marginal longitudinal nonparametric regression locality and efficiency of spline and kernel methods we consider nonparametric regression in a longitudinal marginal model of generalized estimating equation gee type with a time varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large in such models the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations two methods of estimating the nonparametric function can be considered kernel methods and spline methods recently surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent that is working independence in the gee jargon as seen through equivalent kernel results in univariate independent data problems splines and kernels have similar behavior smoothing splines are equivalent to kernel regression with a s

temporal process regression summary we consider regression for response and covariates which are temporal processes observed over intervals a functional generalised linear model is proposed which includes extensions of standard models in multi state survival analysis simple nonparametric esti mators of time indexed parameters are developed using working independence estimating equations and are shown to be uniformly consistent and to converge weakly to gaussian processes the procedure does not require smoothing or a markov assumption unlike approaches based on transition intensities the usual definition of optimal estimating equations for parametric models is then generalised to the functional model and the optimum is identified in a class of functional generalised estimating equations simulations demonstrate large efficiency gains relative to working independence at times where censoring is heavy the estimators are the basis for new tests of the covariate effects and for the estimation of models in which greater structure is imposed on the parameters providing novel goodness of fit tests the methodology s practical utility is illustrated in a data analysis

elastic fields in two joined half spaces subject to point force and uniform ring loads closed form solutions for the elastic field in two joined dissimilar transversely isotropic half spaces subject to point force are derived based on a set of potential functions following integration the solutions for uniform ring loads are obtained in the forms of the complete elliptic integrals these solutions can be degenerated into cases of infinite or semi infinite spaces since the denominator of some expressions tends to zero as r approaches zero the solutions near the z axis for this special case are therefore presented explicitly

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

three dimensional green s function and its derivative for materials with general anisotropic magneto electro elastic coupling explicit expressions of green s function and its derivative for three dimensional infinite solids are presented in this paper the medium is allowed to exhibit a fully magneto electro elastic mee coupling and general anisotropic behaviour in particular new explicit expressions for the first order derivative of green s function are proposed the derivation combines extended stroh formalism radon transform and cauchy s residue theory in order to cover mathematical degenerate and non degenerate materials in the stroh formalism context a multiple residue scheme is performed expressions are explicit in terms of stroh s eigenvalues this being a feature of special interest in numerical applications such as boundary element methods as a particular case simplifications for mee materials with transversely isotropic symmetry are derived details on the implementation and numerical stability of the proposed solutions for degenerate cases are studied

elastic solutions of displacements for a transversely isotropic half space subjected to three dimensional buried parabolic rectangular loads this paper presents the closed form solutions for estimating the displacements in a transversely isotropic half space subjected to three dimensional buried linearly varying uniform and parabolic rectangular loads the loading types include an upward linearly varying load a downward linearly varying load a uniform load a concave parabolic load and a convex parabolic load on a rectangle the planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half space the presented solutions are obtained from integrating of the point load solutions in a cartesian co ordinate system for the transversely isotropic half space the solutions for a transversely isotropic medium subjected to parabolic rectangular loads are never mentioned in the literature the parabolic loads might be more realistic than linear variable or uniform loads acting on foundations the buried depth the dimensions of loaded area the type and degree of material anisotropy and the loading type for transversely isotropic half spaces influence these solutions an illustrative example is presented to investigate the effect of the type and degree of rock anisotropy and the loading types on the displacement the proposed solutions can provide reasonably results to estimate the induced displacements in the isotropic transversely isotropic geomaterials subjected to three dimensional buried parabolic rectangular loads for practical purposes

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

statistical analysis of music and subspace rotation estimates of sinusoidal frequencies consideration is given to the analysis of the large sample second order properties of multiple signal classification music and subspace rotation sur methods such as esprit for sinusoidal frequency estimation explicit expressions for the covariance elements of the estimation errors associated with either method are derived these expressions of covariances are then used to analyze and compare the statistical performances of the music and sur estimation sure methods both music and sure are based on the eigendecomposition of a sample data covariance matrix the expressions for the estimation error variances derived are used to study the dependence of music and sure performances on the dimension of the data covariance matrix used

practical issues in using generalized estimating equations for inference on transitions in longitudinal data what is being estimated generalized estimating equations gees are commonly used to estimate transition models when the markov assumption does not hold but first order transition probabilities are still of interest the transition inference is sensitive to the choice of working correlation in this paper we consider a random process transition model as the true underlying data generating mechanism which characterizes subject heterogeneity and complex dependence structure of the outcome process in a very flexible way we formally define two types of transition probabilities at the population level naive transition probabilities that average across all the transitions and population average transition probabilities that average the subject specific transition probabilities through asymptotic bias calculations and finite sample simulations we demonstrate that the unstructured working correlation provides unbiased estimators of the population average transition probabilities while the independence working correlation provides unbiased estimators of the naive transition probabilities for population average transition estimation we demonstrate that the sandwich estimator fails for unstructured gee and recommend the use of either jackknife or bootstrap variance estimates the proposed method is motivated by and applied to the next generation health study where the interest is in estimating the population average transition probabilities of alcohol use in adolescents

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

integral identities for a semi infinite interfacial crack in anisotropic elastic bimaterials the focus of the article is on the analysis of a semi infinite crack at the interface between two dissimilar anisotropic elastic materials loaded by a general asymmetrical system of forces acting on the crack faces recently derived symmetric and skew symmetric weight function matrices are introduced for both plane strain and antiplane shear cracks and used together with the fundamental reciprocal identity betti formula in order to formulate the elastic fracture problem in terms of singular integral equations relating the applied loading and the resulting crack opening the proposed compact formulation can be used to solve many problems in linear elastic fracture mechanics for example various classic crack problems in homogeneous and heterogeneous anisotropic media as piezoceramics or composite materials this formulation is also fundamental in many multifield theories where the elastic problem is coupled with other concurrent physical phenomena

weight functions and fundamental fields for the penny shaped and the half plane crack in three space abstract weight functions permit to represent stress intensity factors as weighted averages of the externally impressed boundary tractions and body forces in this paper the relevant weight functions of all three modes are represented in closed form with the aid of elementary transcendentals their derivation as displacements of fundamental fields is simple and without recourse to integral transforms of any kind

a new perturbation analysis for signal enumeration in rotational invariance techniques the esprit algorithm is a subspace based high resolution method used in source localization and spectral analysis which provides very accurate estimates of the signal parameters however the underlying theory assumes a known model order which is usually not the case in many applications in particular it is well known that underevaluating the model order biases the estimation in this paper we analyze the perturbation induced by an erroneous model order and we present an error bound for the estimated parameters based on this theoretical framework we propose a new method for selecting an appropriate modeling order which consists in minimizing the error bound this approach is applied to both synthetic and musical signals and its performance is compared to that of existing methods such as the information theoretic criteria

a functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error summary covariate measurement error and missing responses are typical features in longitudinal data analysis there has been extensive research on either covariate measurement error or missing responses but relatively little work has been done to address both simultaneously in this paper we propose a simple method for the marginal analysis of longitudinal data with time varying covariates some of which are measured with error while the response is subject to missingness our method has a number of appealing properties assumptions on the model are minimal with none needed about the distribution of the mismeasured covariate implementation is straightforward and its applicability is broad we provide both theoretical justification and numerical results

multidimensional esprit for damped and undamped signals algorithm computations and perturbation analysis in this paper we present and analyze the performance of multidimensional esprit n d esprit method for estimating parameters of n d superimposed damped and or undamped exponentials n d esprit algorithm is based on low rank decomposition of multilevel hankel matrices formed by the n d data in order to reduce the computational complexity for large signals we propose a fast n d esprit using truncated singular value decomposition svd then through a first order perturbation analysis we derive simple expressions of the variance of the estimates in n d multiple tones case these expressions do not involve the factors of the svd we also derive closed form expressions of the variances of the complex modes frequencies and damping factors estimates in the n d single tone case computer results are presented to show effectiveness of the fast version of n d esprit and verify theoretical expressions

marginal mark regression analysis of recurrent marked point process data summary longitudinal studies typically collect information on the timing of key clinical events and on specific characteristics that describe those events random variables that measure qualitative or quantitative aspects associated with the occurrence of an event are known as marks recurrent marked point process data consist of possibly recurrent events with the mark and possibly exposure measured if and only if an event occurs analysis choices depend on which aspect of the data is of primary scientific interest first factors that influence the occurrence or timing of the event may be characterized using recurrent event analysis methods second if there is more than one event per subject then the association between exposure and the mark may be quantified using repeated measures regression methods we detail assumptions required of any time dependent exposure process and the event time process to ensure that linear or generalized linear mixed models and generalized estimating equations provide valid estimates we provide theoretical and empirical evidence that if these conditions are not satisfied then an independence estimating equation should be used for consistent estimation of association we conclude with the recommendation that analysts carefully explore both the exposure and event time processes prior to implementing a repeated measures analysis of recurrent marked point process data

mindlin s problem for an anisotropic piezoelectric half space with general boundary conditions this paper considers mindlin s problem in an anisotropic and piezoelectric halfspace with general boundary conditions including 16 different sets of surface conditions the green s function due to

cramer rao bounds for multiple poles and coefficients of quasi polynomials in colored noise in this paper we provide analytical expressions of the cramer rao bounds for the frequencies damping factors amplitudes and phases of complex exponentials in colored noise these expressions show the explicit dependence of the bounds of each distinct parameter with respect to the amplitudes and phases leading to readily interpretable formulae which are then simplified in an asymptotic context the results are presented in the general framework of the polynomial amplitude complex exponentials pace model also referred to as the quasi polynomial model in the literature which accounts for systems involving multiple poles and represents a signal as a mixture of complex exponentials modulated by polynomials this work looks further and generalizes the studies previously undertaken on the exponential and the quasi polynomial models

some observations on the potential functions for transverse isotropy in the presence of body forces abstract in this paper the potential function formulation for a transversely isotropic material is examined in the presence of body force terms the equations of equilibrium are reduced to poisson type equations with the body force terms on the right hand side the potentials are evaluated for a concentrated body force in an infinite material for a force perpendicular to the isotropic plane it is shown that some degree of ambiguity exists in the choice of the potential which explains the different forms used by previous researchers for a point force parallel to the z 0 isotropic plane the present results for the potentials agree with previous analysis when z 0 but differ for z

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

modeling partly conditional means with longitudinal data abstract we propose a general modeling approach to longitudinal data that is a hybrid of the marginal regression models of zeger and liang and of the classical transition models such as used in time series analyses rather than conditioning at time t only on covariate values as is typical with the marginal approach or on the entire history of the process up to t as is typical with the transition model approach we suggest models that condition on a subset of the process history estimation proceeds using generalized estimating equation methodology but with the restriction that the working covariance matrix is diagonal the proposed regression models share common features with cox regression models for failure time data in that they are composed of a nuisance baseline function of time and a simple parametric function of the covariates two illustrative examples are presented

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

partly conditional estimation of the effect of a time dependent factor in the presence of dependent censoring we propose semiparametric methods for estimating the effect of a time dependent covariate on treatment free survival the data structure of interest consists of a longitudinal sequence of measurements and a potentially censored survival time the factor of interest is time dependent treatment free survival is of interest and is dependently censored by the receipt of treatment patients may be removed from consideration for treatment temporarily or permanently the proposed methods combine landmark analysis and partly conditional hazard regression a set of calendar time cross sections is specified and survival time from cross section date is modeled through weighted cox regression the assumed model for death is marginal in the sense that time varying covariates are taken as fixed at each landmark with the mortality hazard function implicitly averaging across future covariate trajectories dependent censoring is overcome by a variant of inverse probability of censoring weighting ipcw the proposed estimators are shown to be consistent and asymptotically normal with consistent covariance estimators provided simulation studies reveal that the proposed estimation procedures are appropriate for practical use we apply the proposed methods to pre transplant mortality among end stage liver disease esld patients

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

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

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

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

functional association models for multivariate survival processes we consider multivariate temporal processes that are continuously observed within overlapping time windows the intended application is in censored multistate and multivariate survival settings where point processes are continuously observed these data differ from other functional data like longitudinal data which are discretely observed at irregular times existing functional approaches to survival processes use intensity models which require smoothing and depend critically on the choice of smoothing parameters similarly to discretely observed data in this article we study functional mean and association regression models for the point processes with unspecified time varying coefficients the continuous observation scheme is exploited the coefficients may be estimated nonparametrically by extending generalized estimating equations to continuously observed data the estimators automatically converge at the parametric rate without smoothing unlike with discretely observed data uniform consistenc

semiparametric regression for clustered data using generalized estimating equations we consider estimation in a semiparametric generalized linear model for clustered data using estimating equations our results apply to the case where the number of observations per cluster is finite whereas the number of clusters is large the mean of the outcome variable is of the form g xt t where g is a link function x and t are covariates is an unknown parameter vector and t is an unknown smooth function kernel estimating equations proposed previously in the literature are used to estimate the infinite dimensional nonparametric function t and a profile based estimating equation is used to estimate the finite dimensional parameter vector we show that for clustered data this conventional profile kernel method often fails to yield a n consistent estimator of along with appropriate inference unless working independence is assumed or t is artificially undersmoothed in which case asymptotic inference is possible to gain insight into these results we derive the se

constructing green s function for the time dependent maxwell system in anisotropic dielectrics a method of constructing explicit formulae for green s matrix function of the time dependent maxwell system for a homogeneous non dispersive dielectric with a general form of the anisotropy is described this method consists of two parts in the first part a matrix function depending on the time variable and three fourier parameters is determined this matrix function being the fourier image of green s matrix function with respect to three space variables is constructed in an explicit form the second part of the method is the inverse fourier transform of the determined matrix function the robustness and advantages of this method are confirmed by numerical experiments examples of simulations of electromagnetic fields in anisotropic crystals are presented

integral identities based on symmetric and skew symmetric weight functions for a semi infinite interfacial crack in anisotropic magnetoelectroelastic bimaterials abstract in this paper we address a semi infinite interfacial crack problem in an anisotropic magnetoelectroelastic mee bimaterial system subjected to a magnetoelectromechanical asymmetric load on the crack surface first the symmetric and skew symmetric weight functions are derived for a two dimensional 2 d deformation problem using these weight functions and extending the betti formula to mee materials the integral identities are further obtained and the present crack problem is formulated in terms of singular integral equations which establish the relationship between the applied external load and the generalized displacement jump across the crack faces the illustrative examples in relation to mode iii and mode i and mode ii problems show that the method developed in this study avoids the use of green s function and is very convenient for the fracture analysis of mee solids in which a multi field coupled effect is observed

partly functional temporal process regression with semiparametric profile estimating functions summary marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models recent work on fully functional temporal process regression tpr offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying the existing esti mation procedure however prevents successive goodness of fit test for covariate coefficients in comparing a sequence of nested models this article proposes a partly functional tpr model in the line of marginal mean models some covari ate effects are time independent while others are completely unspecified in time this class of models is very rich includ ing the fully functional model and the semiparametric model as special cases to estimate the parameters we propose semiparametric profile estimating equations which are solved via an iterative algorithm starting at a consistent estimate from a fully functional model in the existing work no smoothing is needed in contrast to other varying coefficient meth ods the weak convergence of the resultant estimators are developed using the empirical process theory successive tests of time varying effects and backward model selection procedure can then be carried out the practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients

prediction using partly conditional time varying coefficients regression models summary data collected longitudinally in time provide the opportunity to develop predictive models of future observations given current data for an individual such models may be of particular value in defining individuals at high risk and thereby in suggesting subgroups for targeting of prevention intervention research efforts in this paper we propose a method for estimating predictive functions the method uses an extension of the marginal regression analysis methods of liang and zeger 1986 biometrika73 13 22 and is implemented using simple estimating equations a key feature of the models is that regression coefficients are modelled as smooth functions of the times both at and for prediction data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology criteria for defining individuals to be at high risk can be defined on the basis of estimated predictive functions we suggest methods for evaluating the diagnostic accuracy sensitivity and specificity of such rules using cross validation the method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient s current and past clinical status

profile kernel versus backfitting in the partially linear models for longitudinal clustered data summary we study the profile kernel and backfitting methods in partially linear models for clustered longitudinal data for independent data despite the potential root n inconsist ency of the backfitting estimator noted by rice 1986 the two estimators have the same asymptotic variance matrix as shown by opsomer ruppert 1999 in this paper theoretical comparisons of the two estimators for multivariate responses are investigated we show that for correlated data backfitting often produces a larger asymptotic variance than the profile kernel method that is for clustered data in addition to its bias problem the backfitting estimator does not have the same asymptotic efficiency as the profile kernel estimator consequently the common practice of using the backfitting method to compute profile kernel estimates is no longer advised we illustrate this in detail by following zeger diggle 1994 and lin carroll 2001 with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for para metric estimation numerical performance of the two estimators is investigated through a simulation study their application to an ophthalmology dataset is also described

analysis method of planar cracks of arbitrary shape in the isotropic plane of a three dimensional transversely isotropic magnetoelectroelastic medium abstract the hyper singular boundary integral equation method of crack analysis in three dimensional transversely isotropic magnetoelectroelastic media is proposed based on the fundamental solutions or green s functions of three dimensional transversely isotropic magnetoelectroelastic media and the corresponding somigliana identity the boundary integral equations for a planar crack of arbitrary shape in the plane of isotropy are obtained in terms of the extended displacement discontinuities across crack faces the extended displacement discontinuities include the displacement discontinuities the electric potential discontinuity and the magnetic potential discontinuity and correspondingly the extended tractions on crack face represent the conventional tractions the electric displacement and the magnetic induction boundary values the near crack tip fields and the intensity factors in terms of the extended displacement discontinuities are derived by boundary integral equation approach a solution method is proposed by use of the analogy between the boundary integral equations of the magnetoelectroelastic media and the purely elastic materials the influence of different electric and magnetic boundary conditions i e electrically and magnetically impermeable and permeable conditions electrically impermeable and magnetically permeable condition and electrically permeable and magnetically impermeable condition on the solutions is studied the crack opening model is proposed to consider the real crack opening and the electric and magnetic fields in the crack cavity under combined mechanical electric magnetic loadings an iteration approach is presented for the solution of the non linear model the exact solution is obtained for the case of uniformly applied loadings on the crack faces numerical results for a square crack under different electric and magnetic boundary conditions are displayed to demonstrate the proposed method

on svd for estimating generalized eigenvalues of singular matrix pencil in noise several algorithms for estimating generalized eigenvalues ges of singular matrix pencils perturbed by noise are reviewed the singular value decomposition svd is explored as the common structure in the three basic algorithms direct matrix pencil algorithm pro esprit and tls esprit it is shown that several svd based steps inherent in the algorithms are equivalent to the first order approximation in particular the pro esprit and its variant tls pro esprit are shown to be equivalent and the tls esprit and its earlier version ls esprit are shown to be asymptotically equivalent to the first order approximation for the problem of estimating superimposed complex exponential signals the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first order approximation the second order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal an improved state space algorithm is found to be the most robust to noise

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

efficient semiparametric marginal estimation for longitudinal clustered data we consider marginal generalized semiparametric partially linear models for clustered data lin and carroll derived the semiparametric efficient score function for this problem in the multivariate gaussian case but they were unable to construct a semiparametric efficient estimator that actually achieved the semiparametric information bound here we propose such an estimator and generalize the work to marginal generalized partially linear models we investigate asymptotic relative efficiencies of the estimators that ignore the within cluster correlation structure either in nonparametric curve estimation or throughout we evaluate the finite sample performance of these estimators through simulations and illustrate it using a longitudinal cd4 cell count dataset both theoretical and numerical results indicate that properly taking into account the within subject correlation among the responses can substantially improve efficiency

perturbation analysis of tk method for harmonic retrieval problems the authors present a first order perturbation analysis of the tufts kumaresan tk 1980 method used to estimate frequencies of complex sinusoids in small additive noise several fundamental properties are presented and proved further illustrations are provided through numerical examples

application of hypersingular integral equation method to three dimensional crack in electromagnetothermoelastic multiphase composites a three dimensional crack problem in electromagnetothermoelastic multiphase composites emte mcs under extended loads is investigated in this paper using green s functions the extended general displacement solutions are obtained by the boundary element method this crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations in which the unknown functions are the extended displacement discontinuities then the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main part analysis method of hypersingular integral equations analytical solutions for the extended singular stresses the extended stress intensity factors sifs and the extended energy release rate near the crack front in emte mcs are provided also a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials in addition distributions of extended sifs varying with the shape of the crack are presented the results show that the present method accurately yields smooth variations of extended sifs along the crack front

solutions for transversely isotropic magneto electro elastic body semi infinite body and bi material infinite body subjected to uniform ring loading charge and current based on the general solutions for transversely isotropic magneto electro elastic materials the fundamental solutions of axi symmetric problems are derived by integration and explicit expressions for four possible cases of distinct characteristic roots and multiple roots are all presented in the case of distinct roots based on the green s functions for semi infinite magneto electro elastic body and bi material infinite magneto electro elastic body the green s functions for axi symmetric problems of semi infinite body and bi material infinite body are obtained 2007 published by elsevier ltd

sliding window adaptive svd algorithms the singular value decomposition svd is an important tool for subspace estimation in adaptive signal processing we are especially interested in tracking the svd of a recursively updated data matrix this paper introduces a new tracking technique that is designed for rectangular sliding window data matrices this approach which is derived from the classical bi orthogonal iteration svd algorithm shows excellent performance in the context of frequency estimation it proves to be very robust to abrupt signal changes due to the use of a sliding window finally an ultra fast tracking algorithm with comparable performance is proposed

boundary elements for half space problems via fundamental solutions a three dimensional analysis an efficient solution technique is proposed for the three dimensional boundary element modelling of half space problems the proposed technique uses alternative fundamental solutions of the half space mindlin s solutions for isotropic case and full space kelvin s solutions problems three dimensional infinite boundary elements are frequently employed when the stresses at the internal points are required to be evaluated in contrast to the published works the strongly singular line integrals are avoided in the proposed solution technique while the discretization of infinite elements is independent of the finite boundary elements this algorithm also leads to a better numerical accuracy while the computational time is reduced illustrative numerical examples for typical isotropic and transversely isotropichalf space problems demonstrate the potential applications of the proposed formulations incidentally the results of the illustrative examples also provide a parametric study for the imperfect contact problem copyright 2001 john wiley sons ltd

time harmonic green s functions for anisotropic magnetoelectroelasticity abstract two dimensional 2 d and three dimensional 3 d time harmonic green s functions for linear magnetoelectroelastic solids are derived in this paper by means of radon transform displacement field and electric and magnetic potentials in a fully anisotropic magnetoelectroelastic infinite solid due to a time harmonic point force point charge and magnetic monopole are obtained in form of line integrals over a unit circle in 2 d case and surface integrals over a unit sphere in 3 d case this dynamic fundamental solution is then split into the sum of regular dynamic plus singular terms the singular terms coincide with the green s functions for the static problem and may be further reduced to closed form expressions the proposed green s functions can be used in the corresponding boundary element method bem formulation

performance of esprit for estimating mixtures of complex exponentials modulated by polynomials high resolution hr methods are known to provide accurate frequency estimates for discrete spectra the polynomial amplitude complex exponentials pace model also called quasi polynomial model in the literature was presented as the most general model tractable by hr methods a subspace based estimation scheme was recently proposed derived from the classical esprit algorithm in this paper we focus on the performance of this estimator we first present some asymptotic expansions of the estimated parameters obtained at the first order under the assumption of a high signal to noise ratio snr then the performance of the generalized esprit algorithm for estimating the parameters of this model is analyzed in terms of bias and variance and compared to the cramer rao bounds crb this performance is studied in an asymptotic context and it is proved that the efficiency of undamped single poles estimators is close to the optimality moreover our results show that the best performance is obtained for a proper dimensioning of the data to illustrate the practical capabilities of the generalized esprit algorithm we finally propose an application to arma filter synthesis in the context of system conversion from continuous time to discrete time

the boundary layer phenomena in two dimensional transversely isotropic piezoelectric media by exact symplectic expansion a separable variable method is introduced to find the exact homogeneous solutions of a two dimensional transversely isotropic piezoelectric media to handle general boundary conditions the usual method of separable variables for partial differentiation equations cannot be readily applicable due to the tangling of the unknowns and their derivatives introducing dual variables of stresses we obtain a set of first order hamiltonian equations whose eigensolutions are symplectic spanning over the solution space to cover all possible boundary conditions the solutions consist of two parts the first part is the derogative zero eigenvalue solutions of the saint venant type together with all their jordan chains the second part is the decaying non zero eigenvalue solutions describing the boundary layer effects the classical solutions are actually the zero eigenvalue solutions representing the simple extension bending equipotential field and the uniform electric displacement on the other hand the non zero eigenvalue solutions represent the localized solutions which are sensitive to the boundary conditions and are decaying rapidly with respect to the distance from the boundaries some rate of decay curves of the newly found non zero eigenvalue solutions are shown by numerical examples finally the complete boundary layer effects are quantified for the first time

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

a nonparametric dynamic additive regression model for longitudinal data in this work we study additive dynamic regression models for longitudinal data these models provide a flexible and nonparametric method for investigating the time dynamics of longitudinal data the methodology is aimed at data where measurements are recorded at random time points we model the conditional mean of responses given the full internal history and possibly time varying covariates we derive the asymptotic distribution for a new nonparametric least squares estimator of the cumulative time varying regression functions based on the asymptotic results confidence bands may be computed and inference about time varying coefficients may be drawn we propose two estimators of the cumulative regression function one estimator that involves smoothing and one that does not the latter however has twice the variance as the smoothing based estimator goodness of fit of the model is considered using martingale residuals finally we also discuss how partly conditional mean models in which the mean of the response is regressed onto selected time varying covariates may be analysed in the same framework we apply the methods to longitudinal data on height development for cystic fibrosis patients

singularities interfaces and cracks in dissimilar anisotropic media for a non pathological bimaterial in which an interface crack displays no oscillatory behaviour it is observed that apart possibly from the stress intensity factors the structure of the near tip field in each of the two blocks is independent of the elastic moduli of the other block collinear interface cracks are analysed under this non oscillatory condition and a simple rule is formulated that allows one to construct the complete solutions from mode iii solutions in an isotropic homogeneous medium the general interfacial crack tip field is found to consist of a two dimensional oscillatory singularity and a one dimensional square root singularity a complex and a real stress intensity factors are proposed to scale the two singularities respectively owing to anisotropy a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields however defined does not recover the classical stress intensity factors as the bimaterial degenerates to be non pathological collinear crack problems are also formulated in this context and a strikingly simple mathematical structure is identified interactive solutions for singularity interface and singularity interface crack are obtained the general results are specialized to decoupled antiplane and in plane deformations for this important case it is found that if a material pair is non pathological for one set of relative orientations of the interface and the two solids it is non pathological for any set of orientations for bonded orthotropic materials an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized a complex variable representation is presented for a class of degenerate orthotropic materials throughout the paper the equivalence of the lekhnitskii and stroh formalisms is emphasized the article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids

concentrated ring loadings in a full space or half space solutions for transverse isotropy and isotropy in this analysis solutions for concentrated ring loading in a transversely isotropic full space or half space are found the elastic field is derived by integrating the known fundamental point force solutions along a circular ring three cases of ring loading are considered taking the z axis along the material axis the z 0 plane is the isotropic plane the first case studied is when the ring load is in the z direction referred to as normal loading the other two cases are shear ring loads directed in the plane of isotropy in the first instance the ring load is unidirectional and independently applied in either the x or y direction the second case considers the axisymmetric radial and axisymmetric torsional ring loads the solution for ring loading applied to the surface of a half space is first obtained subsequently the solutions for ring loading in a full space and buried ring loads in a half space are found in all cases the elastic displacement and stress fields are evaluated in terms of closed form expressions containing complete elliptic integrals of the first second and third kinds an interesting feature of the full space solution is that the potential function and its radial derivatives exhibit a cylindrical discontinuity for negative z values however it is shown that these discontinuous functions do provide continuous displacement and stress fields a limiting form of the solutions for transverse isotropy also provides the corresponding results for isotropic materials

parameter estimation of monomial exponential sums in one and two variables we propose a matrix pencil method to identify monomial exponential sums in the univariate case it is based on the qr factorization of hankel matrices in the bivariate case it assures the same accuracy of the univariate case in this paper we propose a matrix pencil method for the numerical identification of the parameters of monomial exponential sums in one and two variables while in the univariate case the proposed method is a variant of that developed by the authors in a preceding paper the bivariate case is treated for the first time here in the bivariate case the method we propose easily extendible to more variables reduces the problem to a pair of univariate problems and subsequently to the solution of a linear system as a result the relative errors in the univariate and in the bivariate case are almost of the same order

efficient semiparametric mean association estimation for longitudinal binary responses semiparametric methods for longitudinal data with association within subjects have recently received considerable attention however existing methods for semiparametric longitudinal binary regression modeling i mainly concern mean structures with association parameters treated as nuisance ii generally require a correct specification of the covariance structure for misspecified covariance structure may lead to inefficient mean parameter estimates and iii usually run into computation and estimation problems when the time points are irregularly and possibly subject specific in this article we propose a semiparametric logistic regression model which simultaneously takes into account both the mean and response association structures via conditional log odds ratio for multivariate longitudinal binary outcomes our main interest lies in efficient estimation of both the marginal and association parameters the estimators of the parameters are obtained via the profile kernel approach we evaluate the proposed methodology through simulation studies and apply it to a real dataset both theoretical and empirical results demonstrate that the proposed method yields highly efficient estimators and performs satisfactorily copyright 2012 john wiley sons ltd

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

solutions for transversely isotropic piezoelectric infinite body semi infinite body and bimaterial infinite body subjected to uniform ring loading and charge abstract based on the fundamental solutions for transversely isotropic piezoelectric materials the fundamental solutions of axisymmetric problems are derived by integration and explicit expressions for three possible cases of different characteristic roots and multiple roots are all presented in the case of s 1 s 2 s 3 s 1 based on the greens functions for semi infinite piezoelectric body and bimaterial infinite piezoelectric body the greens functions for axisymmetric problems of semi infinite body and bimaterial infinite body are obtained taking pzt 4 as an example numerical computations are conducted by use of the fundamental solutions to axisymmetric problems comparison of the calculated results with those of fem shows good agreement between them

fast approximated power iteration subspace tracking this paper introduces a fast implementation of the power iteration method for subspace tracking based on an approximation that is less restrictive than the well known projection approximation this algorithm referred to as the fast approximated power iteration api method guarantees the orthonormality of the subspace weighting matrix at each iteration moreover it outperforms many subspace trackers related to the power iteration method such as past nic np3 and opast while having the same computational complexity the api method is designed for both exponential windows and sliding windows our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

circular disclination loops in nonlocal elasticity abstract solutions for problems of circular twist and wedge disclination loops in an infinitely extended linear isotropic nonlocal elastic medium are obtained assuming an appropriate nonlocal modulus the equilibrium equation is satisfied by introducing the kroner s stress function tensor the laplace and hankel transforms are used to obtain the stress fields and the stored elastic energies the oscillatory integrals containing bessel functions are transformed into integrands which decay exponentially thus producing a solution more amenable to numerical quadrature it is found that maximum stresses are reached at some distance from the defect line the obtained solutions lead to finite values of stresses at this line and reduce to the classical ones in the long wave length limit

inferences for a semiparametric model with panel data summary in a longitudinal study suppose that for each subject repeated measurements of the response variable and covariates are collected at a set of distinct irregularly spaced time points we consider a semiparametric model which relates the mean of the response variable at each time point proportionally to a function of a time dependent covariate vector to analyse such panel data inference procedures for regression parameters are proposed without involving any nonparametric function estimation for the nuisance mean function a dataset from a recent aids clinical trial is used to illustate the new proposal

semiparametric regression models for repeated measures of mortal cohorts with non monotone missing outcomes and time dependent covariates we propose a semiparametric marginal modeling approach for longitudinal analysis of cohorts with data missing due to death and non response to estimate regression parameters interpreted as conditioned on being alive our proposed method accommodates outcomes and time dependent covariates that are missing not at random with non monotone missingness patterns via inverse probability weighting missing covariates are replaced by consistent estimates derived from a simultaneously solved inverse probability weighted estimating equation thus we utilize data points with the observed outcomes and missing covariates beyond the estimated weights while avoiding numerical methods to integrate over missing covariates the approach is applied to a cohort of elderly female hip fracture patients to estimate the prevalence of walking disability over time as a function of body composition inflammation and age

high resolution spectral analysis of mixtures of complex exponentials modulated by polynomials high resolution methods such as the esprit algorithm are of major interest for estimating discrete spectra since they overcome the resolution limit of the fourier transform and provide very accurate estimates of the signal parameters in signal processing literature most contributions focus on the estimation of exponentially modulated sinusoids in a noisy signal this paper introduces a more general class of signals involving both amplitude and frequency modulations it shows that this polynomial amplitude complex exponentials pace model is the most general model tractable by high resolution methods a generalized esprit algorithm is developed for estimating the signal parameters and it is shown that this model can be characterized by means of a geometrical criterion

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

on the accuracy of the kumaresan tufts method for estimating complex damped exponentials recently kumaresan and tufts kt presented a method for estimating the parameters of damped exponential waveforms in additive white noise the kt method uses singular value decomposition svd of the data matrix with truncation and backward prediction to improve the accuracy of the estimates the kt method was demonstrated to have a very good performance in comparison to traditional methods used for the same problem e g prony s method kumaresan and tufts also showed by numerical simulations that the variances of the estimates obtained by their method approaches the cramer rao lower bounds for selected test cases in this correspondence we provide a quantitative accuracy analysis of the kt method the analysis is based on first order taylor series approximations of the estimated parameters around their true values no assumptions are made on the number of data points used but it is assumed that the noise level is small enough for the first order approximations to be valid results of the analysis are illustrated by some numerical examples these results confirm the good performance of the kt method and show the effect of the user chosen parameters on the accuracy of the estimates

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed