on the regular hilbert space representation of a moyal quantization it is shown that in the regular viz phase space representation of a moyal quantization real polynomials in the phase space variables become essentially self adjoint operators and that functions in the positive cone of monomials of even power in the phase space variables yield positive operators conditions on the boundedness of moyal operators are given the classical limit of a moyal operator is defined and used to relate classical with quantum entropy

a regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its l norm the i th singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one we show that near a local maximum however the largest singular value has a lipschitz second derivative but need not have a third derivative using this regularity result we give a quadratically convergent algorithm for computing the l norm of a transfer matrix

quantum locally compact metric spaces abstract we introduce the notion of a quantum locally compact metric space which is the noncommutative analogue of a locally compact metric space and generalize to the non unital setting the notion of quantum metric spaces introduced by rieffel we then provide several examples of such structures including the moyal plane compact quantum metric spaces and locally compact metric spaces this paper provides an answer to the question raised in the literature about the proper notion of a quantum metric space in the non unital setup and offers important insights into noncommutative geometry for non compact quantum spaces

multivariable feedback a personal reminiscence my involvement in the development of linear multivariable feedback theory and its applications is described from a highly personal point of view concentrating on the origin of key ideas and their development in association with many colleagues detailed references are given to all my papers and books and explanatory notes provided where further material may be found

a fundamental approach to the generalized eigenvalue problem for self adjoint operators the generalized eigenvalue problem for an arbitrary self adjoint operator is solved in a gelfand triple consisting of three hilbert spaces the proof is based on a measure theoretical version of the sobolev lemma and the multiplicity theory for self adjoint operators as an application necessary and sufficient conditions are mentioned such that a self adjoint operator in l2 r has generalized eigenfunctions which are tempered distributions

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

c completions and the dfr algebra the aim of this paper is to present the construction of a general family of c algebras which includes as a special case the quantum spacetime algebra introduced by doplicher fredenhagen and roberts it is based on an extension of the notion of c completion from algebras to bundles of algebras compatible with the usual c completion of the appropriate algebras of sections combined with a novel definition for the algebra of the canonical commutation relations using rieffel s theory of strict deformation quantization taking the c algebra of continuous sections vanishing at infinity we arrive at a functor associating a c algebra to any poisson vector bundle and recover the original dfr algebra as a particular example

the magnetic weyl calculus in the presence of a variable magnetic field the weyl pseudodifferential calculus must be modified the usual modification based on the minimal coupling principle at the level of the classical symbols does not lead to gauge invariant formulas if the magnetic field is not constant we present a gauge covariant quantization relying on the magnetic canonical commutation relations the underlying symbolic calculus is a deformation defined in terms of the magnetic flux through triangles of the classical moyal product

multiple imputation in mixture models for nonignorable nonresponse with follow ups abstract one approach to inference for means or linear regression parameters when the outcome is subject to nonignorable nonresponse is mixture modeling mixture models assume separate parameters for respondents and nonrespondents implementation by multiple imputation consists of repeatedly filling in missing values for nonrespondents estimating parameters using the filled in data and then adjusting for variability between imputations we evaluated the performance of this scheme using simulated data with a 25 sample of nonrespondents followed up we conclude that it provides a generally satisfactory and robust approach to inference for means and regression parameters in this case although a greater number of imputations may be required for good performance compared to the number required for estimation when nonresponse is ignorable

estimating propensity scores with missing covariate data using general location mixture models in many observational studies analysts estimate causal effects using propensity scores e g by matching sub classifying or inverse probability weighting based on the scores estimation of propensity scores is complicated when some values of the covariates are missing analysts can use multiple imputation to create completed data sets from which propensity scores can be estimated we propose a general location mixture model for imputations that assumes that the control units are a latent mixture of i units whose covariates are drawn from the same distributions as the treated units covariates and ii units whose covariates are drawn from different distributions this formulation reduces the influence of control units outside the treated units region of the covariate space on the estimation of parameters in the imputation model which can result in more plausible imputations in turn this can result in more reliable estimates of propensity scores and better balance in the true covariate distributions when matching or sub classifying we illustrate the benefits of the latent class modeling approach with simulations and with an observational study of the effect of breast feeding on children s cognitive abilities

the analysis of repeated categorical measurements subject to nonignorable nonresponse abstract conditional likelihood methods have been proposed for analyzing the repeated measurement of categorical responses this article extends the methods to include partially classified subjects the extension allows for an ignorable or nonignorable nonresponse mechanism and uses standard statistical software for the computations two examples of incomplete longitudinal categorical data illustrate the method

affinely invariant matching methods with ellipsoidal distributions matched sampling is a common technique used for controlling bias in observational studies we present a general theoretical framework for studying the performance of such matching methods specifically results are obtained concerning the performance of affinely invariant matching methods with ellipsoidal distributions which extend previous results on equal percent bias reducing methods additional extensions cover conditionally affinely invariant matching methods for covariates with conditionally ellipsoidal distributions these results decompose the effects of matching into one subspace containing the best linear discriminant and the subspace of variables uncorrelated with the discriminant this characterization of the effects of matching provides a theoretical foundation for understanding the performance of specific methods such as matched sampling using estimated propensity scores calculations for such methods are given in subsequent articles

algebras of distributions suitable for phase space quantum mechanics ii topologies on the moyal algebra the topology of the moyal algebra may be defined in three ways the algebra may be regarded as an operator algebra over the space of smooth declining functions either on the configuration space or on the phase space itself or one may construct the algebra via a filtration of hilbert spaces or other banach spaces of distributions the equivalence of the three topologies thereby obtained is proved as a consequence by filtrating the space of tempered distributions by banach subspaces new sufficient conditions are given for a phase space function to correspond to a trace class operator via the weyl correspondence rule

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

symmetries of noncommutative scalar field theory we investigate symmetries of the scalar field theory with a harmonic term on the moyal space with the euclidean scalar product and general symplectic form the classical action is invariant under the orthogonal group if this group acts also on the symplectic structure we find that the invariance under the orthogonal group can also be restored at the quantum level by restricting the symplectic structures to a particular orbit

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

a general theory of phase space quasiprobability distributions we present a general theory of quasiprobability distributions on phase spaces of quantum systems whose dynamical symmetry groups are finite dimensional lie groups the family of distributions on a phase space is postulated to satisfy the stratonovich weyl correspondence with a generalized traciality condition the corresponding family of the stratonovich weyl kernels is constructed explicitly in the presented theory we use the concept of generalized coherent states that brings physical insight into the mathematical formalism

adjusted kaplan meier estimator and log rank test with inverse probability of treatment weighting for survival data estimation and group comparison of survival curves are two very common issues in survival analysis in practice the kaplan meier estimates of survival functions may be biased due to unbalanced distribution of confounders here we develop an adjusted kaplan meier estimator akme to reduce confounding effects using inverse probability of treatment weighting iptw each observation is weighted by its inverse probability of being in a certain group the akme is shown to be a consistent estimate of the survival function and the variance of the akme is derived a weighted log rank test is proposed for comparing group differences of survival functions simulation studies are used to illustrate the performance of akme and the weighted log rank test the method proposed here outperforms the kaplan meier estimate and it does better than or as well as other estimators based on stratification the akme and the weighted log rank test are applied to two real examples one is the study of times to reinfection of sexually transmitted diseases and the other is the primary biliary cirrhosis pbc study

propensity score methods for bias reduction in the comparison of a treatment to a non randomized control group in observational studies investigators have no control over the treatment assignment the treated and non treated that is control groups may have large differences on their observed covariates and these differences can lead to biased estimates of treatment effects even traditional covariance analysis adjustments may be inadequate to eliminate this bias the propensity score defined as the conditional probability of being treated given the covariates can be used to balance the covariates in the two groups and therefore reduce this bias in order to estimate the propensity score one must model the distribution of the treatment indicator variable given the observed covariates once estimated the propensity score can be used to reduce bias through matching stratification subclassification regression adjustment or some combination of all three in this tutorial we discuss the uses of propensity score methods for bias reduction give references to the literature and illustrate the uses through applied examples

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

estimating and using propensity scores with partially missing data abstract investigators in observational studies have no control over treatment assignment as a result large differences can exist between the treatment and control groups on observed covariates which can lead to badly biased estimates of treatment effects propensity score methods are an increasingly popular method for balancing the distribution of the covariates in the two groups to reduce this bias for example using matching or subclassification sometimes in combination with model based adjustment to estimate propensity scores which are the conditional probabilities of being treated given a vector of observed covariates we must model the distribution of the treatment indicator given these observed covariates much work has been done in the case where covariates are fully observed we address the problem of calculating propensity scores when covariates can have missing values in such cases which commonly arise in practice the pattern of missing covariates can be prognostically important and

paper sensitivity integrals for multivariable discrete time systems the purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete time systems we present extensions to both the classical poisson integral and bode s sensitivity integral formulae the main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete time systems due to such system characteristics as open loop unstable poles and nonminimum phase zeros and to such design requirements as stability and bandwidth constraints these formulae are similar to those for multivariable continuous time systems obtained elsewhere and they reveal that feedback design limitations depend on directionality properties of the sensitivity function and on those of unstable poles and nonminimum phase zeros in the open loop transfer function

continuity statements and counterintuitive examples in connection with weyl quantization we use the properties of an integral transform relating a classical function f with the matrix elements between coherent states of its quantal counterpart q f to derive continuity properties of the weyl transform from classes of distributions to classes of quadratic forms we also give examples of pathological behavior of the weyl transform with respect to other topologies e g bounded functions leading to unbounded operators

the spectral action for moyal planes extending a result of vassilevich we obtain the asymptotic expansion for the trace of a spatially regularized heat operator l f e t where is a generalized laplacian defined with moyal products and l f is moyal left multiplication the moyal planes corresponding to any skewsymmetric matrix being spectral triples the spectral action introduced in noncommutative geometry by chamseddine and connes is computed this result generalizes the connes lott action previously computed by gayral for symplectic

quadratic hamiltonians in phase space quantum mechanics the dynamical evolution is described within the phase space formalism by means of the moyal propagator which is the symbol of the evolution operator quadratic hamiltonians on the phase space are distinguished in that their moyal bracket with any function equals their poisson bracket it is shown that for general time independent quadratic hamiltonians the moyal propagators transform covariantly under linear canonical transformations they are then derived and classified in a fully explicit manner using the theory of hamiltonian normal forms the authors present several tables of propagators it is proved that these propagators belong to the moyal algebra of distributions and that the spectrum of the hamiltonian may be obtained directly as the support of the fourier transform of the moyal propagator with respect to time from that the quantum mechanical problem for these hamiltonians is in principle completely solved the appropriate path integral formalism for phase space quantum mechanics leading back to the same results is outlined in an appendix

propensity score estimation with missing values using a multiple imputation missingness pattern mimp approach propensity scores have been used widely as a bias reduction method to estimate the treatment effect in nonrandomized studies since many covariates are generally included in the model for estimating the propensity scores the proportion of subjects with at least one missing covariate could be large while many methods have been proposed for propensity score based estimation in the presence of missing covariates little has been published comparing the performance of these methods in this article we propose a novel method called multiple imputation missingness pattern mimp and compare it with the naive estimator ignoring propensity score and three commonly used methods of handling missing covariates in propensity score based estimation separate estimation of propensity scores within each pattern of missing data multiple imputation and discarding missing data under different mechanisms of missing data and degree of correlation among covariates simulation shows that all adjusted estimators are much less biased than the naive estimator under certain conditions mimp provides benefits smaller bias and mean squared error compared with existing alternatives

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

second order nonsmooth optimization for h synthesis the standard way to compute h feedback controllers uses algebraic riccati equations and is therefore of limited applicability here we present a new approach to the h output feedback control design problem which is based on nonlinear and nonsmooth mathematical programming techniques our approach avoids the use of lyapunov variables and is therefore flexible in many practical situations

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

algebras of distributions suitable for phase space quantum mechanics i the twisted product of functions on r2n is extended to a algebra of tempered distributions that contains the rapidly decreasing smooth functions the distributions of compact support and all polynomials and moreover is invariant under the fourier transformation the regularity properties of the twisted product are investigated a matrix presentation of the twisted product is given with respect to an appropriate orthonormal basis which is used to construct a family of banach algebras under this product

the wigner transformation is of finite order the wigner integral transformation which intertwines the twisted product and the composition of kernels is of order 24 indeed it commutes with and its sixth power equals the fourier cotransformation

dixmier traces on noncompact isospectral deformations abstract we extend the isospectral deformations of connes landi and dubois violette to the case of riemannian spin manifolds carrying a proper action of the noncompact abelian group r l under deformation by a torus action a standard formula relates dixmier traces of measurable operators to integrals of functions on the manifold we show that this relation persists for actions of r l under mild restrictions on the geometry of the manifold which guarantee the dixmier traceability of those operators

characterizing the effect of matching using linear propensity score methods with normal distributions summary matched sampling is a standard technique for controlling bias in observational studies due to specific covariates since rosenbaum rubin 1983 multivariate matching methods based on estimated propensity scores have been used with increasing frequency in medical educational and sociological applications we obtain analytic expressions for the effect of matching using linear propensity score methods with normal distributions these expressions cover cases where the propensity score is either known or estimated using either discriminant analysis or logistic regression as is typically done in current practice the results show that matching using estimated propensity scores not only reduces bias along the population propensity score but also controls variation of components orthogonal to it matching on estimated rather than population propensity scores can therefore lead to relatively large variance reduction as much as a factor of two in common matching settings where close matches are possible approximations are given for the magnitude of this variance reduction which can be computed using estimates obtained from the matching pools related expressions for bias reduction are also presented which suggest that in difficult matching situations the use of population scores leads to greater bias reduction than the use of estimated scores

pattern mixture models for multivariate incomplete data consider a random sample on variables x1 xv with some values of xv missing selection models specify the distribution of x1 xv over respondents and nonrespondents to xv and the conditional distribution that xv is missing given x1 xv in contrast pattern mixture models specify the conditional distribution of x 1 xv given that xv is observed or missing respectively and the marginal distribution of the binary indicator for whether or not xv is missing for multivariate data with a general pattern of missing values the literature has tended to adopt the selection modeling approach see for example little and rubin here pattern mixture models are proposed for this more general problem pattern mixture models are chronically underidentified in particular for the case of univariate nonresponse mentioned above there are no data on the distribution of xv given x1 xv 1 in the stratum with xv missing thus the models require restrictions or prior information to identify the paramet

multivariable gain phase and sensitivity integral relations and design trade offs we present several extensions of the classical bode integral relations to multivariable systems the main contributions are an extended gain phase integral formula and an extended sensitivity integral relation these results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems in particular they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single input single output systems both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

maximum likelihood estimation for mixed continuous and categorical data with missing values summary maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented the general location model of olkin tate 1961 and extensions introduced by krzanowski 1980 1982 form the basis for our methods maximum likelihood estimation with incomplete data is achieved by an application of the em algorithm dempster laird rubin 1977 special cases of the algorithm include orchard woodbury s 1972 algorithm for incomplete normal samples fuchs s 1982 algorithms for log linear modelling of partially classified contingency tables and day s 1969 algorithm for multivariate normal mixtures applications include a imputation of missing values b logistic regression and discriminant analysis with missing predictors and unclassified observations c linear regression with missing continuous and categorical predictors and d parametric cluster analysis with incomplete data methods are illustrated using data from the st louis risk research project some key word8 cluster analysis discriminant analysis em algorithm incomplete data linear regression logistic regression log linear model mixture model

analytic properties of the singular values of a rational matrix abstract it is shown that the singular values of a rational matrix g s where s x jy are locally a set of real analytic functions of x and y a brief discussion is given of their global properties

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

causal inference with confounders missing not at random author s yang s wang l ding p abstract 2019 biometrika trust it is important to draw causal inference from observational studies but this becomes challenging if the confounders have missing values generally causal effects are not identifiable if the confounders are missing not at random in this article we propose a novel framework for nonparametric identification of causal effects with confounders subject to an outcome independent missingness which means that the missing data mechanism is independent of the outcome given the treatment and possibly missing confounders we then propose a nonparametric two stage least squares estimator and a parametric estimator for causal effects

moyal planes are spectral triples axioms for nonunital spectral triples extending those introduced in the unital case by connes are proposed as a guide and for the sake of their importance in noncommutative quantum field theory the spaces r2n endowed with moyal products are intensively investigated some physical applications such as the construction of noncommutative wick monomials and the computation of the connes lott functional action are given for these noncommutative hyperplanes

cotangent bundle quantization entangling of metric and magnetic field for manifolds of noncompact type endowed with an affine connection for example the levi civita connection and a closed 2 form magnetic field we define a hilbert algebra structure in the space and construct an irreducible representation of this algebra in this algebra is automatically extended to polynomial in momenta functions and distributions under some natural conditions this algebra is unique the non commutative product over is given by an explicit integral formula this product is exact not formal and is expressed in invariant geometrical terms our analysis reveals that this product has a front which is described in terms of geodesic triangles in the quantization of functions induces a family of symplectic reflections in and generates a magneto geodesic connection on this symplectic connection entangles on the phase space level the original affine structure on and the magnetic field in the classical approximation the 2 part of the quantum product contains the ricci curvature of and a magneto geodesic coupling tensor