identification of mixture models using support variations abstract we consider the issue of identifying nonparametrically continuous mixture models in these models all observed variables depend on a common and unobserved component but are mutually independent conditional on it such a structure applies for instance to measurement error matching and auction models traditional approaches rely on parametric assumptions or strong functional restrictions we show that these models are actually identified nonparametrically if the supports of the observed variables move with the value of the unobserved component moreover this assumption is testable nonparametrically using tools from extreme value theory we develop an appropriate test and derive its asymptotic properties

central invariants and higher indicators for semisimple quasi hopf algebras in this paper we define the higher frobenius schur fs indicators for finite dimensional modules of a semisimple quasi hopf algebra h via the categorical counterpart developed in a 2005 preprint when h is an ordinary hopf algebra we show that our definition coincides with that introduced by kashina sommerhauser and zhu we find a sequence of gauge invariant central elements of h such that the higher fs indicators of a module v are obtained by applying its character to these elements as an application we show that fs indicators are sufficient to distinguish the four gauge equivalence classes of semisimple quasi hopf algebras of dimension eight corresponding to the four fusion categories with certain fusion rules classified by tambara and yamagami three of these categories correspond to well known hopf algebras and we explicitly construct a quasi hopf algebra corresponding to the fourth one using the kac algebra we also derive explicit formulae for fs indicators for some quasi hopf algebras associated to group cocycles

a higher frobenius schur indicator formula for group theoretical fusion categories group theoretical fusion categories are defined by data concerning finite groups and their cohomology a finite group g endowed with a three cocycle and a subgroup h subset g endowed with a two cochain whose coboundary is the restriction of the objects of the category are g graded vector spaces with suitably twisted h actions the associativity of tensor products is controlled by simple objects are parametrized in terms of projective representations of finite groups namely of the stabilizers in h of right h cosets in g with respect to two cocycles defined by the initial data we derive and study general formulas that express the higher frobenius schur indicators of simple objects in a group theoretical fusion category in terms of the group theoretical and cohomological data defining the category and describing its simples

regressions with berkson errors in covariates a nonparametric approach this paper establishes that so called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with berkson type measurement error in the regressors an estimator is proposed and proven to be consistent its practical performance and feasibility are investigated via monte carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health these examples illustrate that berkson errors can clearly not be neglected in nonlinear regression models and that the proposed method represents an effective remedy

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

hopf bimodules coquasibialgebras and an exact sequence of kac abstract based on the ideas of tannaka krein reconstruction we present a categorical construction that assigns to any cleft hopf algebra inclusion k h a coquasibialgebra having k as a hopf subalgebra as a special case the construction gives an intrinsic connection between the bismash product k q and the double cross product q k constructed from the same combinatorial data a cocommutative coquasibialgebra is the same as a cocommutative bialgebra equipped with a sweedler three cocycle thus our construction assigns to every bicrossproduct or hopf algebra extension of a commutative and a cocommutative factor a corresponding cocommutative double crossproduct equipped with a sweedler three cocycle based on this observation we use the construction to prove generalizations of kac s exact sequence for the group of hopf algebra extensions of a group algebra by a dual group algebra

a sufficient condition for the existence of bound states for scalar spherically symmetric potentials we consider the class of three dimensional attractive finite range or similar potentials depending on a strength constant beyond a critical value the potential has at least one bound state for the s wave we propose simple bounds for obtained by formally solving the schrodinger equation for the zero energy bound state the various bounds are compared with the exact value for a set of usual potentials they are also compared with bounds derived in earlier works by glaser et al and by calogero we show that the case is solved by equations very similar to ones

on the estimation of the extreme value index and large quantile estimation l article se constitue de deux parties on donne une preuve simple de la convergence faible de l estimation de pickand pour le parametre principal d une loi de valeurs extremes on donne d autres conditions naturelles pour la convergence forte et pour la normalite asymptotique de l estimation ensuite une grande quantile d une loi est estimee par une combinaison de statistiques d ordre intermediaires ou extremes ceci mene a un intervalle de confiance asymptotique

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

critical behaviour of weakly bound systems we consider the class of three dimensional finite range or similar potentials depending on a strength constant we study the behaviour of the eigenvalue e as a function of where is the critical value at the transition from 0 1 bound state for the case we find whereas the relationship is linear for treating as a continuous parameter in the radial schrodinger equation we give the evolution of the power law between and besides spherically symmetric scalar potentials we also discuss the case of a repulsive scalar potential combined with a spin orbit component of the thomas form

non parametric estimation of finite mixtures from repeated measurements this paper provides methods to estimate finite mixtures from data with repeated measurements non parametrically we present a constructive identification argument and use it to develop simple two step estimators of the component distributions and all their functionals we discuss a computationally efficient method for estimation and derive asymptotic theory simulation experiments suggest that our theory provides confidence intervals with good coverage in small samples

injectivity of a class of integral operators with compactly supported kernels abstract injectivity of integral operators is related to completeness conditions of their corresponding kernel functions completeness provides a useful way of obtaining nonparametric identification in various models including nonparametric regression models with instrumental variables nonclassical measurement error models and auction models etc however the condition is quite abstract for empirical work and lacks a proper economic interpretation we rely on known results regarding the volterra equation to provide sufficient conditions for completeness conditions for densities with compact support our conditions include various smoothness assumptions and monotonously moving support assumptions on the kernel function of the operator we apply our results to establish nonparametric identification in nonparametric iv regression models nonclassical measurement error models and auction models with an accessible interpretation and without specific functional form restrictions

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

weakly bound states in dimensions we study the critical behaviour near the threshold where a first bound state appears at some value of coupling constant in an attractive short range potential in dimensions we obtain a general expression for the binding energy near the threshold and also demonstrate that the critical region is correctly described by an effective separable potential the critical exponent of the radius of weakly the bound state is shown to coincide with the correlation length exponent for the spin model in the large n limit in two dimensions where the binding energy is exponentially small in coupling constant we obtain a general analytic expression for the prefactor

central invariants and frobenius schur indicators for semisimple quasi hopf algebras abstract in this paper we obtain a canonical central element h for each semi simple quasi hopf algebra h over any field k and prove that h is invariant under gauge transformations we show that if k is algebraically closed of characteristic zero then for any irreducible representation of h which affords the character h takes only the values 0 1 or 1 moreover if h is a hopf algebra or a twisted quantum double of a finite group then h is the corresponding frobenius schur indicator we also prove an analog of a theorem of larson radford for split semi simple quasi hopf algebras over any field k using this result we establish the relationship between the antipode s the values of h and certain associated bilinear forms when the underlying field k is algebraically closed of characteristic zero

nonparametric inference in multivariate mixtures summary we consider mixture models in which the components of data vectors from any given subpopulation are statistically independent or independent in blocks we argue that if under this condition of independence we take a nonparametric view of the problem and allow the number of subpopulations to be quite general the distributions and mixing proportions can often be estimated root n consistently indeed we show that if the data are k variate and there are p subpopulations then for each p 2 there is a minimal value of k kp say such that the mixture problem is always nonparametrically identifiable and all distributions and mixture proportions are nonparametrically identifiable when k kp we treat the case p 2 in detail and there we show how to construct explicit distribution density and mixture proportion estimators converging at conventional rates other values of p can be addressed using a similar approach although the methodology becomes rapidly more complex as p increases

identifiability of parameters in latent structure models with many observed variables while hidden class models of various types arise in many statistical applications it is often difficult to establish the identifiability of their parameters focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones we demonstrate a general approach for establishing identifiability utilizing algebraic arguments a theorem of j kruskal for a simple latent class model with finite state space lies at the core of our results though we apply it to a diverse set of models these include mixtures of both finite and nonparametric product distributions hidden markov models and random graph mixture models and lead to a number of new results and improvements to old ones in the parametric setting this approach indicates that for such models the classical definition of identifiability is typically too strong instead generic identifiability holds which implies that the set of nonidentifiable parameters has measure zero so that parameter inference is still meaningful in particular this sheds light on the properties of finite mixtures of bernoulli products which have been used for decades despite being known to have nonidentifiable parameters in the nonparametric setting we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed but we explicitly describe the conditions

on fusion categories using a variety of methods developed in the literature in particular the theory of weak hopf algebras we prove a number of general results about fusion categories in characteristic zero we show that the global dimension of a fusion category is always positive and that the s matrix of any not necessarily hermitian modular category is unitary we also show that the category of module functors between two module categories over a fusion category is semisimple and that fusion categories and tensor functors between them are undeformable generalized ocneanu rigidity in particular the number of such categories functors realizing a given fusion datum is finite finally we develop the theory of frobenius perron dimensions in an arbitrary fusion category at the end of the paper we generalize some of these results to positive characteristic

the local nature of hypothesis tests involving inequality constraints in nonlinear models this paper derives several properties unique to nonlinear model hypothesis testing problems involving linear or nonlinear inequality constraints in the null or alternative hypothesis the paper is organized around a lemma which characterizes the set containing the least favorable parameter value for a nonlinear model inequality constraints hypothesis test we then present two examples which illustrate several implications of this lemma we also discuss the impact of these properties on the empirical implementation and interpretation of these test procedures

on the gauge equivalence of twisted quantum doubles of elementary abelian and extra special 2 groups abstract we establish braided tensor equivalences among module categories over the twisted quantum double of a finite group defined by an extension of a group g by an abelian group with 3 cocycle inflated from a 3 cocycle on g we also prove that the canonical ribbon structure of the module category of any twisted quantum double of a finite group is preserved by braided tensor equivalences we give two main applications first if g is an extra special 2 group of width at least 2 we show that the quantum double of g twisted by a 3 cocycle is gauge equivalent to a twisted quantum double of an elementary abelian 2 group if and only if 2 is trivial second we discuss the gauge equivalence classes of twisted quantum doubles of groups of order 8 and classify the braided tensor equivalence classes of these quasi triangular quasi bialgebras it turns out that there are exactly 20 such equivalence classes

robust and consistent estimation of nonlinear errors in variables models this paper considers the consistent estimation of nonlinear errors in variables models it adopts the functional modeling approach by assuming that the true but unobserved regressors are random variables but making no parametric assumption on the distribution from which the latent variables are drawn this paper shows how the information extracted from the replicate measurements can be used to identify and consistently estimate a general nonlinear errors in variables model the identification is established through characteristic functions the estimation procedure involves nonparametric estimation of the conditional density of the latent variables given the measurements using the identification results at the first stage and at the second stage a semiparametric nonlinear least squares estimator is proposed the consistency of the proposed estimator is also established finite sample performance of the estimator is investigated through a monte carlo study

nonparametric identification of finite mixture models of dynamic discrete choices in dynamic discrete choice analysis controlling for unobserved heterogeneity is an important issue and finite mixture models provide flexible ways to account for it this paper studies nonparametric identifiability of type probabilities and type specific component distributions in finite mixture models of dynamic discrete choices we derive sucient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under dierent assumptions on the markov property stationarity and type invariance in the transition process three elements emerge as the important determinants of identification the time dimension of panel data the number of values the covariates can take and the heterogeneity of the response of dierent types to changes in the co

hopf modules and the double of a quasi hopf algebra we give a different proof for a structure theorem of hausser and nill on hopf modules over quasi hopf algebras we extend the structure theorem to a classification of two sided two cosided hopf modules by yetter drinfeld modules which can be defined in two rather different manners for the quasi hopf case the category equivalence between hopf modules and yetter drinfeld modules leads to a new construction of the drinfeld double of a quasi hopf algebra as proposed by majid and constructed by hausser and nill

doubles of quasi quantum groups in dr1 drinfeld showed that any finite dimensional hopf algebra extends to a quasitriangular hopf algebra the quantum double of based on the construction of a so called diagonal crossed product developed by the authors in hn we generalize this result to the case of quasi hopf algebras as for ordinary hopf algebras as a vector space the quasi quantum double is isomorphic to where denotes the dual of we give explicit formulas for the product the coproduct the r matrix and the antipode on and prove that they fulfill drinfeld s axioms of a quasitriangular quasi hopf algebra in particular becomes an associative algebra containing as a quasi hopf subalgebra on the other hand is not a subalgebra of unless the coproduct on is strictly coassociative it is shown that the category of finite dimensional representations of coincides with what has been called the double category of modules by s majid m2 thus our construction gives a concrete realization of majid s abstract definition of quasi quantum doubles in terms of a tannaka krein like reconstruction procedure the whole construction is shown to generalize to weak quasi hopf algebras with now being linearly isomorphic to a subspace of

estimation of nonlinear models with measurement error this paper presents a solution to an important econometric problem namely the root n consistent estimation of nonlinear models with measurement errors in the explanatory variables when one repeated observation of each mismeasured regressor is available while a root n consistent estimator has been derived for polynomial specifications see hausman ichimura newey and powell 1991 such an estimator for general nonlinear specifications has so far not been available using the additional information provided by the repeated observation the suggested estimator separates the measurement error from the true value of the regressors thanks to a useful property of the fourier transform the fourier transform converts the integral equations that relate the distribution of the unobserved true variables to the observed variables measured with error into algebraic equations the solution to these equations yields enough information to identify arbitrary moments of the true unobserved variables the value of these moments can then be used to construct any estimator that can be written in terms of moments including traditional linear and nonlinear least squares estimators or general extremum estimators the proposed estimator is shown to admit a representation in terms of an influence function thus establishing its root n consistency and asymptotic normality monte carlo evidence and an application to engel curve estimation illustrate the usefulness of this new approach

frobenius schur indicators and exponents of spherical categories we obtain two formulae for the higher frobenius schur indicators one for a spherical fusion category in terms of the twist of its center and the other one for a modular tensor category in terms of its twist the first one is a categorical generalization of an analogous result by kashina sommerhauser and zhu for hopf algebras and the second one extends bantay s 2nd indicator formula for a conformal field theory to higher degrees these formulae imply the sequence of higher indicators of an object in these categories is periodic we define the notion of frobenius schur fs exponent of a pivotal category to be the global period of all these sequences of higher indicators and we prove that the fs exponent of a spherical fusion category is equal to the order of the twist of its center consequently the fs exponent of a spherical fusion category is a multiple of its exponent in the sense of etingof by a factor not greater than 2 as applications of these results we prove that the exponent and the dimension of a semisimple quasi hopf algebra h have the same prime divisors which answers two questions of etingof and gelaki affirmatively for quasi hopf algebras moreover we prove that the fs exponent of h divides dim h 4 in addition if h is a group theoretic quasi hopf algebra the fs exponent of h divides dim h 2 and this upper bound is shown to be tight

nonparametric identification of a binary random factor in cross section data suppose v and u are two independent mean zero random variables where v has an asymmetric distribution with two mass points and u has a symmetric distribution we show that the distributions of v and u are nonparametrically identifled just from observing the sum v u and provide a rate root n estimator we apply these results to the world income distribution to measure the extent of convergence over time where the values v can take on correspond to country types i e wealthy versus poor countries we also extend our results to include covariates x showing that we can nonparametrically identify and estimate cross section regression models of the form y g x d u where d is an unobserved

bertlmann martin inequality for a weakly bound particle the bertlmann martin bm inequality for the rms radius is checked against the exact value in the case of a particle in a weak central potential having a single bound state a number of usual potentials are considered in one and three dimensions the bm inequality is poorly saturated but the correction factor needed to recover the exact rms radius is weakly depending on the shape of the potential except for the hulth n potential for potentials having a hard core component we found that which depends on the bound state energy tends to a universal curve as the hard core radius increases

identification and estimation of nonlinear models with misclassification error using instrumental variables a general solution abstract this paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables the misclassification error is allowed to be correlated with all the explanatory variables in the model it is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns such a claim requires solving a complicated nonlinear system of equations this paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system the solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions therefore the latent model is nonparametrically identifiable and directly estimable using instrumental variables the results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities an alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting the nonparametric identification in this paper directly leads to a n consistent semiparametric estimator the monte carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data

identification and estimation of polynomial errors in variables models abstract methods of estimation of regression coefficients are proposed when the regression function includes a polynomial in a true regressor which is measured with error two sources of additional information concerning the unobservable regressor are considered either an additional indicator of the regressor itself measured with error or instrumental variables which characterize the systematic variation in the true regressor in both cases estimators are constructed by relating moments involving the unobserved variables to moments of observables these relations lead to recursion formulae for computation of the regression coefficients and nuisance parameters e g moments of the measurement error consistency and asymptotic normality of the estimated coefficients is demonstrated and consistent estimators of the asymptotic covariant matrices are provided

s4 symmetry of 6j symbols and frobenius schur indicators in rigid monoidal c categories we show that a left rigid monoidal c category with irreducible monoidal unit is also a sovereign and spherical category defining a frobenius schur type indicator we obtain selection rules for the fusion coefficients of irreducible objects as a main result we prove s4 invariance of 6j symbols in such a category