affine brauer category and parabolic category mathcal o o in types b c d a strict monoidal category referred to as affine brauer category mathcal ab is introduced over a commutative ring kappa containing multiplicative identity 1 and invertible element 2 we prove that morphism spaces in mathcal ab are free over kappa the cyclotomic or level k brauer category mathcal cb f omega is a quotient category of mathcal ab we prove that any morphism space in mathcal cb f omega is free over kappa with maximal rank if and only if the mathbf u admissible condition holds in the sense of 1 32 affine nazarov wenzl algebras nazarov in j algebra 182 3 664 693 1996 and cyclotomic nazarov wenzl algebras ariki et al in nagoya math j 182 47 134 2006 will be realized as certain endomorphism algebras in mathcal ab and mathcal cb f omega respectively we will establish higher schur weyl duality between cyclotomic nazarov wenzl algebras and parabolic bgg categories mathcal o associated to symplectic and orthogonal lie algebras over the complex field mathbb c this enables us to use standard arguments in anderson et al in pac j math 292 1 21 59 2018 rui and song in math zeit 280 3 4 669 689 2015 rui and song in j algebra 444 246 271 2015 to compute decomposition matrices of cyclotomic nazarov wenzl algebras the level two case was considered by ehrig and stroppel in adv math 331 58 142 2018

on finite sample properties of alternative estimators of coefficients in a structural equation with many instruments abstract we compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables as the classical methods we consider the limited information maximum likelihood liml estimator and the two stage least squares tsls estimator and as the semi parametric estimation methods we consider the maximum empirical likelihood mel estimator and the generalized method of moments gmm or the estimating equation estimator tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most linear models of interest and we include some heteroscedastic cases and nonlinear cases we have found that the liml estimator has good performance in terms of the bounded loss functions and probabilities when the number of instruments is large that is the micro econometric models with many instruments in the terminology of recent econometric literature

decomposition matrices of birman murakami wenzl algebras abstract in this paper we calculate decomposition matrices of the birman murakami wenzl algebras over c

t test in a structural equation properties of t ratios associated with the liml tsls and ols estimators in a structural form estimation are studied the existence of moments of these t ratios including the liml form is proved first second monte carlo simulations are performed to find out real sizes of the t test and the likelihood ratio test third asymptotic expansions of the distributions of t ratios are derived under the null hypothesis to find out deviations of real sizes from nominal sizes theoretically the asymptotic power functions are also derived

control variate method for stationary processes abstract the sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample however if some control variate is available it is known that the control variate method reduces the variance of the sample mean the control variate method often assumes that the variable of interest and the control variable are i i d here we assume that these variables are stationary processes with spectral density matrices i e dependent then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator it is shown that this estimator improves the sample mean in the sense of mean square error also this analysis is extended to the case when the mean dynamics is of the form of regression then we propose a control variate estimator for the regression coefficients which improves the least squares estimator lse numerical studies will be given to see how our estimator improves the lse

moment based estimation of smooth transition regression models with endogenous variables nonlinear regression models have been widely used in practice for a variety of time series and cross section datasets for purposes of analyzing univariate and multivariate time series data in particular smooth transition regression str models have been shown to be very useful for representing and capturing asymmetric behavior most str models have been applied to univariate processes and have made a variety of assumptions including stationary or cointegrated processes uncorrelated homoskedastic or conditionally heteroskedastic errors and weakly exogenous regressors under the assumption of exogeneity the standard method of estimation is nonlinear least squares the primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss moment based methods for estimating str models the paper analyzes the properties of the str model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity developing an estimation procedure and a misspecification test for the str model presenting the results of monte carlo simulations to show the usefulness of the model and estimation method and providing an empirical application for inflation rate targeting in brazil we show that str models with endogenous variables can be specified and estimated by a straightforward application of existing results in the literature

estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments abstract a well known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments in this paper we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability these unconditional moments depend on the instruments generated from a generically comprehensively revealing function and they are further projected along the exponential fourier series the objective function is based on the resulting fourier coefficients from which an estimator can be easily computed a novel feature of our method is that the full continuum of unconditional moments is incorporated into each fourier coefficient we show that when the number of fourier coefficients in the objective function grows at a proper rate the proposed estimator is consistent and asymptotically normally distributed an efficient estimator is also readily obtained via the conventional two step gmm method our simulations confirm that the proposed estimator compares favorably with that of dominguez and lobato 2004 econometrica in terms of bias standard error and mean squared error

problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak abstract we draw attention to two problems associated with the use of instrumental variables iv the importance of which for empirical work has not been fully appreciated first the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the iv estimates even if only a weak relationship exists between the instruments and the error in the structural equation second in finite samples iv estimates are biased in the same direction as ordinary least squares ols estimates the magnitude of the bias of iv estimates approaches that of ols estimates as the r 2 between the instruments and the endogenous explanatory variable approaches 0 to illustrate these problems we reexamine the results of a recent paper by angrist and krueger who used large samples from the u s census to estimate wage equations in which quarter of birth is used as an instrument for educational attainment we find evidence that despite huge sample sizes th

the second order bias and mean squared error of nonlinear estimators abstract despite the now widespread use of nonlinear estimators their finite sample properties have received very little attention in either the statistics or econometrics literature we partially redress this problem by deriving and examining the second order bias and mean squared error of a fairly wide class of nonlinear estimators which includes nonlinear least squares maximum likelihood and many generalized method of moments estimators as special cases a number of examples are provided the results from a monte carlo exercise demonstrate how the results can be applied for improved inferences

properties of the cue estimator and a modification with moments abstract in this paper we analyze properties of the continuous updating estimator cue proposed by hansen et al 1996 which has been suggested as a solution to the finite sample bias problems of the two step gmm estimator we show that the estimator should be expected to perform poorly in finite samples under weak identification in particular the estimator is not guaranteed to have finite moments of any order we propose the regularized cue rcue as a solution to this problem the rcue solves a modification of the first order conditions for the cue estimator and is shown to be asymptotically equivalent to cue under many weak moment asymptotics our theoretical findings are confirmed by extensive monte carlo studies

embedded minimal surfaces exotic spheres and manifolds with positive ricci curvature let n be a three dimensional riemannian manifold let e be a closed embedded surface in n then it is a question of basic interest to see whether one can deform in its isotopy class to some canonical embedded surface from the point of view of geometry a natural canonical surface will be the extremal surface of some functional defined on the space of embedded surfaces the simplest functional is the area functional the extremal surface of the area functional is called the minimal surface such minimal surfaces were used extensively by meeks yau my21 in studying group actions on three dimensional manifolds in my2 the theory of minimal surfaces was used to simplify and strengthen the classical dehn s lemma loop theorem and the sphere theorem in the setting there one minimizes area among all immersed surfaces and proves that the extremal object is embedded in this paper we minimize area among all embedded surfaces isotopic to a fixed embedded surface in the category of these surfaces we prove a general existence theorem theorem 1 a particular consequence of this theorem is that for irreducible manifolds an embedded incompressible surface is isotopic to an embedded incompressible surface with minimal area we also prove that there exists an embedded sphere of least area enclosing a fake cell provided the complementary volume is not a standard ball and provided there exists no embedded one sided rp2 by making use of the last result and a cutting and pasting argument we are able to settle a well known problem in the theory of three dimensional manifolds we prove that the covering space of any irreducible orientable three dimensional manifold is irreducible it is possible to exploit our existence theorem to study

information and entropy econometrics editor s view amos golan department of economics american university roper 200 4400 massachusetts ave nw washington dc 20016 usa

instrumental variable estimation in the presence of many moment conditions abstract this paper develops shrinkage methods for addressing the many instruments problem in the context of instrumental variable estimation it has been observed that instrumental variable estimators may behave poorly if the number of instruments is large this problem can be addressed by shrinking the influence of a subset of instrumental variables the procedure can be understood as a two step process of shrinking some of the ols coefficient estimates from the regression of the endogenous variables on the instruments then using the predicted values of the endogenous variables based on the shrunk coefficient estimates as the instruments the shrinkage parameter is chosen to minimize the asymptotic mean square error the optimal shrinkage parameter has a closed form which makes it easy to implement a monte carlo study shows that the shrinkage method works well and performs better in many situations than do existing instrument selection procedures

modified three stage least squares estimator which is third order efficient abstract a modified three stage least squares 3sls estimator is proposed which shares the same asymptotic expansion of the distribution as the fiml estimator to terms of order o 1 t therefore this modified 3sls estimator is third order efficient this estimator includes a modified 2sls estimator and a modified sur estimator as specific cases

thick ideals in deligne s category re_p oδ abstract we describe indecomposable objects in deligne s category re p o and explain how to decompose their tensor products we then classify thick ideals in re p o as an application we classify the indecomposable summands of tensor powers of the standard representation of the orthosymplectic supergroup up to isomorphism

method of moments estimation and identifiability of semiparametric nonlinear errors in variables models abstract this paper deals with a nonlinear errors in variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric using the instrumental variable approach we propose method of moments estimators for the unknown parameters and simulation based estimators to overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals both estimators are consistent and asymptotically normally distributed under fairly general regularity conditions moreover root n consistent semiparametric estimators and a rank condition for model identifiability are derived using the combined methods of the nonparametric technique and fourier deconvolution

the strong halfspace theorem for minimal surfaces d hoffman and w h meeks iii department of mathematics university of massachusetts amherst ma 01003 usa in 6 jorge and xavier constructed examples of complete nonplanar minimal surfaces contained between two parallel planes in 3 recently rosenberg and toubiana have found complete minimally immersed annuli that are proper in an open slab 1 12 on the basis of these and other results the question has arisen as to whether or not there could exist a properly immersed minimal surface in 3 that was contained between two parallel planes the answer is negative an immediate consequence of the following theorem

a consistent nonparametric test for nonlinear causality specification in time series regression abstract since the pioneering work by granger 1969 many authors have proposed tests of causality between economic time series most of them are concerned only with linear causality in mean or if a series linearly affects the conditional mean of the other series it is no doubt of primary interest but dependence between series may be nonlinear and or not only through the conditional mean indeed conditional heteroskedastic models are widely studied recently the purpose of this paper is to propose a nonparametric test for possibly nonlinear causality taking into account that dependence in higher order moments are becoming an important issue especially in financial time series we also consider a test for causality up to the k th conditional moment statistically we can also view this test as a nonparametric omitted variable test in time series regression a desirable property of the test is that it has nontrivial power against t 1 2 local alternatives where t is the sample size also we can form a test statistic accordingly if we have some knowledge on the alternative hypothesis furthermore we show that the test statistic includes most of the omitted variable test statistics as special cases asymptotically the null asymptotic distribution is not normal but we can easily calculate the critical regions by simulation monte carlo experiments show that the proposed test has good size and power properties

borelic pairs for stratified algebras abstract we determine all values of the parameters for which the cell modules form a standard system for a class of cellular diagram algebras including partition brauer walled brauer temperley lieb and jones algebras for this we develop and apply a general theory of finite dimensional algebras with borelic pairs the theory is also applied to give new uniform proofs of the cellular and quasi hereditary properties of the diagram algebras and to construct quasi hereditary 1 covers in the sense of rouquier with exact borel subalgebras in the sense of konig another application of the theory leads to a proof that auslander dlab ringel algebras admit exact borel subalgebras

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

representations of brauer category and categorification abstract we study representations of the locally unital and locally finite dimensional algebra b associated to the brauer category b 0 with defining parameter 0 over an algebraically closed field k with characteristic p 2 the grothendieck group k 0 b mod will be used to categorify the integrable highest weight sl k module v 0 1 2 with the fundamental weight 0 1 2 as its highest weight where b mod is a subcategory of b lfdmod in which each object has a finite flag and sl k is either sl or sl p depending on whether p 0 or 2 p as g modules c z k 0 b mod is isomorphic to v 0 1 2 where g is a lie subalgebra of sl k see definition 4 2 when p 0 standard b modules and projective covers of simple b modules correspond to monomial basis and so called quasi canonical basis of v 0 1 2 respectively

diagrammatic kazhdan lusztig theory for the walled brauer algebra we determine the decomposition numbers for the brauer and walled brauer algebras in characteristic zero in terms of certain polynomials associated to cap and curl diagrams recovering a result of martin in the brauer case we consider a second family of polynomials associated to such diagrams and use these to determine projective resolutions of the standard modules we then relate these two families of polynomials to kazhdan lusztig theory via the work of lascoux schutzenberger and boe inspired by work of brundan and stroppel in the cap diagram case

a regularization approach to the many instruments problem abstract this paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite in order to improve the small sample properties of standard instrumental variable iv estimators we propose three modified iv estimators based on three different ways of inverting the covariance matrix of the instruments these inverses involve a regularization or smoothing parameter it should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation we show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound higher order analysis of the mse reveals that the bias of the modified estimators does not depend on the number of instruments finally we suggest a data driven method for selecting the regularization parameter interestingly our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument

combining minimax shrinkage estimators abstract when one estimates a multivariate normal mean the use of stein estimation entails both the grouping of coordinates and the selection of a set of targets toward which to shrink each group in this article we propose new minimax multiple shrinkage estimators that allow for multiple specifications of these aspects we provide examples that are evaluated on real and simulated data including an estimator that adaptively resolves the issue of combining possibly related estimation problems and an adaptive clustering shrinkage estimator the construction and properties of these estimators are shown to follow from the application of the multiple shrinkage results of george 1986a to general partitioned shrinkage estimators

moment restriction based econometric methods an overview the 2011 special issue of the journal of econometrics discusses papers based on moment restriction based econometric methods in the first paper peter robinson of london school of economics considers asymptotic theory for nonparametric regression with spatial data specifically nonparametric regression with spatial or spatio temporal data the author discusses application of the established conditions to spatial autoregressive models and models defined on a regular lattice liqun wang and cheng hsiao consider method of moments estimation and identifiability of semiparametric nonlinear errors in variables models their paper deals with a nonlinear errors in variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric shih hsun hsu and chung ming kuan examine estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments

the stochastic difference between econometric statistics dans un contexte general et dans divers cas particuliers on calcule l ordre en probabilite de la difference entre des racines consistantes d equations d estimation rivales

tests of specification for parametric and semiparametric models abstract this paper provides a general framework for constructing specification tests for parametric and semiparametric models the paper develops new specification tests using the general framework in particular specification tests for semiparametric partially linear regression and sample selection models are introduced the results apply in time series and cross sectional contexts the method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes

linear programming based estimators in simple linear regression in this paper we introduce a linear programming estimator lpe for the slope parameter in a constrained linear regression model with a single regressor the lpe is interesting because it can be superconsistent in the presence of an endogenous regressor and hence preferable to the ordinary least squares estimator lse two different cases are considered as we investigate the statistical properties of the lpe in the first case the regressor is assumed to be fixed in repeated samples in the second the regressor is stochastic and potentially endogenous for both cases the strong consistency and exact finite sample distribution of the lpe is established conditions under which the lpe is consistent in the presence of serially correlated heteroskedastic errors are also given finally we describe how the lpe can be extended to the case with multiple regressors and conjecture that the extended estimator is consistent under conditions analogous to the ones given herein finite sample properties of the lpe and extended lpe in comparison to the lse and instrumental variable estimator ive are investigated in a simulation study one advantage of the lpe is that it does not require an instrument

an unknotting result for complete minimal surfaces r3 in this note we prove theorem if s is a complete properly embedded minimal surface in r 3 with the euclidean metric and if a is a closed connected complementary domain of z then either a is metrically r 2 0 hi or up to diffeomorphism a is made from a countable or finite collection of building blocks by attaching a proper collection of closed 1 handles each building blocks is a closed 3 ball or an open annulus x 0 1 the first theorem of this kind was b lawson s i l unknottedness theorem for minimal surfaces in s 3 that result was obtained by considering the second variation of arc length because the flat euclidean metric of r 3 does not contribute a favorable curvature term as found in s 3 a dual approach employing stable minimal surfaces dual to lawson s spanning arcs is required the key technical result proved by an analysis of the second variation operator on surfaces is that geometric planes are the only stable minimal surfaces in r 3 c p and f c s from this starting point a more topological theory has been developed by frohman hoffman meeks yau and others our argument is based to a large degree on the methods used by c frohman and w meeks f m to classify 1 ended proper complete minimal imbeddings in r 3 we present four succinct topological assertions about any 3 manifold with boundary a s which is a connected closed complementary region of a complete proper minimal surface in r 3 these statements should be thought of as axioms for this emerging theory deduced from geometry they help to mark the boundary with topology the theorem follows quickly from the axioms axiom 1 occurs explicitly as corollary 3 2 i f m axiom 2 is an immediate consequence of the methods of f m and axiom 3 is proved by an extension of these methods axiom 4 is related to an idea on the ordering of ends m y due to w meeks and s t yau these are the axioms their verification actually only requires that the mean curvature vector of 2 be everywhere zero or pointing towards a

least area incompressible surfaces in 3 manifolds let m be a riemannian manifold and let f be a closed surface a map f f m is called least area if the area of f is less than the area of any homotopic map from f to m note that least area maps are always minimal surfaces but that in general minimal surfaces are not least area as they represent only local stationary points for the area function the existence of least area immersions in a homotopy class of maps has been established when the homotopy class satisfies certain injectivity conditions on the fundamental group 18 17 in this paper we shall consider the possible singularities of such immersions our results show that the general philosophy is that least area surfaces intersect least meaning that the intersections and self intersections of least area immersions are as small as their homotopy classes allow when measured correctly one should note that evidence supporting this view had been found by meeks yau in their embedding theorems for minimal disks and 2 spheres 13 143 our main result asserts that if a least area immersion is homotopic to an embedding then it has no self intersections which clearly exemplifies the above philosophy the precise result is the following

asymptotic theory for nonparametric regression with spatial data nonparametric regression with spatial or spatio temporal data is considered the conditional mean of a dependent variable given explanatory ones is a nonparametric function while the conditional covariance reflects spatial correlation conditional heteroscedasticity is also allowed as well as non identically distributed observations instead of mixing conditions a possibly non stationary linear process is assumed for disturbances allowing for long range as well as short range dependence while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities a basic triangular array setting is employed with the aim of covering various patterns of spatial observation sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates when the cross sectional dependence is sufficiently mild the asymptotic variance in the central limit theorem is the same as when observations are independent otherwise the rate of convergence is slower we discuss the application of our conditions to spatial autoregressive models and models defined on a regular lattice

on the asymptotic optimality of the liml estimator with possibly many instruments we consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables we derive some asymptotic properties of the limited information maximum likelihood liml estimator when the number of instruments is large some of these results are new as well as old and we relate them to results in some recent studies we have found that the variance of the limiting distribution of the liml estimator and its modifications often attain the asymptotic lower bound when the number of instruments is large and the disturbance terms are not necessarily normally distributed that is for the micro econometric models of some cases recently called many instruments and many weak instruments