optimal designs of two phase studies the two phase design is a cost effective sampling strategy to evaluate the effects of covariates on an outcome when certain covariates are too expensive to be measured on all study subjects under

finite element solution of compressible viscous flows using conservative variables abstract a finite element method for solving the compressible navier stokes equations is presented these equations are solved in conservation form and using conservative variables appropriate finite element approximations are discussed when a galerkin variational formulation is used for high speed flows the formulation is stabilized using the stream line upwind petrov galerkin method for which we propose an analytical expression for the matrix a new discontinuity capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients the non linear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual gmres algorithm numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed finite element method

the envelope of spectral power for stochastic processes it is well known that the maximum likelihood ml spectral estimate represents an envelope on spectral power which is consistent with estimated covariance lags however in computing the envelope the ml method allows for spectra corresponding to complex valued stochastic processes we study the respective envelope for processes constrained to be real valued at the outset the resulting envelope is less conservative than the one provided by the ml method a closed form expression exists for the new envelope

on a generalization of the trigonometric moment problem abstract the trigonometric moment problem asks if there exists a positive finite borel measure on the unit circle whose first n trigonometric moments take some specified values this paper treats the case when only some of the first n trigonometric moments are specified a solution of the problem is found when two of the moments are specified and they are real if the moments are complex numbers some partial results are obtained in the case when all the n first moments except the n 1th are specified a complete solution of the problem is presented

some perspectives on the eigenvalue problem this expository paper explores the relationships among a number of algorithms for solving eigenvalue problems including the power method subspace iteration the qr algorithm and the arnoldi and symmetric lanczos algorithms the symmetric lanczos algorithm is shown to be identical to the three term recursion stieltjes procedure for computing orthogonal polynomials with respect to a measure on the real line the connection between measures on the line and symmetric tridiagonal jacobi matrices is investigated if such a matrix is transformed by a step of the qr algorithm there is a corresponding transformation in the measure the tridiagonal matrices are also exploited for the construction of gaussian quadrature formulas for measures on the line the developments on the real line are replicated with suitable modifications on the unit circle via lanczos like procedures for unitary operators the best known procedure of this type is the recursion of szego for computing orthogonal polynomials on the

a maximum entropy approach to the classical moment problem it is shown that a necessary and sufficient condition for the indeterminacy of the classical moment problem is the existence of a solution having finite entropy the entropy maximizers are computed explicitly for a family of logarithmic integrals indexed by a parameter c with im 0 and all the n extremal solutions can be obtained as weak limits of that family by letting approach a real value

supg finite element computation of compressible flows with the entropy and conservation variables formulations abstract supg stabilized finite element formulations of compressible euler equations based on the conservation and entropy variables are investigated and compared the formulation based on the conservation variables consists of the formulation introduced by tezduyar and hughes plus a shock capturing term the formulation based on the entropy variables is the same as the one by hughes franca and mallet which has a shock capturing term built in these formulations are tested on several subsonic transonic and supersonic compressible flow problems it is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables furthermore the solutions obtained using the two formulations are very close and in some cases almost indistinguishable consequently it can be deduced that the relative merits of these two formulations will continue to remain under debate

maximum entropy and spectral estimation a review the method of maximum entropy is reviewed with emphasis on its relationship to entropy rate wiener filters autoregressive processes extrapolation the levinson algorithm lattice all pole and all pass filters and stability

semiparametric modeling of repeated measurements under outcome dependent follow up in regression analysis of repeated measurements that are taken at subject specific times the availability of the outcome data may be related to the past outcome and to other measured variables that are not in the intended regression model in this paper we propose a natural extension of the semiparametric regression procedure of lin and ying j am stat assoc 2001 96 103 126 by building a class of inverse intensity rate ratio weighted estimators that accommodate such outcome dependent follow up the estimators have a closed form are radicaln consistent asymptotically normal and do not require estimation of any infinite dimensional parameters we give several simulations to demonstrate the estimator s performance and show a sensitivity study under follow up with various degrees of dependence on outcome related variables we illustrate our approach using data from a randomized health services research study with noncompliance to scheduled visits

on two dimensional spectral realization reconstruction of a spectral density function from a finite set of covariances can be performed by maximizing an entropy functional the method of the maximum entropy on the mean is used for computing a discrete version of this spectral density and allows one to give a new interpretation of these reconstruction methods in fact the authors show that the choice of the entropy is directly related to a prior distribution in particular they consider processes on z sup 2 steepest descent procedures permit the numerical computation of discrete realizations for a wide class of entropies to ensure the nonnegativity of the solution related to the burg entropy they present a new algorithm based on a fixed point method and the yule walker equations to compute this solution then the solution of the dual problem is obtained as the limit of the trajectory of an ordinary differential equation

maximum entropy and conditional probability it is well known that maximum entropy distributions subject to appropriate moment constraints arise in physics and mathematics in an attempt to find a physical reason for the appearance of maximum entropy distributions the following theorem is offered the conditional distribution of x l given the empirical observation 1 n sum n i l h x i alpha where x 1 x 2 cdots are independent identically distributed random variables with common density g converges to f lambda x e lambda t h x g x suitably normalized where lambda is chosen to satisfy int f lambda x h x dx alpha thus the conditional distribution of a given random variable x is the normalized product of the maximum entropy distribution and the initial distribution this distribution is the maximum entropy distribution when g is uniform the proof of this and related results relies heavily on the work of zabell and lanford

parameter estimation in longitudinal studies with outcome dependent follow up in many observational studies individuals are measured repeatedly over time although not necessarily at a set of prespecified occasions instead individuals may be measured at irregular intervals with those having a history of poorer health outcomes being measured with somewhat greater frequency and regularity i e those individuals with poorer health outcomes may have more frequent follow up measurements and the intervals between their repeated measurements may be shorter in this article we consider estimation of regression parameters in models for longitudinal data where the follow up times are not fixed by design but can depend on previous outcomes in particular we focus on general linear models for longitudinal data where the repeated measures are assumed to have a multivariate gaussian distribution we consider assumptions regarding the follow up time process that result in the likelihood function separating into two components one for the follow up time process the other for the outcome process the practical implication of this separation is that the former process can be ignored when making likelihood based inferences about the latter i e maximum likelihood ml estimation of the regression parameters relating the mean of the longitudinal outcomes to covariates does not require that a model for the distribution of follow up times be specified as a result standard statistical software e g sas proc mixed littell et al 1996 sas system for mixed models can be used to analyze the data however we also demonstrate that misspecification of the model for the covariance among the repeated measures will in general result in regression parameter estimates that are biased furthermore results of a simulation study indicate that the potential bias due to misspecification of the covariance can be quite considerable in this setting finally we illustrate these results using data from a longitudinal observational study lipshultz et al 1995 new england journal of medicine 332 1738 1743 that explored the cardiotoxic effects of doxorubicin chemotherapy for the treatment of acute lymphoblastic leukemia in children

longitudinal studies of binary response data following case control and stratified case control sampling design and analysis we discuss design and analysis of longitudinal studies after case control sampling wherein interest is in the relationship between a longitudinal binary response that is related to the sampling case control variable and a set of covariates we propose a semiparametric modeling framework based on a marginal longitudinal binary response model and an ancillary model for subjects case control status in this approach the analyst must posit the population prevalence of being a case which is then used to compute an offset term in the ancillary model parameter estimates from this model are used to compute offsets for the longitudinal response model examining the impact of population prevalence and ancillary model misspecification we show that time invariant covariate parameter estimates other than the intercept are reasonably robust but intercept and time varying covariate parameter estimates can be sensitive to such misspecification we study design and analysis issues impacting study efficiency namely choice of sampling variable and the strength of its relationship to the response sample stratification choice of working covariance weighting and degree of flexibility of the ancillary model the research is motivated by a longitudinal study following case control sampling of the time course of attention deficit hyperactivity disorder adhd symptoms

on the favard theorem and its extensions in this paper we present a survey on the favard theorem and its extensions c 2001 elsevier science b v all rights reserved

a generalized galerkin method for steady convection diffusion problems with application to quadratic shape function elements abstract a generalization of the standard galerkin finite element method is considered to enable it to deal successfully with steady convection diffusion problems the proposed method employs a generalized governing equation which is obtained by subtracting from the original differential equation the scalar product of its gradient by a vector of free parameters associated with each of the coordinate directions the generalized equation is successively discretized by the standard bubnov galerkin finite element method the effectiveness of the method is illustrated for the case of quadratic local interpolations in one and two space dimensions

on the application of maximum entropy to the moments problem the maximum entropy approach to the solution of classical inverse problem of moments in which one seeks to reconstruct a function p x where x 0 from the values of a finite set n 1 of its moments is studied it is shown that for n 4 such a function always exists while for n 2 and n 3 the acceptable values of the moments are singled out analytically the paper extends to the general case where the results were previously bounded to the case n 2

an estimated likelihood method for continuous outcome regression models with outcome dependent sampling many biomedical observational studies attempt to relate a continuous outcome to an environmental exposure and other important covariates if the outcome is easier or cheaper to measure relative to the exposure of interest then the outcome may be observed for every member of a finite study population whereas exposure measurements may be obtained only for a relatively small subsample of this population rather than selecting a simple random subsample of individuals for exposure measurement investigators may attempt to enhance study efficiency by allowing the selection probabilities to depend on the observed outcomes we refer to such sampling schemes as outcome dependent sampling ods standard estimation methods that ignore the ods design will yield biased and inconsistent parameter estimates furthermore it is generally desirable to use estimators that incorporate all available data as analyses restricted to subjects with complete information are inefficient to this end we extend an estimated likel

asymptotic behaviour of verblunsky coefficients abstract let v z j 1 m z j h k h k and j 1 j 1 m and consider the polynomials orthogonal with respect to v 2 d n v 2 d z where is a finite positive borel measure on the unit circle with infinite points in its support such that the reciprocal of its szeg function has an analytic extension beyond z 1 in this paper we deduce the asymptotic behaviour of their verblunsky coefficients by means of this result an asymptotic representation for these polynomials inside the unit circle is also obtained

a derivation of the gohberg semencul relation signal analysis a simple proof of the gohberg semencul decomposition of the inverse of the correlation matrix of an autoregressive ar process is given the proof is based on the cholesky decomposition and the centrosymmetric property of symmetric toeplitz matrices the gohberg semencul relation is derived in a simple way by doubling the size but not the order of the ar process

quadratic streamline upwinding for finite element method solutions to 2 d convective transport problems abstract during the past decade finite element methods fems have been recognized to be more powerful tools in the solution of various flow problems as opposed to their predecessors finite difference methods on a fundamental level the fem involves approximations to the solution over a given trial space on a discrete mesh rather than finite difference approximations to the differential operators on a discrete mesh in this way the mechanics operators of the fem remain closer to the physical principles associated with a given problem in addition to this the fem incorporates boundary conditions very efficiently into the numerical formulation much current research is aimed at making these fems viable options for convection dominated flows in 1985 mizukami et al published two papers advancing the approach of streamline upwinding within linear elements for fems the purpose of this work is to demonstrate that streamline upwinding of higher ordered elements is a more accurate option the work goes on to show exactly how streamline upwinding effects the stability of iteratively solving the global algebraic system resulting from the fem

differential methods in inverse scattering this paper discusses a new set of differential methods for solving the inverse scattering problem associated to the propagation of waves in an inhomogeneous medium by writing the medium equations in the form of a two component system describing the interaction of rightward and leftward propagating waves the causality of the propagation phenomena is exploited in order to identify the medium layer by layer the recursive procedure that we obtain constitutes a continuous version of an algorithm first derived by schur in order to test for the boundedness of functions analytic inside the unit circle it recovers the local reflectivity function of the medium using similar ideas some other differential methods can also be derived to reconstruct alternative parametrizations of the layered medium in terms of the local impedance or of the potential function the differential inverse scattering methods turn out to be very efficient since in some sense they let the medium perform the inversion by itself and thus

an adaptive petrov galerkin formulation for the compressible euler and navier stokes equations in this paper we combine a stable petrov galerkin formulation for the compressible euler and navier stokes equations with an h adaptive remeshing refinement including directional stretching and stretching ratio in the mesh regeneration procedure the result is an accurate and efficient scheme appropriated to solve problems presenting shocks and boundary layers

nonparametric and semiparametric models for missing covariates in parametric regression robustness of covariate modeling for the missing covariate problem in parametric regression is studied under the missing at random assumption for a simple missing covariate pattern nonparametric covariate model is proposed and is shown to yield a consistent and semiparametrically efficient estimator for the regression parameter total robustness is achieved in this situation for more general missingcovariate patterns a novel semiparametric modeling approach is proposed for the covariates in this approach the covariate distribution is first decomposed into the product of a series of conditional distributions according to the overall missing data patterns and the conditional distributions are then represented in the general odds ratio form the general odds ratios are modeled parametrically and the other components of the covariate distribution are modeled nonparametrically maximum semiparametric likelihood is used to find the parameter estimates the proposed method yields a consistent estimator f

the analysis of retrospective family studies summary case control samples allow straightforward calculation of estimates of the association between covariates and disease status by fitting a prospective logistic regression model in genetic studies of disease investigators often gather additional information on response and covariate variables from family members of cases and controls the objective is to model the responses of all the family members in terms of the covariate data whittemore 1995 has discussed maximum likelihood methods for fitting a special class of logistic models to family data collected according to a particular design in the present paper we show that we can obtain efficient semiparametric maximum likelihood estimates for an arbitrary multivariate binary regression model by fitting a modified prospective model for a wide class of retrospective designs however in contrast to the situation with simple case control studies the prospective model will differ from the original model even when the model is logistic

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

an algorithm for maximizing expected log investment return let the random stock market vector x geq 0 be drawn according to a known distribution function f x x in r m a log optimal portfolio b ast is any portfolio b achieving maximal expected log return w ast sup b e ln b t x where the supremum is over the simplex b geq 0 sum i 1 m b i 1 an algorithm is presented for finding b ast the algorithm consists of replacing the portfolio b by the expected portfolio b b i e b i x i b t x corresponding to the expected proportion of holdings in each stock after one market period the improvement in w b after each iteration is lower bounded by the kullback leibler information number d b b between the current and updated portfolios thus the algorithm monotonically improves the return w an upper bound on w ast is given in terms of the current portfolio and the gradient and the convergence of the algorithm is established

fast matrix factorizations via discrete transmission lines abstract fast algorithms associated with the names of schur and levinson are known for the triangular factorization of symmetric positive definite toeplitz matrices and their inverses in this paper we show that these algorithms can be derived from simple arguments involving causality symmetry and energy conservation in discrete lossless transmission lines the results not only provide a nice interpretation of the classical schur and levinson algorithms and a certain toeplitz inversion formula of gohberg and semencul but they also show immediately that the same fast algorithms apply not only to toeplitz matrices but to all matrices with so called displacement inertia 1 1 the results have been helpful in suggesting new digital filter structures and in the study of nonstationary second order processes

power spectral density bounds corresp the determination of a power density spectrum from a finite set of correlation samples is an ill posed problem furthermore it is not possible even to bound the values that consistent power density spectra can take on at a particular point a more reasonable problem is to try to determine the total spectral power in some frequency interval although this power cannot be determined exactly upper and lower bounds on its possible values can be determined this observation leads to a unified treatment of certain classical and modern spectral estimation techniques and to new interpretations for two data adaptive spectral estimators maximum likelihood method mlm and data adaptive spectral estimator dase according to these new interpretations mlm and dase provide upper bounds on spectral power in a specified frequency region subject to the assumption that the spectral density is constant in that region these methods make no use of an extendibility constraint that can be used to obtain tight upper bounds as well as nontrivial lower bounds on power cybenko has studied a related problem of bounding windowed power for an arbitrary window with no assumptions about the form of the spectral density a new type of classical resolution limit for these bounds is derived and a numerical example is presented

likelihood analysis of power spectra and generalized moment problems we develop an approach to the spectral estimation that has been advocated by a ferrante et al time and spectral domain relative entropy a new approach to multivariate spectral estimation ieee trans autom control vol 57 no 10 pp 2561 2575 oct 2012 and in the context of the scalar valued covariance extension problem by p enqvist and j karlsson minimal itakura saito distance and covariance interpolation in proc 47th ieee conf decision control 2008 pp 137 142 the aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying gaussian stochastic process to that of a prior the approach is analogous to the framework of earlier work by byrnes georgiou and lindquist and can also be viewed as a generalization of the classical work by burg and jaynes on the maximum entropy method in this paper we present a new fast algorithm in the general case i e for general gaussian priors and show that for priors with a specific structure the solution can be given in closed form

on generalized spectral functions the parametrization of block hankel and block jacobi matrices and some root location problems abstract the parametrization of a strongly regular block hankel matrix in terms of certain block entries of an appropriately chosen sequence of block inverses is established this leads to a new recipe for solving the generalized spectral problem for jacobi matrices a generalized spectral function is introduced and together with the parametrization referred to above is used to investigate the root location of certain orthogonal matrix polynomials the matrix analogues of two classical stability tests are discussed

geometric aspects of the caratheodory extension problem abstract both euclidean geometric and non euclidean geometric descriptions for the regions of the solution set to the caratheodory extension problem are discussed in particular it is shown that all the solution functions are located inside a euclidean disk the weyl disk and a hyperbolic disk the apollonian disk the radius of each disk depends on the norm of the parametrizing schur functions moreover the so called maximum entropy solution is exactly the hyperbolic center of the apollonian disk while the associated power spectral density function is the geometric mean center of the real region where the weyl disk is projected to sensitivity analysis on the weyl radius and apollonian center due to the perturbation of the given finite moments is presented the applications of these results to the spectrum estimation and inverse scattering problems are discussed

maxentropic reconstruction of fourier and laplace transforms in this note the first of a series we present a maxentropic procedure to recover a function from the knowledge of a finite number of values of a linear integral transform and apply it to the case of the fourier or the laplace transforms also we consider the case in which the values of the transform are known to be polluted by noise

polynomials with no zeros on a face of the bidisk abstract we present a hilbert space geometric approach to the problem of characterizing the positive bivariate trigonometric polynomials that can be represented as the square of a two variable polynomial possessing a certain stability requirement namely no zeros on a face of the bidisk two different characterizations are given using a hilbert space structure naturally associated to the trigonometric polynomial one is in terms of a certain orthogonal decomposition the hilbert space must possess called the split shift orthogonality condition and another is an operator theoretic or matrix condition closely related to an earlier characterization due to the first two authors this approach allows several refinements of the characterization and it also allows us to prove a sums of squares decomposition which at once generalizes the cole wermer sums of squares result for two variable stable polynomials as well as a sums of squares result related to the schur cohn method for counting the roots of a univariate polynomial in the unit disk

semiparametric and nonparametric regression analysis of longitudinal data this article deals with the regression analysis of repeated measurements taken at irregular and possibly subject specific time points the proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable y at time t is related to the vector of possibly time varying covariates x through the equations e y t x t 0 t 0x t and e y t x t 0 t 0 t x t where 0 t is an arbitrary function of t 0 is a vector of constant regression coefficients and 0 t is a vector of time varying regression coefficients the stochastic structure of the process y is completely unspecified we develop a class of least squares type estimators for 0 which is proven to be n consistent and asymptotically normal with simple variance estimators furthermore we develop a closed form estimator for a cumulative function of 0 t which is shown to be n consistent and on proper normalization converges weakly to a zero mean gaussian pr

outcome vector dependent sampling with longitudinal continuous response data stratified sampling based on summary statistics the analysis of longitudinal trajectories usually focuses on evaluation of explanatory factors that are either associated with rates of change or with overall mean levels of a continuous outcome variable in this manuscript we introduce valid design and analysis methods that permit outcome dependent sampling of longitudinal data for scenarios where all outcome data currently exist but a targeted sub study is being planned in order to collect additional key exposure information on a limited number of subjects we propose a stratified sampling based on specific summaries of individual longitudinal trajectories and we detail an ascertainment corrected maximum likelihood approach for estimation using the resulting biased sample of subjects in addition we demonstrate that the efficiency of an outcome based sampling design relative to use of a simple random sample depends highly on the choice of outcome summary statistic used to direct sampling and we show a natural link between the goals of the longitudinal regression model and corresponding desirable designs using data from the childhood asthma management program where genetic information required retrospective ascertainment we study a range of designs that examine lung function profiles over four years of follow up for children classified according to their genotype for the il 13 cytokine

a unified systolic array for discrete cosine and sine transforms a linear systolic array for the discrete cosine transform discrete sine transform and their inverses is developed it generates the transform kernel values recursively compared to the scheme with the transform kernel values prestored in memory either inside or outside each processing element the clock period is shortened by a memory access time in addition the array pays no cost for prestorage the systolic array has the advantages of pipelinability regularity locality and scalability making it quite suitable for vlsi signal processing

semiparametric methods for response selective and missing data problems in regression summary suppose that data are generated according to the model f ylx 0 g x where y is a response and x are covariates we derive and compare semiparametric likelihood and pseudolikelihood methods for estimating 0 for situations in which units generated are not fully observed and in which it is impossible or undesirable to model the covariate distribution the probability that a unit is fully observed may depend on y and there may be a subset of covariates which is observed only for a subsample of individuals our key assumptions are that the probability that a unit has missing data depends only on which of a finite number of strata that y x belongs to and that the stratum membership is observed for every unit applications include case control studies in epidemiology field reliability studies and broad classes of missing data and measurement error problems our results make fully efficient estimation of 0 feasible and they generalize and provide insight into a variety of methods that have been proposed for specific problems

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

existence conditions and spreading properties of extreme entropy d dimensional distributions abstract the extremization of the information theoretic measures fisher information shannon entropy tsallis entropy which complementary describe the spreading of the physical states of natural systems gives rise to fundamental equations of motion and or conservation laws at times the associated extreme entropy distributions are known for some given constraints usually moments or radial expectation values in this work first we give the existence conditions of the maxent probability distributions in a d dimensional scenario where two moments not necessarily of consecutive order are known then we find general relations which involve four elements the extremized entropy the other two information theoretic measures and the variance of the extremum density in scenarios with different dimensionalities and moment constraints

reflection coefficient schur parameter representation for convex compact sets in the plane we obtain a one to one relation between the shape and orientation of a convex compact planar set and a complex valued reflection coefficient schur 1917 parameter sequence such that 1 the reflection coefficient magnitudes are less than or equal to one 2 if any reflection coefficient has a magnitude equal to one then all subsequent reflection coefficients are equal to zero and 3 the first reflection coefficient is equal to zero three additional independent parameters specify the position of the set in the plane and the size of the set specifically its circumference for a finite duration reflection coefficient sequence if the last nonzero reflection coefficient has a magnitude that is less than one then the boundary of the set is an infinitely differentiable convex curve the boundary is a convex polygon if and only if the magnitude of the last reflection coefficient is equal to one the number of sides of the polygon is equal to the index of the last reflection coefficient almost all planar convex compact sets have reflection coefficient sequences of infinite duration such sets can be accurately approximated with convex compact sets that are generated from relatively small numbers of reflection coefficients

lattice filter parameterization and modeling of nonstationary processes a general theory of constant parameter modular lattice models for discrete time nonstationary second order processes is presented a complete parametrization of such processes in terms of schur and congruence coefficients is derived by developing a natural connection between the displacement structure of a covariance matrix and schur s test for positive definiteness of matrices schur coeffieients provide a simple solution to problems of covariance extension and rational spectral approximation for nonstationary covariances and they coincide with the well known reflection or parcor coefficients when the covariance is stationary the congruence coefficients provide the time varying gains of a tapped delay line realization of the whitening filter for the process a constant parameter realization of the same filter is derived by combining a lattice filter structure with a tapped delay line both with time invariant gains this configuration also provides a recursive relation for the congruence coefficients namely a generalized levinson szego recursion the tapped delay line part of the realization can be eliminated by introducing the concept of admissibility admissibility also reduces the parametrization of a nonstationary process to schur coefficients alone in analogy to stationary processes which are completely characterized by their parcor coefficients

displacement pressure based mixed finite element formulations for acoustic fluid structure interaction problems summary we present reliable finite element discretizations based on displacement pressure interpolations for the analysis of acoustic fluid structure interaction problems the finite element interpolations are selected using the inf sup condition and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation we show that with our analysis procedure no spurious non zero frequencies are encountered as heretofore calculated with other displacement based discretizations 1997 by john wiley sons ltd

inverse scattering for discrete transmission line models this paper presents several methods for the identification of the impedance and reflection coefficient profile of a nonuniform discrete transmission line from its response to a given forcing function this problem is the prototype for a wealth of one dimensional inverse scattering problems arising in various fields a unified straightforward approach is presented providing all known inversion procedures and some novel ones the derivations readily follow from causality of signal propagation on the transmission line it is shown that a direct exploitation of the signal propagation model leads to recursive computationally efficient and reliable inversion algorithms in particular the relationships between layer peeling schur type difference equation and layer adjoining levinson type integral equation algorithms are clearly displayed

a constructive proof of the gohberg semencul formula abstract gohberg and semencul gave some elegant formulas for the inverse of a toeplitz matrix as a difference of products of lower and upper triangular toeplitz matrices there are several algebraic and analytic proof of these formulas here we give a constructive proof for two of the gohberg semencul formulas under the assumption that the matrices are strongly nonsingular i e all leading minors are nonzero this assumption is stronger than necessary but it enables fast o n 2 constructions for the entries in the gohberg semencul formulas our method also gives a new proof of the relation between the reflection coefficients of a toeplitz matrix and its inverse

unitary orthogonalization process all methods for solving least squares problems involve orthogonalization in one way or another certain fundamental estimation and prediction problems of signal processing and time series analysis can be formulated as least squares problems in these problems the sequence that is to be orthogonalized is generated by an underlying unitary operator a prime example of an efficient orthogonalization procedure for this class of problems is gragg s isometric arnoldi process which is the abstract encapsulation of a number of concrete algorithms in this paper we discuss a two sided orthogonalization process that is equivalent to gragg s process but has certain conceptual strengths that warrant its introduction the connections with classical algorithms of signal processing are discussed

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

conditional likelihood inference under complex ascertainment using data augmentation summary in many applications particularly in genetics samples are drawn under complex ascertainment rules for example families may only be selected for study if two or more siblings have trait values exceeding some threshold the correct likelihood for inference in such situations involves the probabilities of ascertainment and these are frequently intractable a consistent but not fully efficient method of analysis of such studies is proposed the main idea is to augment the data with additional pseudo observations simulated under the ascertainment scheme and to analyse using a conditional likelihood for discrimination between true observations and pseudoobservations ascertainment probabilities cancel in this likelihood the method is illustrated with a simple example involving left truncated failure times

properties of cross entropy minimization the principle of minimum cross entropy minimum directed divergence minimum discrimination information is a general method of inference about an unknown probability density when there exists a prior estimate of the density and new information in the form of constraints on expected values various fundamental properties of cross entropy minimization are proven and collected in one place cross entropy s well known properties as an information measure are extended and strengthened when one of the densities involved is the result of cross entropy minimization the interplay between properties of cross entropy minimization as an inference procedure and properties of cross entropy as an information measure is pointed out examples are included and general analytic and computational methods of finding minimum cross entropy probability densities are discussed

maximum entropy and maximum likelihood in spectral estimation the power spectral measure an informative feature of a stationary time discrete stochastic process describes the relative strength of uncorrelated frequency components that compose the process in spectral estimation one wants to describe the spectral measures of processes having a prescribed initial block of autocorrelation coefficients in the continuum of possibilities two types are frequently distinguished the one parameter family of maximum likelihood spectral measures so named because they carry the largest possible weight at one specified frequency and the maximum entropy spectral measure which is often considered to be the most representative of the entire set of possible solutions although these choices are very different representing respectively the most and least predictable of the eligible processes we show that the maximum entropy measure is exactly the uniform average of the family of maximum likelihood measures over its parameter

existence of smooth solutions to the classical moment problems let s 0 s 1 be a given sequence and define s n s n for n 0 if n q m s m n 0 holds for all finite sequences n n z then it is known that there is a positive borel measure on the circle t such that s n 75 e int d t and conversely our main theorem provides a necessary and sufficient condition on the sequence s n that the measure may be chosen to be smooth

comments on and correction to axiomatic derivation of the principle of maximum entropy and the principle of minimum cross entropy jan 80 26 37 corresp an error in the subject paper is pointed out when the axioms given there are restricted to the discrete case they do not imply the discrete case of the principle of minimum cross entropy the principle is shown to follow however from the adoption of an additional axiom if new information is consistent with a prior estimate of a probability distribution then the posterior estimate equals the prior minor other improvements and corrections to the arguments in the paper are made

orthogonal polynomials on the unit circle distribution of zeros departamento de matemritica aplicada escuela tpcnica superior de ingenieros industriales universidad de vigo apartado de correos no 62 36280 vigo spain received 30 august 1990 revised 29 january 1991 abstract marcellan f and e godoy orthogonal polynomials on the unit circle distribution of zeros journal of computational and applied mathematics 37 1991 195 208 in this paper we summarize some results concerning zeros of orthogonal polynomials with respect to an indefinite inner product we analyze the inverse problem i e a discrete representation for the functional in terms of the n th orthogonal polynomial finally some numerical examples are shown keywords toeplitz matrices orthogonal polynomials on the unit circle zeros quadrature formulas

solution of the general moment problem via a one parameter imbedding this paper presents a computational theory for the general scalar moment problem the formalism is sufficiently general to encompass problems in sensor arrays with arbitrary geometry and dynamics and in nonuniform multidimensional sampling given a finite set of moments the theory provides a test for the existence of a positive measure which is consistent with such data at the same time the theory also provides a characterization of all such consistent positive measures it should be noted that classical results e g in the theory of the trigonometric moment problem hamburger stieljes nevanlinna pick interpolation etc are not applicable to the general setting sought herein where there is no natural shift operator in the space spanned by the integration kernels the centerpiece of the theory is a differential equation which depends on the given finite set of moments and on an arbitrary positive function spl psi which plays the role of a free parameter the differential equation has an exponentially attractive point of equilibrium if and only if there exists a consistent positive measure for each spl psi the fixed point determines a corresponding measure suitable choice of spl psi allows recovering any measure which is consistent with the data the fixed point of the differential equation corresponds to an extremum of an entropy like functional and the differential equation is constructed via an appropriate homotopy that follows changes in the lagrange multipliers from a convenient starting value to a value for the multipliers that corresponds to the given moments

a semiparametric empirical likelihood method for data from an outcome dependent sampling scheme with a continuous outcome summary outcome dependent sampling ods schemes can be a cost effective way to enhance study efficiency the case control design has been widely used in epidemiologic studies however when the outcome is measured on a continuous scale dichotomizing the outcome could lead to a loss of efficiency recent epidemiologic studies have used ods sampling schemes where in addition to an overall random sample there are also a number of supplemental samples that are collected based on a continuous outcome variable we consider a semiparametric empirical likelihood inference procedure in which the underlying distribution of covariates is treated as a nuisance parameter and is left unspecified the proposed estimator has asymptotic normality properties the likelihood ratio statistic using the semiparametric empirical likelihood function has wilks type properties in that under the null it follows a chi square distribution asymptotically and is independent of the nuisance parameters our simulation results indicate that for data obtained using an ods design the semiparametric empirical likelihood estimator is more efficient than conditional likelihood and probability weighted pseudolikelihood estimators and that ods designs along with the proposed estimator can produce more efficient estimates than simple random sample designs of the same size we apply the proposed method to analyze a data set from the collaborative perinatal project cpp an ongoing environmental epidemiologic study to assess the relationship between maternal polychlorinated biphenyl pcb level and children s iq test performance

euler equations implicit schemes and boundary conditions implicit boundary condition procedures are presented for use with implicit finite difference schemes for the unsteady euler equations this new boundary point treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations along with the theoretical background the practical application of the method to several types of boundaries is also explained using several examples the specific boundary conditions covered include subsonic inflow and outflow surface tangency and shock waves the example problems include one dimensional laval nozzle flow dual throat rocket engine nozzle flow and supersonic flow past a sphere the implicit boundary treatment permits the use of large time steps allowing the finite difference algorithm to converge to the asymptotic steady state much faster than schemes that use explicitly applied boundary conditions at least an order of magnitude increase in computational speed is demonstrated in the examples shown background t he growing popularity of solutions to the euler equations in transonics and their continued application in supersonics have increased the need for quicker solutions the potential of implicit schemes in this direction has not been fully exploited for want of correct implicit application of boundary conditions the predominant use of implicit algorithms for the navier stokes equations has partly been responsible for the neglect of implicit boundary point treatment for the euler equations thus there is a need for correct and stable procedures for the easy implicit application of boundary conditions such methods will serve the two purposes of 1 reaching time asymptotic steady state faster and 2 permitting a time step for truly unsteady flow that is not necessarily restricted by the cfl stability criterion but is based upon the magnitude of the transients for clues and information on how to construct such boundary condition procedures one must turn to the mathematical theory of characteristi cs for hyperbolic systems of equations the unsteady euler equations belong to this category the theory for hyperbolic systems is rich with information on signal propagation directions the characteristics theory clearly points to the number of boundary conditions that may and need be prescribed without overdetermining the solution boundary condition procedures based on this theory have been known and applied for several years by kentzer 1 porter and coakley 2 de neef 3 and others in earlier work by this author 4 5 easily understood and implementable methods for boundary point treatment were presented however all of the above techniques were developed for explicit finite difference schemes it seems that it must be easy to extend such methodologies based on mathematical theory for hyperbolic systems to implicit finite difference schemes and indeed it is simple enough the rest of this paper describes such implicit boundary condition procedures the given examples illustrate in detail the application of the proposed methodology to specific types of boundaries and demonstrate the merits of the new scheme

singularly positive definite sequences and parametrization of extreme points abstract in the truncated classical moment problems the set of all solutions constitutes a convex set of positive measures we are concerned with extreme points of this convex set it is shown that the extreme points can be characterized in terms of the singularly positive definite extensions of a given positive definite finite sequence

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

on a parabolic quadrilateral finite element for compressible flows abstract we present a 9 node finite element for compressible flow solutions a high order derivative upwind term and a shock capturing term are employed for stability and accuracy of the formulation we give the solutions of various example problems to illustrate our experiences with the element

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

truncated trigonometric moment problems and determinate measures abstract we consider the problem of deciding whether or not a given positive borel measure on the n dimensional torus t n is s determinate which means that is entirely determined by the subset of its fourier coefficients k k s where s is an arbitrary subset of z n containing 0 and with the property that k s whenever k s we give necessary and sufficient conditions for s determinacy and show that when s is a finite set the validity of this property can be verified algebraically by an algorithmic procedure involving trigonometric polynomials with spectrum in s vanishing on the support of and satisfying certain positivity properties

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100