isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

improving the performance of random coefficients demand models the role of optimal instruments abstract we shed new light on the performance of berry levinsohn and pakes 1995 gmm estimator of the aggregate random coefficient logit model based on an extensive monte carlo study we show that the use of chamberlain s 1987 optimal instruments overcomes many problems that have recently been documented with standard non optimal instruments optimal instruments reduce small sample bias but they prove even more powerful in increasing the estimator s efficiency and stability we consider a wide variety of data generating processes and an empirical application to the automobile market we also consider the gains of other recent methodological advances when combined with optimal instruments

efficient high dimensional importance sampling the paper describes a simple generic and yet highly accurate efficient importance sampling eis monte carlo mc procedure for the evaluation of high dimensional numerical integrals eis is based upon a sequence of auxiliary weighted regressions which actually are linear under appropriate conditions it can be used to evaluate likelihood functions and byproducts thereof such as ml estimators for models which depend upon unobservable variables a dynamic stochastic volatility model and a logit panel data model with unobserved heterogeneity random effects in both dimensions are used to provide illustrations of eis high numerical accuracy even under small number of mc draws mc simulations are used to characterize the finite sample numerical and statistical properties of eis based ml estimators

complements to models for noncommuting operators abstract this paper develops a dilation theory for two noncommutative operators many of the results and techniques in dilation theory for one operator are extended to this setting this is done by extending the schaffer construction for one operator to the fock space setting a new wold decomposition for two isometrics with orthogonal range is obtained this wold decomposition and the schaffer construction is used to extend the sz nagy foias lifting theorem and the characteristic function theory to the noncommutative setting the characteristic function is operator valued and defined in a fock space

an exact likelihood analysis of the multinomial probit model abstract we develop new methods for conducting a finite sample likelihood based analysis of the multinomial probit model using a variant of the gibbs sampler an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors this approach avoids direct evaluation of the likelihood and thus avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches both simulated and actual consumer panel data are used to fit six dimensional choice models we also develop methods for analyzing random coefficient and multiperiod probit models

injective hulls of simple modules over finite dimensional nilpotent complex lie superalgebras abstract we show that the finite dimensional nilpotent complex lie superalgebras g whose injective hulls of simple u g modules are locally artinian are precisely those whose even part g 0 is isomorphic to a nilpotent lie algebra with an abelian ideal of codimension 1 or to a direct product of an abelian lie algebra and a certain 5 dimensional or a certain 6 dimensional nilpotent lie algebra

an efficient decomposition of the expectation of the maximum for the multivariate normal and related distributions abstract in structural dynamic discrete choice models monte carlo integration has been the only way to evaluate the expectation of the maximum when errors are normally distributed in this paper however i show that the expectation of the maximum can be decomposed as a linear combination of multivariate normal cdfs for related distributions such as the multivariate t distribution this expectation has a similar decomposition my computational results show speed benefits of my proposed method for models with a low number of choices although the speed gains are contingent on the use of analytical derivatives as opposed to numerical derivatives

a computationally efficient quadrature procedure for the one factor multinomial probit model a problem of estimation that has long confronted many economists is the difficulty of estimating the parameters of equations with limited dependent variables on cross section time series i e panel data while there are widely available packaged computer programs for estimating either a cross section probit and tobit models or b simple permanent transitory random effects panel models with continuous dependent variables there are no available computationally feasible methods of combining these two models this is because the likelihood function that arises in such a combined model contains multivariate normal integrals whose evaluation is quite difficult if not impossible with conventional approximation methods there is a widespread feeling among those working in the area that one possible method of evaluation the use of quadrature techniques is in principle possible but is in practice computationally too burdensome to consider e g albright et al 2 p 13 hausman and wise 6 p 12 in this note we point out that this is true only of standard quadrature techniques such as trapezoidal integration or its improved variants gaussian quadrature on the other hand is extremely efficient and is well within the bounds of computational feasibility on modern computers in what follows we state the nature of the integrals that need to be evaluated provide a brief exposition of gaussian quadrature and provide a numerical illustration of its use in

sparse grid quadrature nonlinear filtering in this paper a novel nonlinear filter named sparse grid quadrature filter sgqf is proposed the filter utilizes weighted sparse grid quadrature points to approximate the multi dimensional integrals in the nonlinear bayesian estimation algorithm the locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method then the univariate quadrature point sets are extended to form a multi dimensional grid using the sparse grid theory compared with the conventional point based methods the estimation accuracy level of the sgqf can be flexibly controlled and the number of sparse grid quadrature points for the sgqf is a polynomial of the dimension of the system which alleviates the curse of dimensionality for high dimensional problems the unscented kalman filter ukf is proven to be a subset of the sgqf at the level 2 accuracy the performance of this filter is demonstrated by an orbit estimation problem the simulation results show that the sgqf achieves higher accuracy than the extended kalman filter ekf the ukf and the cubature kalman filter ckf in addition the sgqf is computationally much more efficient than the multi dimensional gauss hermite quadrature filter ghqf with the same performance

meromorphic interpolation in several variables abstract we obtain a multivariable nudel man type interpolation theorem for meromorphic operators on fock spaces and for operator valued meromorphic functions on the open unit ball of c n n 1 as consequences we provide new caratheodory fejer nevanlinna pick type interpolation results and rosenblum rovnyak type restriction theorem for meromorphic operators in the particular case when n 1 our indefinite generalization of nudel man s theorem provides new interpolation results for meromorphic functions having a finite number of poles in the open unit disc

caratheodory interpolation on the non commutative polydisk the caratheodory problem in the n variable non commutative herglotz agler class and the caratheodory fejer problem in the n variable non commutative schur agler class are posed it is shown that the caratheodory resp caratheodory fejer problem has a solution if and only if the non commutative polynomial with given operator coefficients the data of the problem indexed by an admissible set takes operator values with positive semidefinite real part resp contractive operator values on n tuples of jointly nilpotent contractive n n matrices for all n n

the method of simulated scores for the estimation of ldv models the method of simulated scores mss is presented for estimating limited dependent variables models ldv with flexible correlation structure in the unobservables we propose simulators that are continuous in the unknown parameter vectors and hence standard optimization methods can be used to compute the mss estimators that employ these simulators the first continuous method relies on a recursive conditioning of the multivariate normal density through a cholesky triangularization of its variance covariance matrix the second method combines results about the conditionals of the multivariate normal distribution with gibbs resampling techniques we establish consistency and asymptotic normality of the mss estimators and derive suitable rates at which the number of simulations must rise if biased simulators are used

a decomposition strategy for the variational inference of complex systems markov chain monte carlo approaches have been widely used for bayesian inference the drawback of these methods is that they can be computationally prohibitive especially when complex models are analyzed in such cases variational methods may provide an efficient and attractive alternative however the variational methods reported to date are applicable to relatively simple models and most are based on a factorized approximation to the posterior distribution here we propose a variational approach that is capable of handling models that consist of a system of differential algebraic equations and whose posterior approximation can be represented by a multivariate distribution under the proposed approach the solution of the variational inference problem is decomposed into three steps a maximum a posteriori optimization which is facilitated by using an orthogonal collocation approach a preprocessing step which is based on the estimation of the eigenvectors of the posterior covariance matrix and an e

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

panel data analysis of household brand choices abstract the paper examines theoretical and empirical issues arising in panel data studies of household brand choices we develop a dynamic utility maximization model with habit formation that yields a discrete choice model that is linear in a vector of observable individual and brand characteristics the lagged choice an unobservable permanent individual brand specific effect and an unobservable time varying error component we estimate the model using panel data on household yogurt purchases we compare traditional estimation procedures with the method recently proposed by honore and kyriazidou panel data discrete choice models with lagged dependent variables econometrica 68 839 874 the methods robustness with respect to underlying assumptions is investigated in monte carlo simulations

using penalized likelihood to select parameters in a random coefficients multinomial logit model abstract this paper is about estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters some of which may be zero the paper gives conditions under which with probability approaching 1 as the sample size increases penalized maximum likelihood pml estimation with the adaptive lasso al penalty distinguishes correctly between zero and non zero parameters the paper also gives conditions under which pml reduces the asymptotic mean square estimation error of any continuously differentiable function of the model s parameters the paper describes a method for computing pml estimates and presents the results of monte carlo experiments that illustrate their performance it also presents the results of pml estimation of a random coefficients logit model of choice among brands of butter and margarine in the british groceries market

uncertainty quantification for a 1d thermo hyperelastic coupled problem using polynomial chaos projection and p fems numerical solutions of non linear stochastic thermo hyperelastic problems at finite strains are addressed these belong to a category of non linear coupled problems that impose challenges on their numerical treatment both in the physical and stochastic spaces combining the high order finite element methods fems for discretizing the physical space and the polynomial chaos projection pcp method for discretizing the stochastic space a non intrusive scheme is obtained manifesting an exponential convergence rate the method is applied to a 1 d coupled stationary thermo hyperelastic system with stochastic material properties we derive exact stochastic solutions that serve for comparison to numerical results allowing their verification these demonstrate that stochastic coupled problems intractable by standard monte carlo mc methods may be easily computed by combining high order fems with the pcp method controlling discretization errors

characteristic functions and joint invariant subspaces let t t1 tn be an n tuple of operators on a hilbert space such that t is a completely non coisometric row contraction we establish the existence of a one to one correspondence between the joint invariant subspaces under t1 tn and the regular factorizations of the characteristic function t associated with t in particular we prove that there is a non trivial joint invariant subspace under the operators t1 tn if and only if there is a non trivial regular factorization of t we also provide a functional model for the joint invariant subspaces in terms of the regular factorizations of the characteristic function and prove the existence of joint invariant subspaces for certain classes of n tuples of operators we obtain criteria for joint similarity of n tuples of operators to cuntz row isometries in particular we prove that a completely non coisometric row contraction t is jointly similar to a cuntz row isometry if and only if the characteristic function of t is an invertible multi analytic operator

a note on gauss hermite quadrature summary for gauss hermite quadrature we consider a systematic method for transforming the variable of integration so that the integrand is sampled in an appropriate region the effectiveness of the quadrature then depends on the ratio of the integrand to some gaussian density being a smooth function well approximated by a low order polynomial it is pointed out that in this approach order one gauss hermite quadrature becomes the laplace approximation thus the quadrature as implemented here can be thought of as a higher order laplace approximation

identification of discontinuous nonlinear systems via a multivariate pade approach we present a nonlinear system identification technique based on multi dimensional rational polynomials a multi dimensional pade legendre approximation is developed to circumvent challenges in dealing with sharp shocks the purpose of this paper is to investigate the accuracy of such approximations for identification of various nonlinear systems particularly systems with a non smooth response surface this identification approach utilizes the generalized form of a pade legendre approximation for studying multivariable functions in the studied problems the nonlinearity is a function of state variables displacement and velocity which requires multi dimensional formulation furthermore a spatial filter is applied to minimize the effects of the singular points in the applicable rational function of the response surface this study presents different types of nonlinearities including smooth irregular and hysteretic functions in order to demonstrate the performance of the approach under different conditions in order to study the robustness of the method in comparison to other identification techniques based on plain polynomial representation a nonlinear system with a sharp discontinuous restoring force surface is considered the performance of both approaches is investigated for different degrees of sharpness in addition the accuracy of the identified models to represent the nonlinear system is verified by comparing the output of the system computed on the basis of the identified model from data sets corresponding to different excitations than those used for identification purposes it is shown that the proposed approach provides a robust identification technique for a broad class of highly nonlinear systems and it is particularly advantageous to use when dealing with systems incorporating discontinuous properties

simulated latent variable estimation of models with ordered categorical data this paper addresses the problem that occurs when estimating a linear regression model in which some of the explanatory variables are represented by categorical indicators we replace the categorical variable with a simulated latent variable slv drawn from a truncated multivariate normal distribution using the gibbs sampler consistent and efficient parameter estimates are derived using generalized two stage least squares where the instrument set contains a second slv drawn from the same distribution consistent estimates of the parameter covariance matrix are derived using a two stage procedure we illustrate this methodology using a monte carlo simulation and also investigate the consequences of incorrect distributional assumptions the simulated latent variable procedure is shown to be superior to conventional methods involving dummy variables or conditional means

free pluriharmonic majorants and commutant lifting in this paper we initiate the study of sub pluriharmonic curves and free pluriharmonic majorants on the noncommutative open ball b h n 1 x1 xn b h n x1x1 xnxn 1 2 1 where b h is the algebra of all bounded linear operators on a hilbert space h several classical results from complex analysis have analogues in this noncommutative multivariable setting we present basic properties for sub pluriharmonic curves characterize the class of sub pluriharmonic curves that admit free pluriharmonic majorants and find in this case the least free pluriharmonic majorants we show that for any free holomorphic function on b h n 1 the map 0 1 c r1 rn r rr1 rrn rr1 rrn is a sub pluriharmonic curve in the cuntz toeplitz algebra generated by the right creation operators r1 rn on the full fock space with n generators we prove that is in the noncommutative hardy space hball2 if and only if has a free pluriharmonic majorant in this case we find herglotz riesz and poisson type representations for the least pluriharmonic majorant of moreover we obtain a characterization of the unit ball of hball2 and provide a parametrization and concrete representations for all free pluriharmonic majorants of when is in the unit ball of hball2 in the second part of this paper we introduce a generalized noncommutative commutant lifting gncl problem which extends to our noncommutative multivariable setting several lifting problems including the classical sz nagy foias commutant lifting problem and the extensions obtained by treil volberg foias frazho kaashoek and biswas foias frazho as well as their multivariable noncommutative versions we solve the gncl problem and using the results regarding sub pluriharmonic curves and free pluriharmonic majorants on noncommutative balls we provide a complete description of all solutions in particular we obtain a concrete schur type description of all solutions in the noncommutative commutant lifting theorem

free holomorphic functions and interpolation in this paper we obtain a noncommutative multivariable analogue of the classical nevanlinna pick interpolation problem for analytic functions with positive real parts on the open unit disc given a function f lambda to mathbb c where lambda is an arbitrary subset of the open unit ball mathbb b n z in mathbb c n z 1 we find necessary and sufficient conditions for the existence of a free holomorphic function g with complex coefficients on the noncommutative open unit ball b mathcal h n 1 such that rm re g geq 0 quad rm and quad g z f z quad z in lambda where b mathcal h is the algebra of all bounded linear operators on a hilbert space mathcal h the proof employs several results from noncommutative multivariable operator theory and a noncommutative cayley transform introduced and studied in the present paper acting from the set of all free holomorphic functions with positive real parts to the set of all bounded free holomorphic functions all the results of this paper are obtained in the more general setting of free holomorphic functions with operator valued coefficients as consequences we deduce some results concerning operator valued analytic interpolation on the unit ball mathbb b n

on fixed points of self maps of the free ball abstract in this paper we study the structure of the fixed point sets of noncommutative self maps of the free ball we show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear subspace we provide an application for the completely isometric isomorphism problem of multiplier algebras of noncommutative complete pick spaces

curvature invariant for hilbert modules over free semigroup algebras abstract we introduce a notion of relative curvature resp euler characteristic for finite rank contractive hilbert modules over c f n the complex free semigroup algebra generated by the free semigroup f n on n generators asymptotic formulas and basic properties for both the curvature and the euler characteristic are established in particular it is shown that the standard relative curvature invariant resp euler characteristic of a hilbert module h is a nonnegative number less than or equal to the rank of h and it depends only on the properties of the completely positive map t x ni 1 tixt i where t1 tn is the row contraction of not necessarily commuting operators uniquely determined by the c f n module structure of h moreover we prove that for every t 0 there is a hilbert module h such that curv h h t the module structure defined by the left creation operators on the full fock space f2 hn on n generators occupies the position of the rank one free module in the algebraic theory we obtain a complete description of the closed submodules resp quotients of the free hilbert module f2 hn and calculate their curvature invariant it is shown that the curvature is a complete invariant for the finite rank submodules of the free hilbert module f2 hn k where k is a finite dimensional hilbert space a noncommutative version of the gauss bonnet chern theorem from riemannian geometry is obtained for graded hilbert modules over c f n in particular it is proved that the curvature and euler characteristic coincide for certain classes of pure hilbert modules our investigation is based on noncommutative poisson transforms noncommutative dilation theory and harmonic analysis on fock spaces

simulated maximum likelihood estimation of dynamic discrete choice statistical models some monte carlo results this article reports monte carlo results on the simulated maximum likelihood estimation of discrete dynamic panel models introduced by james heckman 1981a the simulated maximum likelihood method is numerically stable even for long panels regression models and polya and renewal models can be better estimated than markov models with a moderate number of simulation draws most of these complex models can be adequately estimated for panels with length up to 30 polya and renewal models can be accurately estimated for panels up to 50 periods estimates of markov models can be sensitive to misspecified initial states but polya renewal and habit persistence models may not

endomorphisms of b h ii finitely correlated states on on we identify sets of conjugacy classes of ergodic endomorphisms of b h where h is a fixed separable hilbert space they correspond to certain equivalence classes of pure states on the cuntz algebras onwherenis the powers index these states called finitely correlated states and strongly asymptotically shift invariant states are defined and characterized the subsets of these states defining shifts will in general be identified in a later work but here an interesting cross section for the conjugacy classes of shifts called diagonalizable shifts is introduced and studied

econometric illustrations of novel numerical integration strategies for bayesian inference abstract recent progress with numerical techniques for implementing bayesian methods for irregular multi parameter likelihoods is reviewed and illustrated with two econometric examples the numerical integration strategies involve novel iterative adaptive uses of cartesian product and spherical rule quadrature formulae together with importance sampling techniques

explaining individual response using aggregated data abstract empirical analysis of individual response behavior is sometimes limited due to the lack of explanatory variables at the individual level in this paper we put forward a new approach to estimate the effects of covariates on individual response where the covariates are unknown at the individual level but observed at some aggregated level this situation may for example occur when the response variable is available at the household level but covariates only at the zip code level we describe the missing individual covariates by a latent variable model which matches the sample information at the aggregate level parameter estimates can be obtained using maximum likelihood or a bayesian analysis we illustrate the approach estimating the effects of household characteristics on donating behavior to a dutch charity donating behavior is observed at the household level while the covariates are only observed at the zip code level

likelihood approximation by numerical integration on sparse grids the calculation of likelihood functions of many econometric models requires the evaluation of integrals without analytical solutions approaches for extending gaussian quadrature to multiple dimensions discussed in the literature are either very specific or suffer from exponentially rising computational costs in the number of dimensions we propose an extension that is very general and easily implemented and does not suffer from the curse of dimensionality monte carlo experiments for the mixed logit model indicate the superior performance of the proposed method over simulation techniques

a simple nonparametric approach to estimating the distribution of random coefficients in structural models abstract we explore least squares and likelihood nonparametric mixtures estimators of the joint distribution of random coefficients in structural models the estimators fix a grid of heterogeneous parameters and estimate only the weights on the grid points an approach that is computationally attractive compared to alternative nonparametric estimators we provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions we verify most of the consistency conditions for three discrete choice models we also derive the convergence rates of the least squares nonparametric mixtures estimator under additional restrictions we perform a monte carlo study on a dynamic programming model

fully symmetric interpolatory rules for multiple integrals over infinite regions with gaussian weight fully symmetric interpolatory integration rules are constructed for multidimensional integrals over infinite integration regions with a gaussian weight function the points for these rules are determined by successive extensions of the one dimensional three point gauss hermite rule the new rules are shown to be efficient and only moderately unstable

smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models abstract we apply a new simulation method that solves the multidimensional probability integrals that arise in maximum likelihood estimation of a broad class of limited dependent variable models the simulation method has four key features the simulated choice probabilities are unbiased they are a continuous and differentiable function of the parameters of the model they are bounded between 0 and 1 and their computation takes an effort that is nearly linear in the dimension of the probability integral independent of the magnitudes of the true probabilities we also show that the new simulation method produces probability estimates with substantially smaller variance than those generated by acceptance rejection methods or by stern s 1992 method the simulated probabilities can therefore be used to revive the lerman and manski 1981 procedure of approximating the likelihood function using simulated choice probabilities by overcoming its computational disadvantages

non intrusive reduced order modelling of the navier stokes equations abstract this article presents two new non intrusive reduced order models based upon proper orthogonal decomposition pod for solving the navier stokes equations the novelty of these methods resides in how the reduced order models are formed that is how the coefficients of the pod expansions are calculated rather than taking a standard approach of projecting the underlying equations onto the reduced space through a galerkin projection here two different techniques are employed the first method applies a second order taylor series to calculate the pod coefficients at each time step from the pod coefficients at earlier time steps the second method uses a smolyak sparse grid collocation method to calculate the pod coefficients where again the coefficients at earlier time steps are used as the inputs the advantage of both approaches are that they are non intrusive and so do not require modifications to a system code they are therefore very easy to implement they also provide accurate solutions for modelling flow problems and this has been demonstrated by the simulation of flows past a cylinder and within a gyre it is demonstrated that accuracy relative to the high fidelity model is maintained whilst cpu times are reduced by several orders of magnitude in comparison to high fidelity models

a smooth likelihood simulator for dynamic disequilibrium models abstract this article considers the simulation of likelihood functions for dynamic disequilibrium models without sample separation information a recursive simulation algorithm is proposed the recursive simulation algorithm is computationally tractable for a class of dynamic disequilibrium models and serially correlated disturbance models the simulated likelihood functions are smooth in parameters monte carlo studies are provided to demonstrate the computational efficiency of this approach and investigate finite sample properties of simulated likelihood estimators and likelihood ratio test statistics regime classification rules based on simulated likelihood are introduced finite sample results of the simulated likelihood approach are encouraging

generating moment matching scenarios using optimization techniques an optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming the main advantage of the method is its flexibility it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order and the distribution can be defined over an arbitrary set this allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand the method is based on a semi infinite linear programming formulation of the problem that is shown to be solvable with polynomial iteration complexity a practical column generation method is implemented the column generation subproblems are polynomial optimization problems however they need not be solved to optimality it is found that the columns in the column generation approach can be efficiently generated by random sampling the number of scenarios generated matches a lower

central intertwining lifting suboptimization and interpolation in several variables in this paper we obtain an explicit central intertwining lifting for row contractions this is used to prove kaftal larson weiss and foias frazho h h2 suboptimization type results for the noncommutative resp commutative analytic toeplitz algebra f n resp w n the algebra f n resp w n can be viewed as a multivariable noncommutative resp commutative analogue of the hardy space h similar results are provided for f n b k k and w n b k k where b k k is the set of all bounded linear operators acting on hilbert spaces new extensions of the sarason caratheodory and nevanlinna pick type interpolation results are obtained for f n b k k and some consequences to the operator valued analytic interpolation in the unit ball of cn are considered

multivariable nehari problem and interpolation abstract in this paper we obtain a multivariable nehari type theorem for hankel operators extending the classical result as well as treil volberg generalization the result is based on a new generalization of the noncommutative commutant lifting theorem which extends to several variables the commutant lifting result obtained by treil and volberg and recently generalized by biswas foias and frazho an extension of i s iokhvidov ky fan theorem is obtained and used to prove a multivariable adamian arov krein type theorem for generalized hankel operators as consequences we obtain caratheodory and nevanlinna pick type interpolation results for meromorphic operators on fock spaces resp operator valued meromorphic functions on the unit ball of c n the nehari type results are used to obtain descriptions of hankel operators acting on fock spaces or weighted fock spaces multivariable dirichlet type spaces and to solve new weighted interpolation problems e g sarason for noncommutative analytic toeplitz algebras which have consequences to the operator valued analytic interpolation in the unit ball of c n moreover using central intertwining liftings we obtain explicit formulas for certain solutions of the weighted interpolation problems as another application of the generalized noncommutative commutant lifting theorem we derive an abstract interpolation problem for multipliers this is used to solve a left tangential nevanlinna pick type interpolation problem with operatorial argument for noncommutative analytic toeplitz algebras

spectral lifting in banach algebras and interpolation in several variables let a be a unital banach algebra and let j be a closed two sided ideal of a we prove that if any invertible element of a j has an invertible lifting in a4 then the quotient homomorphism 1 a a4 j is a spectral interpolant this result is used to obtain a noncommutative multivariable analogue of the spectral commutant lifting theorem of bercovici foia and tannenbaum this yields spectral versions of sarason nevanlinna pick and caratheodory type interpolation for fn 3b 1c the wot closed algebra generated by the spatial tensor product of the noncommutative analytic toeplitz algebra f and b ac the algebra of bounded operators on a finite dimensional hilbert space kc a spectral tangential commutant lifting theorem in several variables is considered and used to obtain a spectral tangential version of the nevanlinna pick interpolation for f n03b kc in particular we obtain interpolation theorems for matrix valued bounded analytic functions on the open unit ball of cn in which one bounds the spectral radius of the interpolant and not the norm

on injective hulls of simple modules we characterize a ring over which every left module of finite length has an injective hull of finite length using this we show that finite normalizing extensions of such a ring also have the same property we also consider rings having the property that the injective hull of every simple module is artinian we show that certain noncommutative noetherian rings have this property

alternative sampling methods for estimating multivariate normal probabilities we study the performance of alternative sampling methods for estimating multivariate normal probabilities through the ghk simulator the sampling methods are randomized versions of some quasi monte carlo samples halton niederreiter niederreiter xing sequences and lattice points and some samples based on orthogonal arrays latin hypercube orthogonal array and orthogonal array based latin hypercube samples in general these samples turn out to have a better performance than monte carlo and antithetic monte carlo samples improvements over these are large for low dimensional 4 and 10 cases and still significant for dimensions as large as 50

gradient based design optimization under uncertainty via stochastic expansion methods abstract we present a computational framework for robust and reliability based design optimization which combines stochastic expansion methods namely polynomial chaos expansion with design sensitivity analysis it is well known that the statistical moments and their gradients with respect to design variables can be readily obtained from the polynomial chaos expansion however the evaluation of the failure probabilities of the cost and constraint functions and their gradients requires integrations over failure regions to simplify this we introduce an indicator function into the integrand whereby the integration region becomes the known range of random variables and to alleviate the non differentiable property of the indicator function a smooth approximation is adopted to facilitate the sensitivity analysis both intrusive and non intrusive polynomial chaos approaches for uncertainty propagation are employed in the design optimization of linear elastic structures guidelines to assess the computational costs associated with both polynomial chaos approaches are also presented

a method for smoothing simulated moments of discrete probabilities in multinomial probit models there has been much interest over the years in estimating discrete choice models however with the exception of multinomial logit models agents have been restricted to few choices so that multivariate integrals could be feasibly integrated numerically 2 pakes and pollard 1989 and mcfadden 1989 have independently developed the method of simulated moments msm to deal with estimating a wide class of models of which high order discrete choice models are a subset one of the problems a researcher must handle when using msm for a discrete choice model is how to smooth the discrete simulated random variables this is necessary to keep small the number of draws required to simulate derivatives and to simulate variation in the data geweke 1989 and mcfadden 1989 have suggested importance sampling methods and other methods to smooth the simulated variables for general error structures in this paper i present a factor analytic smoothing method that can be applied to probit problems although it is not as general as the methods geweke and mcfadden suggest it is easy to use and has clear intuition furthermore simulated probabilities will be unbiased will be bounded between zero and unity and will have smaller variances than unsmoothed probabilities always and smaller variances than importance sampling estimates for a large class of probabilities the second section of this paper develops notation defines the problem and presents the smoothing method and an algorithm to employ it the last section presents monte carlo comparisons of the smoothing method to the importance sampling method

topology optimization under uncertainty via non intrusive polynomial chaos expansion abstract this paper presents a systematic approach for topology optimization under uncertainty that integrates non intrusive polynomial chaos expansion with design sensitivity analysis for reliability based and robust topology optimization uncertainty is introduced in loading and in geometry to address the manufacturing variability the manufacturing variability is modeled via a thresholding technique in which the threshold field is represented by a reduced dimensional random field response metrics such as compliance and volume are characterized as polynomial chaos expansions of the underlying uncertain parameters thus allowing accurate and efficient estimation of statistical moments failure probabilities and their sensitivities the number of simulations is reduced for linear structures under loading uncertainty by means of superposition efficiency of the non intrusive polynomial chaos approach is highlighted by comparison with the monte carlo method in terms of the number of simulations to demonstrate the effect of uncertainty optimized designs that consider uncertainty are compared to those that do not comparisons of polynomial chaos expansion to existing analytical methods on a benchmark numerical example are also provided for reliability based and worst case designs

smolyak cubature of given polynomial degree with few nodes for increasing dimension some recent investigations see e g gerstner and griebel 5 novak and ritter 9 and 10 novak ritter and steinbauer 11 wasilkowski and wo niakowski 18 or petras 13 show that the so called smolyak algorithm applied to a cubature problem on the d dimensional cube seems to be particularly useful for smooth integrands the problem is still that the numbers of nodes grow polynomially but fast for increasing dimensions we therefore investigate how to obtain smolyak cubature formulae with a given degree of polynomial exactness and the asymptotically minimal number of nodes for increasing dimension d and obtain their characterization for a subset of smolyak formulae error bounds and numerical examples show their good behaviour for smooth integrands a modification can be applied successfully to problems of mathematical finance as indicated by a further numerical example

a method of simulated moments for estimation of discrete response models without numerical integration this paper proposes a simple modification of a conventional method of moments estimator for a discrete response model replacing response probabilities that require numerical integration with estimators obtained by monte carlo simulation this method of simulated moments msm does not require precise estimates of these probabilities for consistency and asymptotic normality relying instead on the law of large numbers operating across observations to control simulation error and hence can use simulations of practical size the method is useful for models such as high dimensional multinomial probit mnp where computation has restricted applications

a multilevel excess hazard model to estimate net survival on hierarchical data allowing for non linear and non proportional effects of covariates the excess hazard regression model is an approach developed for the analysis of cancer registry data to estimate net survival that is the survival of cancer patients that would be observed if cancer was the only cause of death cancer registry data typically possess a hierarchical structure individuals from the same geographical unit share common characteristics such as proximity to a large hospital that may influence access to and quality of health care so that their survival times might be correlated as a consequence correct statistical inference regarding the estimation of net survival and the effect of covariates should take this hierarchical structure into account it becomes particularly important as many studies in cancer epidemiology aim at studying the effect on the excess mortality hazard of variables such as deprivation indexes often available only at the ecological level rather than at the individual level we developed here an approach to fit a flexible excess hazard model including a random effect to describe the unobserved heterogeneity existing between different clusters of individuals and with the possibility to estimate non linear and time dependent effects of covariates we demonstrated the overall good performance of the proposed approach in a simulation study that assessed the impact on parameter estimates of the number of clusters their size and their level of unbalance we then used this multilevel model to describe the effect of a deprivation index defined at the geographical level on the excess mortality hazard of patients diagnosed with cancer of the oral cavity copyright 2016 john wiley sons ltd

inference in semiparametric dynamic models for binary longitudinal data this article deals with the analysis of a hierarchical semiparametric model for dynamic binary longitudinal responses the main complicating components of the model are an unknown covariate function and serial correlation in the errors existing estimation methods for models with these features are of o n3 where n is the total number of observations in the sample therefore nonparametric estimation is largely infeasible when the sample size is large as in typical in the longitudinal setting here we propose a new o n markov chain monte carlo based algorithm for estimation of the nonparametric function when the errors are correlated thus contributing to the growing literature on semiparametric and nonparametric mixed effects models for binary data in addition we address the problem of model choice to enable the formal comparison of our semiparametric model with competing parametric and semiparametric specifications the performance of the methods is illustrated with detailed studies involving simul

a numerically stable quadrature procedure for the one factor random component discrete choice model abstract the gaussian quadrature formula had been popularized by butler and moffitt 1982 econometrika 50 761 764 for the estimation of the error component probit panel model borjas and sueyoshi 1994 journal of econometrics 64 164 182 pointed out some numerical and statistical difficulties of applying it to models with group effects with a moderate or large number of individuals in a group the likelihood function of the model evaluated by the gaussian quadrature formula can be numerically unstable and at worst impossible to evaluate statistical inference may also be inaccurate we point out that some of these difficulties can be overcome with a carefully designed algorithm and the proper selection of the number of quadrature points however with a very large number of individuals in a group the gaussian quadrature formulation of integral may have large numerical approximation errors

interpolation problems in several variables abstract we obtain a noncommutative nudel man type interpolation theorem in several variables and a commutative analogue forh b n the hardy space of bounded analytic functions in the open ball of c n using this result we obtain an operatorial analogue in several variables of the rosenblum rovnyak restriction theorem as well as an extension to the noncommutative analytic toeplitz algebraf we provide new extensions of the caratheodory fejer and nevanlinna pick interpolation theorems forf

structure and entropy for positive definite toeplitz kernels on free semigroups abstract in this article we study the structure of positive definite toeplitz kernels on free semigroups called also multi toeplitz and its implications in noncommutative dilation theory harmonic analysis on fock spaces prediction and interpolation theory for stationary stochastic processes a parametrization of positive definite multi toeplitz kernels in terms of generalized schur sequences of contractions is obtained this leads to explicit minimal naimark dilations cholesky factorizations szego type limit theorems and entropy for positive definite multi toeplitz kernels maximal outer factors are associated with positive definite multi toeplitz kernels and are used to obtain inner outer factorization for operators on fock spaces with coefficients in hilbert spaces the kolmogorov wiener prediction problem for stochastic processes having as covariance kernels positive definite multi toeplitz kernels is considered the predication error operator is calculated in terms of schur parameters resp maximal outer factor associated with the covariance kernel of the process and a connection with a szego type infimum problem is established we solve the caratheodory interpolation problem for positive definite multi toeplitz kernels we obtain a parametrization of all solutions in terms of schur sequences and we find the maximal entropy solution the results of this article can be used to develop a theory of stochastic n linear systems

a convex optimization approach for computing correlated choice probabilities with many alternatives a popular discrete choice model that incorporates correlation information is the multinomial probit mnp model where the random utilities of the alternatives are chosen from a multivariate normal distribution computing the choice probabilities is challenging in the mnp model when the number of alternatives is large mishra et al ieee transactions on automatic control 2012 have proposed a semidefinite optimization approach to compute choice probabilities for the distribution of the random utilities that maximizes expected agent utility given only the mean variance and covariance information their model is referred to as the cross moment cmm model computing the choice probabilities with many alternatives is challenging in the cmm model since one needs to solve large scale semidefinite programs we develop a simpler formulation as a representative agent model by maximizing over the choice probabilities in the unit simplex where the objective function is the sum of the expected utilities and a strongly concave perturbation function by characterizing the perturbation function for the cmm model and its gradient we develop a simple first order gradient method with inexact line search to compute choice probabilities we establish local linear convergence of this algorithm under mild assumptions on the choice probabilities an implication of our results is that inverting the choice probabilities to compute the mean utilities is straightforward given any positive definite covariance matrix numerical experiments show that this method can compute choice probabilities for a large number of alternatives within a reasonable amount of time while explicitly capturing the correlation information comparisons with simulation methods for mnp and semidefinite programming methods for cmm indicate the efficacy of the method

simulation estimation of dynamic switching regression and dynamic disequilibrium models some monte carlo results abstract this article considers the estimation of dynamic exogenous switching regression models and dynamic endogenous switching models with autocorrelation in disturbances or latent lagged dependent variables likelihood functions of such models involve high dimensional integrals and a huge number of summations over unobserved regime paths simulated likelihood methods and simulated methods of moments are available these approaches simulate both continuous and discrete latent dependent variables by monte carlo experiments it is found that the performances of various approaches depend crucially on how discrete state variables are simulated the valuable approach is to simulate regime paths with regime probabilities based on the current and past sample information

simulation and the asymptotics of optimization estimators on demontre un theoreme de limite centrale general pour des estimateurs definis par minimisation de la longueur d une fonction de critere aleatoire a valeurs vectorielles aucune hypothese de regularite suffisante n est imposee sur la fonction de critere pour que les resultats puissent etre appliques a une classe d estimlateurs de simulation assez large des analyses completes de deux estimateurs de simulation l un introduit par pakes l autre par mcfadden illustrent l application des theoremes generaux

gem a novel evolutionary optimization method with improved neighborhood search a new optimization technique called grenade explosion method gem is introduced and its underlying ideas including the concept of optimal search direction osd are elaborated the applicability and efficiency of the technique is demonstrated using standard benchmark functions comparison of the results with those of other widely used evolutionary algorithms shows that the proposed algorithm outperforms its rivals both in the success rate and rate of convergence the method is also shown to be capable of finding most or even all optima of functions having multiple global optima moreover it is shown that the performance of gem is invariant against shifting and scaling of the search space and objective function

estimating marginal properties of quantitative real time pcr data using nonlinear mixed models summary a unified modeling framework based on a set of nonlinear mixed models is proposed for flexible modeling of gene expression in real time pcr experiments focus is on estimating the marginal or population based derived parameters cycle thresholds and but retaining the conditional mixed model structure to adequately reflect the experimental design additionally the calculation of model average estimates allows incorporation of the model selection uncertainty the methodology is applied for estimating the differential expression of a phosphate transporter gene ospt6 in rice in comparison to a reference gene at several states after phosphate resupply in a small simulation study the performance of the proposed method is evaluated and compared to a standard method

simple modules and their essential extensions for skew polynomial rings let r be a commutative noetherian ring and alpha an automorphism of r this paper addresses the question when does the skew polynomial ring s r theta alpha satisfy the property diamond that for every simple s module v the injective hull e s v of v has all its finitely generated submodules artinian the question is largely reduced to the special case where s is primitive for which necessary and sufficient conditions are found which however do not between them cover all possibilities nevertheless a complete characterisation is found when r is an affine algebra over a field k and alpha is a k algebra automorphism in this case diamond holds if and only if all simple s modules are finite dimensional over k this leads to a discussion involving close study of some families of examples of when this latter condition holds for affine k algebras s r theta alpha the paper ends with a number of open questions

minimality of the data in wavelet filters abstract orthogonal wavelets or wavelet frames for l2 r are associated with quadrature mirror filters qmf a set of complex numbers which relate the dyadic scaling of functions on r to the z translates in this paper we show that generically the data in the qmf systems of wavelets are minimal in the sense that the data cannot be nontrivially reduced the minimality property is given a geometric formulation in the hilbert space l2 z and it is then shown that minimality corresponds to irreducibility of a wavelet representation of the algebra o 2 and so our result is that this family of representations of o 2 on the hilbert space l2 z is irreducible for a generic set of values of the parameters which label the wavelet representations

statistical inference in the multinomial multiperiod probit model abstract statistical inference in multinomial multiperiod probit models has been hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions posterior distributions or moment conditions in these models we describe three alternative estimators implemented using simulation based approaches to inference that circumvent the integration problem posterior means computed using gibbs sampling and data augmentation gibbs simulated maximum likelihood sml estimation using the ghk probability simulator and method of simulated moment msm estimation using ghk we perform a set of monte carlo experiments to compare the sampling distributions of these estimators although all three estimators perform reasonably well some important differences emerge our most important finding is that holding simulation size fixed the relative and absolute performance of the classical methods especially sml gets worse when serial correlation in disturbances is strong in data sets with an ar 1 parameter of 0 50 the rmses for sml and msm based on ghk with 20 draws exceed those of gibbs by 9 and 0 respectively but when the ar 1 parameter is 0 80 the rmses for sml and msm based on 20 draws exceed those of gibbs by 79 and 37 respectively and the number of draws needed to reduce the rmses to within 10 of gibbs are 160 and 80 respectively also the sml estimates of serial correlation parameters exhibit significant downward bias thus while conventional wisdom suggests that 20 draws of ghk is enough to render the bias and noise induced by simulation negligible our results suggest that much larger simulation sizes are needed when serial correlation in disturbances is strong

a multilevel sparse kernel based stochastic collocation finite element method for elliptic problems with random coefficients abstract a new stochastic collocation finite element method is proposed for the numerical solution of elliptic boundary value problems bvp with random coefficients assuming that the randomness is well approximated by a finite number of random variables with given probability distributions the proposed method consists of a finite element approximation in physical space along with a stochastic collocation quadrature approach utilizing the recent multilevel sparse kernel based interpolation musik technique georgoulis et al 2013 musik is based on a multilevel sparse grid type algorithm with the basis functions consisting of directionally anisotropic gaussian radial basis functions kernels placed at directionally uniform grid points we prove that musik is interpolatory at these nodes and therefore can be naturally used to define a quadrature scheme numerical examples are also presented assessing the performance of the new algorithm in the context of high dimensional stochastic collocation finite element methods

numerical quadrature for high dimensional singular integrals over parallelotopes we introduce and analyze a family of algorithms for an efficient numerical approximation of integrals of the form email protected c 1 c 2 f x y y x dydx where c 1 c 2 are d dimensional parallelotopes i e affine images of d hypercubes and f has a singularity at y x 0 such integrals appear in galerkin discretization of integral operators in r d we construct a family of quadrature rules q n with n function evaluations for a class of integrands f which may have algebraic singularities at y x 0 and are email protected regular for y x 0 the main tool is an explicit regularizing coordinate transformation simultaneously simplifying the singular support and the domain of integration for the full tensor product variant of the suggested quadrature family we prove that q n achieves the exponential convergence rate o exp rn c with the exponent c 1 email protected 1 in the special case of a singularity of the form email protected a with real a we prove that the improved convergence rate of c 1 email protected is achieved if a certain modified one dimensional gauss jacobi quadrature rule is used in the singular direction we give numerical results for various types of the quadrature rules in particular based on tensor product rules standard smolyak optimized and adaptive sparse grid quadratures and sobol sequences

performance of cubature formulae in probabilistic model analysis and optimization in probabilistic model analysis and optimization expected values of a model output f x in face of continuous random inputs x are estimated through n dimensional integrals where n d i m x cubature formulae are approximations of these integrals by a weighted sum of function evaluations at carefully chosen points when each function evaluation corresponds to a heavy computational simulation and particularly in optimization problems one needs very efficient formulae with few integration points even though only having modest accuracy in this paper we evaluate the performance of several cubature formulae with few points including smolyak type formulae also known as sparse grid integration and recently proposed thinned cubatures constructed using orthogonal arrays tests are made for a wide family of smooth and non oscillatory functions f x possibly with significant anisotropy and covering both normal and uniform input probability distributions two practical case studies are also presented one of analysis of a large scale mass transfer model with uncertain parameters and a second one of optimal production planning under uncertain market conditions results clearly indicate that cubatures with large negative weights including smolyak type formulae are not reliable contrary to positive thinned cubatures that produce very reasonable estimates up to dimension 24 these thinned cubatures may also surpass quasi monte carlo methods also up to dimension 24

a computationally practical simulation estimator for panel data in this paper i develop a practical extension of mcfadden s method of simulated moments estimator for limited dependent variable models to the panel data case the method is based on a factorization of the msm first order condition into transition probabilities along with the development of a new highly accurate method for similating these transition probabilities a series of monte carlo tests show that this msm estimator performs quite well relative to quadrature based ml estimators even when large numbers of quadrature points are employed the estimator also performs well relative to simulated ml even when a highly accurate method is used to simulate the choice probabilities in terms of computational speed complex panel data models involving random effects and arma errors may be estimated via msm in times similar to those necessary for estimation of simple random effects models via ml quadrature

a bayesian analysis of the multinomial probit model with fully identified parameters we present a new prior and corresponding algorithm for bayesian analysis of the multinomial probit model our new approach places a prior directly on the identified parameter space the key is the specification of a prior on the covariance matrix so that the 1 1 element if fixed at 1 and it is possible to draw from the posterior using standard distributions analytical results are derived which can be used to aid in assessment of the prior

uncertainty quantification for personalized analyses of human proximal femurs computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads which affect the simulation results to quantify the influence we developed a probabilistic framework based on polynomial chaos pc that propagates stochastic input variables through any computational model we considered a stochastic e relationship and a stochastic hip contact force representing realistic variability of experimental data their influence on the prediction of principal strains 1 and 3 was quantified for one human proximal femur including sensitivity and reliability analysis large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck with coefficients of variation of 40 between 60 and 80 of the variance in 1 and 3 are attributable to the uncertainty in the e relationship while 10 are caused by the load magnitude and 5 30 by the load direction principal strain directions were unaffected by material and loading uncertainties the antero superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure however all were very small pf 0 001 in summary uncertainty quantification with pc has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs which increases the credibility and explanatory power of personalized analyses of human proximal femurs

application of polynomial chaos to quantify uncertainty in deterministic channel models a non intrusive formulation of the polynomial chaos method is applied to quantify the uncertainties in deterministic models of the indoor radio channel deterministic models based on the finite difference time domain fdtd method and ray tracing are examined various sources of parameter uncertainty are considered including randomness in the material properties building geometry and the spatial location of transmitting and receiving antennas the polynomial chaos results are confirmed against monte carlo simulations and experimental measurements the analysis shows the expected variation in the sector averaged path loss can be considerable for relatively small input parameter uncertainties leading to the conclusion that a single simulation run using nominal values may be insufficient to adequately characterize the indoor radio channel

maximum likelihood estimation of limited and discrete dependent variable models with nested random effects abstract gauss hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models unfortunately the estimates are biased for large cluster sizes and or intraclass correlations we show that adaptive quadrature largely overcomes these problems we then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables the models can include several nested random effects intercepts and coefficients representing unobserved heterogeneity at different levels of a hierarchical dataset the required multivariate integrals are evaluated efficiently using spherical quadrature rules simulations show that adaptive quadrature performs well in a wide range of situations