wasserstein and in the l framework we also prove the variational convergence of cheeger energies in the naturally adapted mosco sense and the convergence of the spectra of the laplacian in the case of spaces either uniformly bounded or satisfying the rcd k condition with k 0 when applied to riemannian manifolds our results allow for sequences with diverging dimensions

inference on factor structures in heterogeneous panels this paper develops an estimation and testing framework for a stationary large panel model with observable regressors and unobservable common factors we allow for slope heterogeneity and for correlation between the common factors and the regressors we propose a two stage estimation procedure for the unobservable common factors and their loadings based on common correlated effects estimator and the principal component estimator we also develop two tests for the null of no factor structure one for the null that loadings are cross sectionally homogeneous and one for the null that common factors are homogeneous over time our tests are based on using extremes of the estimated loadings and common factors the test statistics have an asymptotic gumbel distribution under the null and have power versus alternatives where only one loading or common factor differs from the others monte carlo evidence shows that the tests have the correct size and good power

ricci curvature for metric measure spaces via optimal transport we dene a notion of a measured length space x having nonnegative n ricci curvature for n 2 1 1 or having1 ricci curvature bounded below byk fork2 r the denitions are in terms of the displacement convexity of certain functions on the associated wasserstein metric space p2 x of probability measures we show that these properties are preserved under measured gromov hausdor limits we give geometric and analytic consequences this paper has dual goals one goal is to extend results about optimal transport from the setting of smooth riemannian manifolds to the setting of length spaces a second goal is to use optimal transport to give a notion for a measured length space to have ricci curvature bounded below we refer to 11 and 44 for background material on length spaces and optimal transport respectively further bibliographic notes on optimal transport are in appendix f in the present introduction we motivate the questions that we address and we state the main results to start on the geometric side there are various reasons to try to extend notions of curvature from smooth riemannian manifolds to more general spaces a fairly general setting is that of length spaces meaning metric spaces x d in which the distance between two points equals the inmum of the lengths of curves joining the points in the rest of this introduction we assume that x is a compact length space alexandrov gave a good notion of a length space having curvature bounded below by k with k a real number in terms of the geodesic triangles in x in the case of a riemannian manifold m with the induced length structure one recovers the riemannian notion of having sectional curvature bounded below by k length spaces with alexandrov curvature bounded below by k behave nicely with respect to the gromovhausdor topology on compact metric spaces modulo isometries they form

lower bounds on ricci curvature and the almost rigidity of warped products the basic rigidity theorems for manifolds of nonnegative or positive ricci curvature are the volume cone implies metric cone theorem the maximal diameter theorem cg and the splitting theorem cg each asserts that if a certain geometric quantity volume or diameter is as large as possible relative to the pertinent lower bound on ricci curvature then the metric on the manifold in question is a warped product metric of a particular type in this paper we provide quantitative generalizations of the above mentioned results among the applications are the splitting theorem for gromovhausdorff limit spaces x where mn x ricmn i see fy other applications include the assertion that for complete manifolds m with ricmf 0 and euclidean volume growth all tangent cones at infinity are metric cones compare bkn ct p1 via resealing arguments there are also strong consequences for the local structure of manifolds whose ricci curvature satisfies a fixed lower bound and for their gromov hausdorff limits some of these are announced in ccol for a more detailed discussion see cco2 cco3 cco4 our work further develops and significantly extends techniques which were introduced in col co2 and significantly extended in co3 in order to prove certain stability conjectures of anderson cheeger gromov and perelman the results of col co3 were announced in co4 we briefly review some of those results let dgh denote the gromov hausdorff distance between metric spaces see glp let s denote the unit sphere and recall that s is the unique complete

localization and tensorization properties of the curvature dimension condition for metric measure spaces abstract this is an addendum to the paper k bacher k t sturm localization and tensorization properties of the curvature dimension condition for metric measure spaces j funct anal 259 2010 28 56 we prove the tensorization property for the curvature dimension condition add some detailed calculations including explicit dependence of constants and comment on assumptions and conjectures concerning the local to global statement in bacher and sturm 2010 1 and villani 2009 6 respectively