on completeness and consistency in nonparametric instrumental variable models this paper provides positive testability results for the identification condition in a nonparametric instrumental variable model known as completeness and it links the outcome of the test to properties of an estimator of the structural function in particular i show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator this is the case for a large class of complete distributions as well as certain incomplete distributions as a byproduct the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself

complete metric approximation property for q araki woods algebras abstract by adapting an ultraproduct technique of junge and zeng we prove that radial completely bounded multipliers on q gaussian algebras transfer to q araki woods algebras as a consequence we establish the w complete metric approximation property for all q araki woods algebras we apply the latter result to show that the canonical ultraweakly dense c subalgebras of q araki woods algebras are always qwep

free products of compact quantum groups we construct and study compact quantum groups from free products ofc algebras in this connection we discover two mysterious classes of natural compact quantum groups a u m anda o m thea u m s respectivelya o m s are non isomorphic to each other for differentm s and are not obtainable by the ordinary quantization method we also clarify some basic concepts in the theory of compact quantum groups

on the testability of identification in some nonparametric models with endogeneity this paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity the first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions these conditions are typically referred to as completeness conditions the second and third hypothesis testing problems we examine concern testing for identification directly in some nonparametric models with endogeneity involving quantile independence restrictions for each of these hypothesis testing problems we provide conditions under which any test will have power no greater than size against any alternative in this sense we conclude that no nontrivial tests for these hypothesis testing problems exist publication abstract

quantum deformation of lorentz group a one parameter quantum deformations l 2 ofsl 2 is introduced and investigated an analog of the iwasawa decomposition is proved the compact part of this decomposition coincides withs u 2 whereas the solvable part is identified as a pontryagin dual ofs u 2 it shows thats l 2 is the result of the dual version of drinfeld s double group construction applied tos u 2 the same construction applied to any compact quantum groupgc is discussed in detail in particular the explicit formulae for the haar measures on the pontryagin dualgd ofgc and on the double groupg are given we show that there exists remarkable 1 1 correspondence between representations ofg and bicovariant bimodules tensor bundles overgc the theory of smooth representations ofs l 2 is the same as that ofsl 2 clebsh gordon coefficients are however modified the corresponding tame bicovariant bimodules ons u 2 are classified an application to 4d differential calculus is presented the nonsmooth case is also discussed

the free wreath product of a compact quantum group by a quantum automorphism group in this thesis we define and study the free wreath product of a compact quantum group by a quantum automorphism group and in this way we generalize the previous notion of free wreath product by the quantum symmetric group introduced by bichon our investigation is divided into two part in the first we define the free wreath product of a discrete group by a quantum automorphism group we show how to describe its intertwiners by making use of decorated noncrossing partitions and from this thanks to a result of lemeux we deduce the irreducible representations and the fusion rules then we prove some properties of the operator algebras associated to this compact quantum group such as the simplicity of the reduced c algebra and the haagerup property of the von neumann algebra the second part is a generalization of the first one we start by defining the notion of free wreath product of a compact quantum group by a quantum automorphism group we generalize the description of the spaces of the intertwiners obtained in the discrete case and by adapting a monoidal equivalence result of lemeux and tarrago we find the irreducible representations and the fusion rules then we prove some stability properties of the free wreath product operation in particular we find under which conditions two free wreath products are monoidally equivalent or have isomorphic fusion semirings we also establish some analytic and algebraic properties of the dual quantum group and of the operator algebras associated to a free wreath product as a last result we prove that the free wreath product of two quantum automorphism groups can be seen as the quotient of a suitable quantum automorphism group

drinfeld center and representation theory for monoidal categories motivated by the relation between the drinfeld double and central property t for quantum groups given a rigid c tensor category mathcal c and a unitary half braiding on an ind object we construct a representation of the fusion algebra of mathcal c this allows us to present an alternative approach to recent results of popa and vaes who defined c algebras of monoidal categories and introduced property t for them as an example we analyze categories mathcal c of hilbert bimodules over a ii1 factor we show that in this case the drinfeld center is monoidally equivalent to a category of hilbert bimodules over another ii1 factor obtained by the longo rehren construction as an application we obtain an alternative proof of the result of popa and vaes stating that property t for the category defined by an extremal finite index subfactor n subset m is equivalent to popa s property t for the corresponding se inclusion of ii1 factors in the last part of the paper we study muger s notion of weakly monoidally morita equivalent categories and analyze the behavior of our constructions under the equivalence of the corresponding drinfeld centers established by schauenburg in particular we prove that property t is invariant under weak monoidal morita equivalence

applied nonparametric instrumental variables estimation instrumental variables are widely used in applied econometrics to achieve identification and carry out estimation and inference in models that contain endogenous explanatory variables in most applications the function of interest e g an engel curve or demand function is assumed to be known up to finitely many parameters e g a linear model and instrumental variables are used identify and estimate these parameters however linear and other finite dimensional parametric models make strong assumptions about the population being modeled that are rarely if ever justified by economic theory or other a priori reasoning and can lead to seriously erroneous conclusions if they are incorrect this paper explores what can be learned when the function of interest is identified through an instrumental variable but is not assumed to be known up to finitely many parameters the paper explains the differences between parametric and nonparametric estimators that are important for applied research describes an easily implemented nonparametric instrumental variables estimator and presents empirical examples in which nonparametric methods lead to substantive conclusions that are quite different from those obtained using standard parametric estimators

ccap for universal discrete quantum groups we show that the discrete duals of the free orthogonal quantum groups have the haagerup property and the completely contractive approximation property analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite dimensional c algebras the proof relies on the monoidal equivalence between free orthogonal quantum groups and su q 2 quantum groups on the construction of a sufficient supply of bounded central functionals for su q 2 quantum groups and on the free product techniques of ricard and xu our results generalize previous work in the kac setting due to brannan on the haagerup property and due to the second author on the ccap

lacunary fourier series for compact quantum groups this paper is devoted to the study of sidon sets lambda p sets and some related notions for compact quantum groups we establish several different characterizations of sidon sets and in particular prove that any sidon set in a discrete group is a strong sidon set in the sense of picardello we give several relations between sidon sets lambda p sets and lacunarities for lp fourier multipliers generalizing a previous work by blendek and michalicek we also prove the existence of lambda p sets for orthogonal systems in noncommutative lp spaces and deduce the corresponding properties for compact quantum groups central sidon sets are also discussed and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central sidon sets several examples are also included

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

the boundary of universal discrete quantum groups exactness and factoriality we study the c algebras and von neumann algebras associated with the universal discrete quantum groups they give rise to full prime factors and simple exact c algebras the main tool in our work is the study of an amenable boundary action yielding the akemann ostrand property finally this boundary can be identified with the martin or the poisson boundary of a quantum random walk

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

quantum symmetry groups of finite spaces we determine the quantum automorphism groups of finite spaces these are compact matrix quantum groups in the sense of woronowicz

symmetries of levy processes on compact quantum groups their markov semigroups and potential theory quantum markov semigroups qms i e strongly continuous semigroups of unital completely positive maps on compact quantum groups are studied we show that translation invariant qmss on the universal or reduced c algebra of a compact quantum group are in one to one correspondence with levy processes on its hopf algebra we use the theory of levy processes on involutive bialgebras to characterize symmetry properties of the associated qms it turns out that the qms is self adjoint resp kms symmetric if and only if the generating functional of the levy process is invariant under the antipode resp the unitary antipode furthermore we study levy processes whose marginal states are invariant under the adjoint action finally some related aspects of the potential theory as dirichlet form derivation and spectral triple are investigated we discuss how the above results apply to compact groups group c algebras of discrete groups free orthogonal quantum groups on and twisted suq 2 quantum group

annular representation theory for rigid c tensor categories abstract we define annular algebras for rigid c tensor categories providing a unified framework for both ocneanu s tube algebra and jones affine annular category of a planar algebra we study the representation theory of annular algebras and show that all sufficiently large full annular algebras for a category are isomorphic after tensoring with the algebra of matrix units with countable index set hence have equivalent representation theories annular algebras admit a universal c algebra closure analogous to the universal c algebra for groups these algebras have interesting corner algebras indexed by some set of isomorphism classes of objects which we call centralizer algebras the centralizer algebra corresponding to the identity object is canonically isomorphic to the fusion algebra of the category and we show that the admissible representations of the fusion algebra of popa and vaes are precisely the restrictions of arbitrary non degenerate representations of full annular algebras this allows approximation and rigidity properties defined for categories by popa and vaes to be interpreted in the context of annular representation theory this perspective also allows us to define higher weight approximation properties based on other centralizer algebras of an annular algebra using the analysis of annular representations due to jones and reznikoff we identify all centralizer algebras for the tlj categories for 2

approximation properties and absence of cartan subalgebra for free araki woods factors abstract we show that all the free araki woods factors h r u t have the complete metric approximation property using ozawa popa s techniques we then prove that every nonamenable subfactor n h r u t which is the range of a normal conditional expectation has no cartan subalgebra we finally deduce that the type iii1 factors constructed by connes in the 70s can never be isomorphic to any free araki woods factor which answers a question of shlyakhtenko and vaes

positive solutions to the equations ax c and xb d for hilbert space operators abstract the paper studies the equation a x c for bounded linear operators between hilbert spaces gives conditions for the existence of hermitian solutions and positive solutions and obtains the formula for the general form of these solutions then the common hermitian and positive solutions to the equations a x c and x b d are studied and new representations of the general solutions are given many results for matrices are recovered as special cases and the results of phadke and thakare s v phadke n k thakare generalized inverses and operator equations linear algebra appl 23 1979 191 199 are corrected

unique cartan decomposition for ii1 factors arising from arbitrary actions of free groups we prove that for any free ergodic probability measure preserving action mathbb f n curvearrowright x mu of a free group on n generators mathbb f n 2 leq n leq infty the associated group measure space ii1 factor l infty x rtimes mathbb f n has l x as its unique cartan subalgebra up to unitary conjugacy we deduce that group measure space ii1 factors arising from actions of free groups with different number of generators are never isomorphic we actually prove unique cartan decomposition results for ii1 factors arising from arbitrary actions of a much larger family of groups including all free products of amenable groups and their direct products

the connes embedding property for quantum group von neumann algebras for a compact quantum group g of kac type we study the existence of a haar trace preserving embedding of the von neumann algebra l g into an ultrapower of the hyperfinite ii 1 factor the connes embedding property for l g we establish a connection between the connes embedding property for l g and the structure of certain quantum subgroups of g and use this to prove that the ii 1 factors l o n and l u n associated to the free orthogonal and free unitary quantum groups have the connes embedding property for all n 4 as an application we deduce that the free entropy dimension of the standard generators of l o n equals 1 for all n 4 we also mention an application of our work to the problem of classifying the quantum subgroups of o n

some incomplete but boundedly complete location families a general result concerning noncompleteness of location families of probability measures on euclidean space is pointed out examples include boundedly complete families such as those generated by certain scale mixtures of the standard gaussian distribution these examples illuminate completeness criteria for location families and compare favourably in simplicity with previously known examples of incomplete boundedly complete nonlocation families

examples of weakly amenable discrete quantum groups abstract we prove that the free orthogonal and free unitary quantum groups f o n and f u n are weakly amenable and that their cowling haagerup constant is equal to 1 this is achieved by estimating the completely bounded norm of the projections on the coefficients of irreducible representations of their compact duals an argument of monoidal equivalence then allows us to extend this result to quantum automorphism groups of finite spaces and even yields some examples of weakly amenable non unimodular discrete quantum groups with the haagerup property

uniform confidence bands for functions estimated nonparametrically with instrumental variables abstract this paper is concerned with developing uniform confidence bands for functions estimated nonparametrically with instrumental variables we show that a sieve nonparametric instrumental variables estimator is pointwise asymptotically normally distributed the asymptotic normality result holds in both mildly and severely ill posed cases we present methods to obtain a uniform confidence band and show that the bootstrap can be used to obtain the required critical values monte carlo experiments illustrate the finite sample performance of the uniform confidence band

sieve wald and qlr inferences on semi nonparametric conditional moment models this paper considers inference on functionals of semi nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals which include all of the nonlinear nonparametric instrumental variables iv as special cases these models are often ill posed and hence it is difficult to verify whether a possibly nonlinear functional is root n estimable or not we provide computationally simple unified inference procedures that are asymptotically valid regardless of whether a functional is root n estimable or not we establish the following new useful results 1 the asymptotic normality of a plug in penalized sieve minimum distance psmd estimator of a possibly nonlinear functional 2 the consistency of simple sieve variance estimators for the plug in psmd estimator and hence the asymptotic chi square distribution of the sieve wald statistic 3 the asymptotic chi square distribution of an optimally weighted sieve quasi likelihood ratio qlr test under the null hypothesis 4 the asymptotic tight distribution of a non optimally weighted sieve qlr statistic under the null 5 the consistency of generalized residual bootstrap sieve wald and qlr tests 6 local power properties of sieve wald and qlr tests and of their bootstrap versions 7 asymptotic properties of sieve wald and sqlr for functionals of increasing dimension simulation studies and an empirical illustration of a nonparametric quantile iv regression are presented

amenability and co amenability of algebraic quantum groups ii abstract we continue our study of the concepts of amenability and co amenability for algebraic quantum groups in the sense of a van daele and our investigation of their relationship with nuclearity and injectivity one major tool for our analysis is that every non degenerate representation of the universal c algebra associated to an algebraic quantum group has a unitary generator which may be described in a concrete way

an analytic family of uniformly bounded representations of free groups harmonic analysis on a free group f has attracted considerable attention in the last ten years or so there seem to be two reason for that one is the discovery of deep analogy of certain aspects of harmonic analysis on a free group and harmonic analysis on sl 2 r cf e g fundamental works of p cartier 4 a figa talamanca and m a picardello 8 the other being the interest in the c algebra generated by the regular representation of f cf a connes 5 j cuntz 6 u haagerup 10 m pimsner and d voiculescu 14

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

the baum connes conjecture for free orthogonal quantum groups we prove an analogue of the baum connes conjecture for free orthogonal quantum groups more precisely we show that these quantum groups have a element and that 1 it follows that free orthogonal quantum groups are k amenable we compute explicitly their k theory and deduce in the unimodular case that the corresponding reduced c algebras do not contain nontrivial idempotents our approach is based on the reformulation of the baum connes conjecture by meyer and nest using the language of triangulated categories an important ingredient is the theory of monoidal equivalence of compact quantum groups developed by bichon de rijdt and vaes this allows us to study the problem in terms of the quantum group suq 2 the crucial part of the argument is a detailed analysis of the equivariant kasparov theory of the standard podle

inference in nonparametric instrumental variables with partial identification this paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework we construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction the same test statistic can be employed under identification in which case the hypothesis is whether the true model satisfies the posited property an almost sure consistent bootstrap procedure is provided for obtaining critical values possible applications include testing for semiparametric specifications as well as building confidence regions for certain functionals on the identified set as an illustration we obtain confidence intervals for the level and slope of brazilian fuel engel curves a monte carlo study examines finite sample performance

ergodic coactions with large multiplicity and monoidal equivalence of quantum groups we construct new examples of ergodic coactions of compact quantum groups in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter these examples are obtained using a bijective correspondence between certain ergodic coactions on c algebras and unitary fiber functors on the representation category of a compact quantum group we classify these unitary fiber functors on the universal orthogonal and unitary quantum groups the associated c algebras and von neumann algebras can be defined by generators and relations but are not yet well understood

semi nonparametric iv estimation of shape invariant engel curves this paper studies a shape invariant engel curve system with endogenous total expenditure in which the shape invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric engel curves we focus on the identification and estimation of both the nonparametric shapes of the engel curves and the parametric specification of the demographic scaling parameters the identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions allowing for endogeneity we establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support root n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of low level sufficient conditions our empirical application using the u k family expenditure survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of engel curves

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

irreducible unitary representations of quantum lorentz group a complete classification of irreducible unitary representations of a one parameter deformations q l 2 c 0 q 1 ofsl 2 c is given it shows that in spite of a popular belief the representation theory fors q l 2 c is not a smooth deformation of the one forsl 2 c

amenability of hopf von neumann algebras and kac algebras abstract let m be a hopf von neumann algebra the operator predualm ofmis a completely contractive banach algebra with multiplicationm m m m we call m operator amenableif the completely contractive banach algebram isoperator amenable i e for every operatorm bimodulev every completely bounded derivation fromm into the dualm bimodulev is inner there is a weaker notion of amenability introduced by d voiculescu we say that a hopf von neumann algebra m isvoiculescu amenableif there exists a left invariant mean onm we show that if a hopf von neumann algebra m is operator amenable then it is voiculescu amenable for kac algebras there is astrong voiculescu amenability we show that for discrete kac algebras these amenabilities are all equivalent in fact if we letk m be a discrete kac algebra and letk m be its compact dual kac algebra then the following are equivalent 1 kis operator amenable 2 kis voiculescu amenable 3 the von neumann algebramis hyperfinite 4 kis strong voiculescu amenable 5 kis operator amenable 6 m has a bounded approximate identity

an algebraic framework for group duality abstract a hopf algebra is a pair a whereais an associative algebra with identity and a homomorphism formatoa asatisfying certain conditions if we drop the assumption thatahas an identity and if we allow to have values in the so called multiplier algebram a a we get a natural extension of the notion of a hopf algebra we call this a multiplier hopf algebra the motivating example is the algebra of complex functions with finite support on a group with the comultiplication defined as dual to the product in the group also for these multiplier hopf algebras there is a natural notion of left and right invariance for linear functionals called integrals in hopf algebra theory we show that if such invariant functionals exist they are unique up to a scalar and faithful for a regular multiplier hopf algebra a i e with invertible antipode with invariant functionals we construct in a canonical way the dual it is again a regular multiplier hopf algebra with invariant functionals it is also shown that the dual of is canonically isomorphic with the original multiplier hopf algebra a it is possible to generalize many aspects of abstract harmonic analysis here one can define the fourier transform one can prove plancherel s formula because any finite dimensional hopf algebra is a regular multiplier hopf algebra and has invariant functionals our duality theorem applies to all finite dimensional hopf algebras then it coincides with the usual duality for such hopf algebras but our category of multiplier hopf algebras also includes in a certain way the discrete quantum groups and the compact quantum groups our duality includes the duality between discrete quantum groups and compact quantum groups in particular it includes the duality between compact abelian groups and discrete abelian groups one of the nice features of our theory is that we have an extension of this duality to the non abelian case but within one category this is shown in the last section of our paper where we introduce the algebras of compact type and the algebras of discrete type we prove that also these are dual to each other we treat an example that is sufficiently general to illustrate most of the different features of our theory it is also possible to construct the quantum double of drinfel d within this category this provides a still wider class of examples so we obtain many more than just the compact and discrete quantum within this setting

specification testing in nonparametric instrumental variable estimation abstract in nonparametric instrumental variable estimation the function being estimated is the solution to an integral equation a solution may not exist if for example the instrument is not valid this paper discusses the problem of testing the null hypothesis that a solution exists against the alternative that there is no solution we give necessary and sufficient conditions for existence of a solution and show that uniformly consistent testing of an unrestricted null hypothesis is not possible uniformly consistent testing is possible however if the null hypothesis is restricted by assuming that any solution to the integral equation is smooth many functions of interest in applied econometrics including demand functions and engel curves are expected to be smooth the paper presents a statistic for testing the null hypothesis that a smooth solution exists the test is consistent uniformly over a large class of probability distributions of the observable random variables for which the integral equation has no smooth solution the finite sample performance of the test is illustrated through monte carlo experiments

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

comparison of unitary duals of drinfeld doubles and complex semisimple lie groups we determine a substantial part of the unitary representation theory of the drinfeld double of a q deformation of a compact lie group in terms of the complexification of the compact lie group using this we show that the dual of every q deformation of a higher rank compact lie group has central property t we also determine the unitary dual of sl q n mathbb c

adaptive nonparametric instrumental variables estimation empirical choice of the regularization parameter abstract in nonparametric instrumental variables estimation the mapping that identifies the function of interest g is discontinuous and must be regularized to permit consistent estimation the optimal regularization parameter depends on population characteristics that are unknown in applications this paper presents a theoretically justified empirical method for choosing the regularization parameter in series estimation the method adapts to the unknown smoothness of g and other unknown functions the resulting estimator of g converges at least as fast as the optimal rate multiplied by log n 1 2 the asymptotic integrated mean square error aimse of the estimator is within a specified factor of the optimal aimse