conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

the z spl pi m algorithm a method for interferometric image reconstruction in sar sas this paper presents an effective algorithm for absolute phase not simply modulo 2 spl pi estimation from incomplete noisy and modulo 2 spl pi observations in interferometric aperture radar and sonar insar insas the adopted framework is also representative of other applications such as optical interferometry magnetic resonance imaging and diffraction tomography the bayesian viewpoint is adopted the observation density is 2 spl pi periodic and accounts for the interferometric pair decorrelation and system noise the a priori probability of the absolute phase is modeled by a compound gauss markov random field cgmrf tailored to piecewise smooth absolute phase images we propose an iterative scheme for the computation of the maximum a posteriori probability map absolute phase estimate each iteration embodies a discrete optimization step z step implemented by network programming techniques and an iterative conditional modes icm step spl pi step accordingly the algorithm is termed z spl pi m where the letter m stands for maximization an important contribution of the paper is the simultaneous implementation of phase unwrapping inference of the 2 spl pi multiples and smoothing denoising of the observations this improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low pass filtered prior to unwrapping a set of experimental results comparing the proposed algorithm with alternative methods illustrates the effectiveness of our approach

exponential family mixture models with least squares estimators pour une densite arbitraire d une famille exponentielle a un parametre on montre comment construire une distribution de melange sur le parametre de telle sorte que la distribution resultante soit une famille exponentielle a deux ou plusieurs parametres

a combined estimating function approach for fitting stationary point process models a composite likelihood technique based on pairwise contributions provides a computationally simple but potentially inefficient approach for fitting spatial point process models we propose a new estimation procedure that improves the efficiency our approach combines estimating functions derived from pairwise composite likelihood estimation and estimating functions that account for correlations among the pairwise contributions our method can be used to fit a variety of parametric spatial point process models and can yield more efficient estimators for the clustering parameters than pairwise composite likelihood estimation we demonstrate the efficacy of our proposed method through a simulation study and an application to the longleaf pine data

lorelogram a regression approach to exploring dependence in longitudinal categorical responses abstract we propose flexible regression estimators of the marginal pairwise log odds ratio measure of association for longitudinal categorical responses the function that we estimate is the log odds ratio analog of the correlogram hence we name the function the lorelogram measuring the association of categorical responses on the log odds scale allows ease of interpretation and allows pairwise association to remain unconstrained by the marginal means a feature not shared by correlations with binary or multinomial responses estimation of the function is achieved through the use of standard parametric estimating equations or through an extension of generalized additive models that allows nonparametric estimation of dependence functions for fixed smoothing parameters we apply the methodology to binary longitudinal data where scientific interest focuses on the dependence structure

quadratic inference functions for varying coefficient models with longitudinal data nonparametric smoothing methods are used to model longitudinal data but the challenge remains to incorporate correlation into nonparametric estimation procedures in this article we propose an efficient estimation procedure for varying coefficient models for longitudinal data the proposed procedure can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models the proposed approach yields a more efficient estimator than the generalized estimation equation approach when the working correlation is misspecified for varying coefficient models it is often of interest to test whether coefficient functions are time varying or time invariant we propose a unified and efficient nonparametric hypothesis testing procedure and further demonstrate that the resulting test statistics have an asymptotic chi squared distribution in addition the goodness of fit test is applied to test whether the model assumption is satisfied the corresponding test is also useful for choosing basis functions and the number of knots for regression spline models in conjunction with the model selection criterion we evaluate the finite sample performance of the proposed procedures with monte carlo simulation studies the proposed methodology is illustrated by the analysis of an acquired immune deficiency syndrome aids data set

new classes of analytic solutions of the two level problem a simple technique to find analytic solutions of the time dependent schrodinger equations is introduced a number of three parametric classes of the two level problem integrable in terms of the gauss hypergeometric function including all presently known analytically solvable models are derived

assessing robustness of generalised estimating equations and quadratic inference functions in the presence of data contamination or outliers some empirical studies have indicated that the two methods of generalised estimating equations and quadratic inference functions appear to have rather different robustness behaviour this paper presents a theoretical investigation from the perspective of the influence function to identify the causes for the difference we show that quadratic inference functions lead to bounded influence functions and the corresponding m estimator has a redescending property but the generalised estimating equation approach does not we also illustrate that unlike generalised estimating equations quadratic inference functions can still provide consistent estimators even if part of the data is contaminated we conclude that the quadratic inference function is a preferable method to the generalised estimating equation as far as robustness is concerned this conclusion is supported by simulations and real data examples

phase unwrapping via graph cuts phase unwrapping is the inference of absolute phase from modulo 2pi phase this paper introduces a new energy minimization framework for phase unwrapping the considered objective functions are first order markov random fields we provide an exact energy minimization algorithm whenever the corresponding clique potentials are convex namely for the phase unwrapping classical lp norm with pges1 its complexity is kt n 3n where k is the length of the absolute phase domain measured in 2pi units and t n m is the complexity of a max flow computation in a graph with n nodes and m edges for nonconvex clique potentials often used owing to their discontinuity preserving ability we face an np hard problem for which we devise an approximate solution both algorithms solve integer optimization problems by computing a sequence of binary optimizations each one solved by graph cut techniques accordingly we name the two algorithms puma for phase unwrapping max flow min cut a set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state of the art phase unwrapping algorithms

improving generalised estimating equations using quadratic inference functions summary generalised estimating equations enable one to estimate regression parameters consistently in longitudinal data analysis even when the correlation structure is misspecified however under such misspecification the estimator of the regression parameter can be inefficient in this paper we introduce a method of quadratic inference functions that does not involve direct estimation of the correlation parameter and that remains optimal even if the working correlation structure is misspecified the idea is to represent the inverse of the working correlation matrix by the linear combination of basis matrices a representation that is valid for the working correlations most commonly used both asymptotic theory and simulation show that under misspecified working assumptions these estimators are more efficient than estimators from generalised estimating equations this approach also provides a chi squared inference function for testing nested models and a chi squared regression misspecification test furthermore the test statistic follows a chi squared distribution asymptotically whether or not the working correlation structure is correctly specified

using the matrix pencil method to solve phase unwrapping this correspondence presents a phase unwrapping pu algorithm based on the matrix pencil mp method a brief discussion is given on the relationship between pu and instantaneous frequency estimation the pu algorithm and its properties are presented in detail results show a significant improvement in pu with respect to previous algorithms

incorporating correlation for multivariate failure time data when cluster size is large we propose a new estimation method for multivariate failure time data using the quadratic inference function qif approach the proposed method efficiently incorporates within cluster correlations therefore it is more efficient than those that ignore within cluster correlation furthermore the proposed method is easy to implement unlike the weighted estimating equations in cai and prentice 1995 biometrika 82 151 164 it is not necessary to explicitly estimate the correlation parameters this simplification is particularly useful in analyzing data with large cluster size where it is difficult to estimate intracluster correlation under certain regularity conditions we show the consistency and asymptotic normality of the proposed qif estimators a chi squared test is also developed for hypothesis testing we conduct extensive monte carlo simulation studies to assess the finite sample performance of the proposed methods we also illustrate the proposed methods by analyzing primary biliary cirrhosis pbc data

model diagnostic tests for selecting informative correlation structure in correlated data in the generalized method of moments approach to longitudinal data analysis unbiased estimating functions can be constructed to incorporate both the marginal mean and the correlation structure of the data increasing the number of parameters in the correlation structure corresponds to increasing the number of estimating functions thus building a correlation model is equivalent to selecting estimating functions this paper proposes a chi squared test to choose informative unbiased estimating functions we show that this methodology is useful for identifying which source of correlation it is important to incorporate when there are multiple possible sources of correlation this method can also be applied to determine the optimal working correlation for the generalized estimating equation approach

bayesian approaches to phase unwrapping theoretical study the problem of phase unwrapping of two dimensional 2 d phase signals has gained a considerable interest it deals with the problem of estimating reconstructing an absolute phase from the observation of its noisy principal wrapped values this is an ill posed problem since many possible solutions correspond to a given observation many phase unwrapping algorithms have been proposed relying on different constraints for the phase signal sampling process or the nature e g smoothness regularity of the phase signal we look at these algorithms from the bayesian point of view estimation theory and analyze the role of the prior assumptions studying their equivalencies to the regularization constraints already used this study leads to the development of the two new phase unwrapping algorithms which are able to work in quite difficult conditions of aliasing and noise the theoretical study of the analyzed schemes is illustrated by some experiments on synthetic phase signals

absolute phase image reconstruction a stochastic nonlinear filtering approach this paper formulates and proposes solutions to the problem of estimating reconstructing the absolute not simply modulo 2 spl pi phase of a complex random field from noisy observations of its real and imaginary parts this problem is representative of a class of important imaging techniques such as interferometric synthetic aperture radar optical interferometry magnetic resonance imaging and diffraction tomography we follow a bayesian approach then not only a probabilistic model of the observation mechanism but also prior knowledge concerning the phase image to be reconstructed are needed we take as prior a nonsymmetrical half plane autoregressive nshp ar gauss markov random field gmrf based on a reduced order state space formulation of the linear nshp ar model and on the nonlinear observation mechanism a recursive stochastic nonlinear filter is derived the corresponding estimates are compared with those obtained by the extended kalman bucy filter a classical linearizing approach to the same problem a set of examples illustrate the effectiveness of the proposed approach

blind source separation semiparametric statistical approach the semiparametric statistical model is used to formulate the problem of blind source separation the method of estimating functions is applied to this problem it is shown that an estimator of the mixing matrix or its learning version can be described in terms of an estimating function the statistical efficiencies of these algorithms are studied the main results are as follows 1 the space consisting of all the estimating functions is derived 2 the space is decomposed into the orthogonal sum of the admissible part and a redundant ancillary part for any estimating function one can find a better or equally good estimator in the admissible part 3 the fisher efficient that is asymptotically best estimating functions are derived 4 the stability of learning algorithms is studied

estimating equations for parameters in means and covariances of multivariate discrete and continuous responses generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response these equations are to be solved jointly with score equations from a generalized linear model for mean parameters a class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion and proposals for the use of such equations are developed comments on the relative merits of the ad hoc and model based approaches to estimation are given and a regression illustration with a bivariate response is provided

building adaptive estimating equations when inverse of covariance estimation is difficult summary to construct an optimal estimating function by weighting a set of score functions we must either know or estimate consistently the covariance matrix for the individual scores in problems with high dimensional correlated data the estimated covariance matrix could be unreliable the smallest eigenvalues of the covariance matrix will be the most important for weighting the estimating equations but in high dimensions these will be poorly determined generalized estimating equations introduced the idea of a working correlation to minimize such problems however it can be difficult to specify the working correlation model correctly we develop an adaptive estimating equation method which requires no working correlation assumptions this methodology relies on finding a reliable approximation to the inverse of the variance matrix in the quasi likelihood equations we apply a multivariate generalization of the conjugate gradient method to find estimating equations that preserve the information well at fixed low dimensions this approach is particularly useful when the estimator of the covariance matrix is singular or close to singular or impossible to invert owing to its large size

two dimensional phase unwrapping using a minimum spanning tree algorithm phase unwrapping refers to the determination of phase from modulo 2 pi data some of which may not be reliable in 2d this is equivalent to confining the support of the phase function to one or more arbitrarily shaped regions a phase unwrapping algorithm is presented which works for 2d data known only within a set of nonconnected regions with possibly nonconvex boundaries the algorithm includes the following steps segmentation to identify connectivity phase unwrapping within each segment using a taylor series expansion phase unwrapping between disconnected segments along an optimum path and filling of phase information voids the optimum path for intersegment unwrapping is determined by a minimum spanning tree algorithm although the algorithm is applicable to any 2d data the main application addressed is magnetic resonance imaging mri where phase maps are useful

conditional estimation for generalized linear models when covariates are subject specific parameters in a mixed model for longitudinal measurements the relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest and a relevant framework is that of a generalized linear model with covariates that are subject specific random effects in a linear mixed model for the longitudinal measurements naive implementation by imputing subject specific effects from individual regression fits yields biased inference and several methods for reducing this bias have been proposed these require a parametric normality assumption on the random effects which may be unrealistic adapting a strategy of stefanski and carroll 1987 biometrika74 703 716 we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution the methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause

a new class of analytic solutions of the two state problem a new class of solutions of the time dependent schrodinger equation is found for the two state problem often encountered in quantum optics magnetic resonance and atomic collisions the authors use the riemann papperitz differential equation to find exact solutions in terms of hypergeometric functions they consider only cases in which the final occupation probabilities are elementary functions of the parameters of the model

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

joint models for a primary endpoint and multiple longitudinal covariate processes summary joint models are formulated to investigate the association between a primary endpoint and features of multiple longitudinal processes in particular the subject specific random effects in a multivariate linear random effects model for multiple longitudinal processes are predictors in a generalized linear model for primary endpoints li zhang and davidian 2004 biometrics60 1 7 proposed an estimation procedure that makes no distributional assumption on the random effects but assumes independent within subject measurement errors in the longitudinal covariate process based on an asymptotic bias analysis we found that their estimators can be biased when random effects do not fully explain the within subject correlations among longitudinal covariate measurements specifically the existing procedure is fairly sensitive to the independent measurement error assumption to overcome this limitation we propose new estimation procedures that require neither a distributional or covariance structural assumption on covariate random effects nor an independence assumption on within subject measurement errors these new procedures are more flexible readily cover scenarios that have multivariate longitudinal covariate processes and can be implemented using available software through simulations and an analysis of data from a hypertension study we evaluate and illustrate the numerical performances of the new estimators

expansions for some confluent hypergeometric functions power series for the parabolic cylinder function dv z are derived from known addition theorems thus enabling a more compact and efficient expression of the function one of the expansions is applied to find an asymptotic approximation for the function as mod v mod to infinity with mod arg v mod pi next a large argument z asymptotic addition theorem is derived from an integral representation of dv z before extending this type of summation theorem to the two general confluent hypergeometric functions motivating mathematical applications to three integration problems are given as examples of the practical usefulness of the formulae

when is the student t statistic asymptotically standard normal let x x i i in mathbb n be independent identically distributed random variables it is shown that the student t statistic based upon the sample x i i 1 n is asymptotically n 0 1 if and only if x is in the domain of attraction of the normal law it is also shown that for any x if the self normalized sums u n sum i 1 n x i sum i 1 n x i 2 1 2 n in mathbb n are stochastically bounded then they are uniformly subgaussian that is sup n mathbb e exp lambda u n 2 infty for some lambda 0

model based phase unwrapping of 2 d signals a parametric model and a corresponding parameter estimation algorithm for unwrapping 2 d phase functions are presented the proposed algorithm performs global analysis of the observed signal since this analysis is based on parametric model fitting the proposed phase unwrapping algorithm has low sensitivity to phase aliasing due to low sampling rates and noise as well as to local errors in its first step the algorithm fits a 2 d polynomial model to the observed phase the estimated phase is then used as a reference information that directs the actual phase unwrapping process the phase of each sample of the observed field is unwrapped by increasing decreasing it by the multiple of 2 spl pi which is the nearest to the difference between the principle value of the phase and the estimated phase value at this coordinate in practical applications the entire phase function cannot be approximated by a single 2 d polynomial model hence the observed field is segmented and each segment is fit with its own model once the phase model of the observed field has been estimated we can repeat the model based unwrapping procedure described earlier for the case of a single segment and a single model field

identification and restoration of noisy blurred images using the expectation maximization algorithm a maximum likelihood approach to the blur identification problem is presented the expectation maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way in order to improve the performance of the identification algorithm low order parametric image and blur models are incorporated into the identification method the resulting iterative technique simultaneously identifies and restores noisy blurred images

improved methods for the marginal analysis of longitudinal data in the presence of time dependent covariates generalized estimating equations gees are commonly used for the marginal analysis of longitudinal data in order to obtain consistent regression parameter estimates these estimating equations must be unbiased however in the presence of certain types of time dependent covariates these equations can be biased unless they incorporate the independence working correlation structure moreover in this case regression parameter estimation can be very inefficient because not all valid moment conditions are incorporated within the corresponding estimating equations therefore approaches based on the generalized method of moments or quadratic inference functions have been proposed in order to utilize all valid moment conditions however we have found in previous studies as well as the current study that such methods will not always provide valid inference and can also be improved upon in terms of finite sample regression parameter estimation therefore we propose both a modified gee approach and a method selection strategy in order to ensure valid inference with the goal of improving regression parameter estimation in a simulation study and application example we compare existing and proposed methods and demonstrate that our modified gee approach performs well and the correlation information criterion has good accuracy with respect to selecting the best approach in terms of regression parameter estimation copyright 2017 john wiley sons ltd

a basic two state model for bosonic field theories with a cubic nonlinearity a basic nonlinear two state model generic in classical and bosonic field theories with a cubic nonlinearity is considered for the class of models with constant external field amplitude a general strategy for attacking the problem is developed based on the reduction of the initial system of equations for the semi classical atom molecule amplitudes to a nonlinear volterra integral equation for the molecular probability a uniformly convergent series solution to the problem is constructed for the weak interaction limit the landau zener model is considered as a specific example the first approximation term is derived and an asymptotic expression for the nonlinear transition probability is established in the weak interaction regime

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

analytic treatment of the polariton problem for a smooth interface we study the polariton problem for smooth boundaries i e whether or not there exist some localized solutions of maxwell s equations for different types of smooth spatial variation of complex dielectric and or magnetic permittivity tensors for a particular dielectric permittivity profile varying according to the hyperbolic tangent law the singular term is mathematically strongly taken into account in maxwell s equations not in the boundary conditions the problem is then reduced to the canonical form of heun s equation possessing four regular singular points the solution to heun s equation as a power series is constructed and an approximate solution involving a combination of two incomplete betafunctions is derived further the exact eigenvalue solution to the polariton problem as a series in terms of incomplete beta functions or equivalently gauss hypergeometric functions is constructed it is shown that the dispersion relation for the polariton wavenumber does not depend on the interface transition layer width i e it is always exactly the same as the one derived in the limit of abrupt interface we conjecture that the polariton wavenumber eigenvalue depends on either zeros of the dielectric permittivity variance profile or the poles of the logarithmic derivative of the latter

semiparametric inference in matched case control studies with missing covariate data summary we consider the problem of matched studies with a binary outcome that are analysed using conditional logistic regression and for which data on some covariates are missing for some study participants methods for this problem involve either modelling the distribution of missing covariates or modelling the probability of data being missing for this second approach the previously proposed method did not make use of data for those persons with missing covariate data except in the model for the missingness we propose a new class of estimators that use outcome and available covariate data for all study participants and show that a particular member of this class always has better efficiency than the previously proposed estimator we illustrate the efficiency gains that are possible with our approach using simulated data

unsupervised image restoration and edge location using compound gauss markov random fields and the mdl principle discontinuity preserving bayesian image restoration typically involves two markov random fields one representing the image intensities gray levels to be recovered and another one signaling discontinuities edges to be preserved the usual strategy is to perform joint maximum a posterori map estimation of the image and its edges which requires the specification of priors for both fields instead of taking an edge prior we interpret discontinuities in fact their locations as deterministic unknown parameters of the compound gauss markov random field cgmrf which is assumed to model the intensities this strategy should allow inferring the discontinuity locations directly from the image with no further assumptions however an additional problem emerges the number of parameters edges is unknown to deal with it we invoke the minimum description length mdl principle according to mdl the best edge configuration is the one that allows the shortest description of the image and its edges taking the other model parameters noise and cgmrf variances also as unknown we propose a new unsupervised discontinuity preserving image restoration criterion implementation is carried out by a continuation type iterative algorithm which provides estimates of the number of discontinuities their locations the noise variance the original image variance and the original image itself restored image experimental results with real and synthetic images are reported

phase unwrapping of mr phase images using poisson equation the authors have developed a technique based on a solution of the poisson equation to unwrap the phase in magnetic resonance mr phase images the method is based on the assumption that the magnitude of the inter pixel phase change is less than spl pi per pixel therefore the authors obtain an estimate of the phase gradient by wrapping the gradient of the original phase image the problem is then to obtain the absolute phase given the estimate of the phase gradient the least squares ls solution to this problem is shown to be a solution of the poisson equation allowing the use of fast poisson solvers the absolute phase is then obtained by mapping the ls phase to the nearest multiple of 2 k from the measured phase the proposed technique is evaluated using mr phase images and is proven to be robust in the presence of noise an application of the proposed method to the 3 point dixon technique for water and fat separation is demonstrated

exactly soluble two state quantum models with linear couplings a class of exact analytic solutions of the time dependent schrequation is presented for a two state quantum system coherently driven by a nonresonant external field the coupling is a linear function of time with a finite duration and the detuning is constant four special models are considered in detail namely the shark double shark tent and zigzag models the exact solution is derived by rotation of the landau zener propagator at an angle of 4 and is expressed in terms of weber s parabolic cylinder function approximations for the transition probabilities are derived for all four models by using the asymptotics of the weber function these approximations demonstrate various effects of physical interest for each model

new classes of analytic solutions of the three state problem a rich multiparametric class of solutions of the time dependent schrodinger equations including many integrable cases known at present of the three state problem is derived in addition the class contains an infinite number of new multiparametric integrable subfamilies examples of such four parametric new subfamilies of asymmetric in general amplitude and frequency modulation functions permitting solution of the three state problem in terms of the clausen function are presented

using modified approaches on marginal regression analysis of longitudinal data with time dependent covariates quadratic inference functions qifs and estimating equations using the conjugate gradient method cgm for fitting marginal models to longitudinal data show appealing features in improving the efficiency without making assumptions on the correlation structure however our simulation study shows that both methods produce biased and inefficient estimates of regression parameters when time dependent covariates are present in this paper we extend both the qif and cgm methods for fitting marginal models to longitudinal data with time dependent covariates the idea is to restrict the moment conditions to the ones that are only valid to certain types of time dependent covariates our simulations show that efficiency on estimating regression parameters is achieved using modified approaches furthermore we apply the modified approach to anthropometric screening data to evaluate the association between body mass index and morbidity in children in the philippines

phase local approximation phasela technique for phase unwrap from noisy data the local polynomial approximation lpa is a nonparametric regression technique with pointwise estimation in a sliding window we apply the lpa of the argument of cos and sin in order to estimate the absolute phase from noisy wrapped phase data using the intersection of confidence interval ici algorithm the window size is selected as adaptive pointwise varying this adaptation gives the phase estimate with the accuracy close to optimal in the mean squared sense for calculations we use a gauss newton recursive procedure initiated by the phase estimates obtained for the neighboring points it enables tracking properties of the algorithm and its ability to go beyond the principal interval pi pi and to reconstruct the absolute phase from wrapped phase observations even when the magnitude of the phase difference takes quite large values the algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state of the art algorithms developed for noisy phase unwrap the theoretical analysis produced for the accuracy of the pointwise estimates is used for justification of the ici adaptation algorithm

on the use of a working correlation matrix in using generalised linear models for repeated measures summary in a seminal paper liang zeger 1986 extended the use of generalised linear models to repeated measures data they based the analysis on specifications for the means and variances of the observations as usual for generalised linear models but showed how specifications for the correlations between measurements made on the same unit could be avoided by using a working correlation matrix in some cases the parameters involved in this matrix are subject to an uncertainty of definition which can lead to a breakdown of the asymptotic properties of the estimators

the integrability of the two state problem in terms of confluent hypergeometric functions the reduction of the two state problem to the confluent hypergeometric equation via complex transformations of independent variables is considered it is shown that all the known analytically integrable cases can be generalized to a single formula a new class of integrable models of the two state problem in terms of confluent hypergeometric functions is presented

marginal regression analysis of longitudinal data with time dependent covariates a generalized method of moments approach summary we develop a new approach to using estimating equations to estimate marginal regression models for longitudinal data with time dependent covariates our approach classifies time dependent covariates into three types types i ii and iii the type of covariate determines what estimating equations can be used involving the covariate we use the generalized method of moments to make optimal use of the estimating equations that are made available by the covariates previous literature has suggested the use of generalized estimating equations with the independent working correlation when there are time dependent covariates we conduct a simulation study that shows that our approach can provide substantial gains in efficiency over generalized estimating equations with the independent working correlation when a time dependent covariate is of types i or ii and our approach remains consistent and comparable in efficiency with generalized estimating equations with the independent working correlation when a time dependent covariate is of type iii we apply our approach to analyse the relationship between the body mass index and future morbidity among children in the philippines

optimal combination of estimating equations in the analysis of multilevel nested correlated data multilevel nested correlated data often arise in biomedical research examples include teeth nested within quadrants in a mouth or students nested within classrooms in schools in some settings cluster sizes may be large relative to the number of independent clusters and the degree of correlation may vary across clusters when cluster sizes are large fitting marginal regression models using generalized estimating equations with flexible correlation structures that reflect the nested structure may fail to converge and result in unstable covariance estimates also the use of patterned nested working correlation structures may not be efficient when correlation varies across clusters this paper describes a flexible marginal regression modeling approach based on an optimal combination of estimating equations particular within cluster and between cluster data contrasts are used without specification of the working covariance structure and without estimation of covariance parameters the method involves estimation of the covariance matrix only for the vector of component estimating equations which is typically of small dimension rather than the covariance matrix of the observations within a cluster which may be of large dimension in settings where the number of clusters is large relative to the cluster size the method is stable and is highly efficient while maintaining appropriate coverage levels performance of the method is investigated with simulation studies and an application to a periodontal study

reducing sensitivity to nuisance parameters in semiparametric models a quasi score method summary this paper proposes a semiparametric extension of the projected score method of waterman lindsay 1996 for the elimination of nuisance parameters the procedure addresses cases where only the mean and the variance of the response variable are specified and where the mean function involves both parameters of interest and nuisance parameters important applications of the semiparametric model include quasilikelihood models for matched designs and for measurement error models carroll stefanski 1990 as a result of the optimality and information unbiasedness of the quasi score function a second order quasi score basis of estimating functions for the nuisance parameter is derived second order locally ancillary estimating functions small mcleish 1994 pp 81 4 are then obtained by solving a simple linear system that corresponds to a true projection for canonical exponential family distributions asymptotic arguments and simulation work show that the impact of nuisance parameters is considerably reduced when adopting the proposed approach

solutions of the two level problem in terms of biconfluent heun functions five four parametric classes of quantum mechanical two level models permitting solutions in terms of the biconfluent heun function are derived three of these classes are generalizations of the well known classes of landau zener nikitin and crothers it is shown that two other classes describe superand sublinear and essentially nonlinear level crossings as well as processes with three crossing points in particular these classes include two level models where the field amplitude is constant and the detuning varies as 0t 2t 3 or t 1 3 for the essentially nonlinear cubic crossing model t 2t 3 the general solution of the two level problem is shown to be expressed as series of confluent hypergeometric functions

regularized field map estimation in mri in fast magnetic resonance mr imaging with long readout times such as echo planar imaging epi and spiral scans it is important to correct for the effects of field inhomogeneity to reduce image distortion and blurring such corrections require an accurate field map a map of the off resonance frequency at each voxel standard field map estimation methods yield noisy field maps particularly in image regions with low spin density this paper describes regularized methods for field map estimation from two or more mr scans having different echo times these methods exploit the fact that field maps are generally smooth functions the methods use algorithms that decrease monotonically a regularized least squares cost function even though the problem is highly nonlinear results show that the proposed regularized methods significantly improve the quality of field map estimates relative to conventional unregularized methods

recursive structure of noncausal gauss markov random fields an approach is developed for noncausal gauss markov random fields gmrfs that enables the use of recursive procedures while retaining the noncausality of the field recursive representations are established that are equivalent to the original field this is achieved by first presenting a canonical representation for gmrfs that is based on the inverse of the covariance matrix which is called the potential matrix it is this matrix rather than the field covariance that reflects in a natural way the mrf structure from its properties two equivalent one sided representations are derived each of which is obtained as the successive iterates of a riccati type equation for homogeneous fields these unilateral descriptions are symmetrized versions of each other the study of only one riccati equation being required it is proven that this riccati equation converges at a geometric rate therefore the one sided representations are asymptotically invariant these unilateral representations make it possible to process the fields with well known recursive techniques such as kalman bucy filters and two point smoothers

explicit estimating equations for semiparametric generalized linear latent variable models summary we study generalized linear latent variable models without requiring a distributional assumption of the latent variables using a geometric approach we derive consistent semiparametric estimators we demonstrate that these models have a property which is similar to that of a sufficient complete statistic which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations we further show that the explicit estimators have the usual root n consistency and asymptotic normality we explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies the advantage of our estimators over the existing likelihood approach is also shown via numerical comparison we employ the method to analyse a real data example from economics

locally ancillary quasi score models for errors in covariates we use the notion of locally ancillary estimating functions to develop a quasi score method for fitting regression models containing measurement error in the covariates suppose that interest is on the model e y u w for response y the observed data are y x w and x is a mismeasured surrogate for u we take a functional modeling approach treating the u as a fixed nuisance parameter beginning with quasi scores for the regression parameter and the unknown u we derive a bias corrected quasi score for the regression parameter that is second order locally ancillary for the nuisance u our method for this requires only the correct specification of the mean and variance functions for y and x in terms of u w and the regression parameter when an estimator for u is plugged into the corrected quasi score local approximations show that the bias is small we present simulations verifying this result and an example from child psychiatry both using log linear regression models

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

regression analysis of networked data this paper concerns regression methodology for assessing relationships between multi dimensional response variables and covariates that are correlated within a network to address analytical challenges associated with the integration of network topology into the regression analysis we propose a hybrid quadratic inference method that uses both prior and data driven correlations among network nodes a godambe information based tuning strategy is developed to allocate weights between the prior and data driven network structures so the estimator is efficient the proposed method is conceptually simple and computationally fast and has appealing large sample properties it is evaluated by simulation and its application is illustrated using neuroimaging data from an association study of the effects of iron deficiency on auditory recognition memory in infants