cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

expressions for predicting fundamental natural frequencies of non cylindrical helical springs abstract numerical and analytical studies are performed for the free vibration analysis of non cylindrical conical barrel and hyperboloidal types helical springs the stiffness matrix method is used in the numerical analysis a total of 12 degrees of freedom six displacements and six rotations is described for an element the exact element stiffness matrix and the exact concentrated element inertia matrix are used in the formulation the rotary inertia the shear and extensional deformation effects are considered in the analysis comparison of the numerical results with the reported results obtained numerically and experimentally gives satisfactory values after verification of the numerical frequencies the non dimensional fundamental frequencies of fixed fixed non cylindrical helical springs with circular section are expressed in a simple formula with a maximum absolute relative error of 5 using those numerical values for the constant helix pitch angles 5 10 and 15 these expressions restricted to the fundamental frequencies are also verified with ansys results

free vibration analysis of cylindrical helical springs by the pseudospectral method abstract the pseudospectral method is applied to the free vibration analysis of cylindrical helical springs the displacements and the rotations are approximated by the series expansions of chebyshev polynomials and the governing equations are collocated the number of collocation points is chosen to be less than the number of the expansion terms to handle the boundary condition numerical examples are provided for fixed fixed free free fixed free and hinged hinged boundary conditions the results show good agreement with those of the transfer matrix method and the dynamic stiffness method the formulation of the pseudospectral method is straightforward and shows an exponential rate of convergence with mesh refinement

adjusted score tests of homogeneity for poisson processes abstract tests of homogeneity are being increasingly used for the analysis of event time data but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes here we consider tests of homogeneity for recurrent event data in which the null model is a poisson process and the alternative is a mixed poisson process we examine score and adjusted score statistics in the context of parametric and semiparametric regression models where the adjustments correct for the bias induced by substituting the maximum likelihood estimates of the parameters into the test statistic we report the results of simulation studies suggesting that the adjusted score statistics are superior in terms of size and power we also find that the adjusted score test in the semiparametric regression model does not perform particularly well in small samples but the adjusted score test based on a piecewise exponential model has satisfactory performance the latter thus prov

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

testing the correlation for clustered categorical and censored discrete time to event data when covariates are measured without with errors summary in the analysis of clustered categorical data it is of common interest to test for the correlation within clusters and the heterogeneity across different clusters we address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models for clustered nominal and ordinal categorical responses we extend the results to accommodate clustered censored discrete time to event data we next consider such tests in the situation where covariates are measured with errors we propose using the simex method to construct the score tests for the null hypothesis that the variance components are zero key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates the asymptotic properties of the proposed tests are studied we illustrate these tests by analyzing two data sets and evaluate their performance with simulations

embedded trees estimation of gaussian processes on graphs with cycles graphical models provide a powerful general framework for encoding the structure of large scale estimation problems however the graphs describing typical real world phenomena contain many cycles making direct estimation procedures prohibitively costly in this paper we develop an iterative inference algorithm for general gaussian graphical models it operates by exactly solving a series of modified estimation problems on spanning trees embedded within the original cyclic graph when these subproblems are suitably chosen the algorithm converges to the correct conditional means moreover and in contrast to many other iterative methods the tree based procedures we propose can also be used to calculate exact error variances although the conditional mean iteration is effective for quite densely connected graphical models the error variance computation is most efficient for sparser graphs in this context we present a modeling example suggesting that very sparsely connected graphs with cycles may provide significant advantages relative to their tree structured counterparts thanks both to the expressive power of these models and to the efficient inference algorithms developed herein the convergence properties of the proposed tree based iterations are characterized both analytically and experimentally in addition by using the basic tree based iteration to precondition the conjugate gradient method we develop an alternative accelerated iteration that is finitely convergent simulation results are presented that demonstrate this algorithm s effectiveness on several inference problems including a prototype distributed sensing application

multiscale autoregressive models and wavelets the multiscale autoregressive mar framework was introduced to support the development of optimal multiscale statistical signal processing its power resides in the fast and flexible algorithms to which it leads while the mar framework was originally motivated by wavelets the link between these two worlds has been previously established only in the simple case of the haar wavelet the first contribution of this paper is to provide a unification of the mar framework and all compactly supported wavelets as well as a new view of the multiscale stochastic realization problem the second contribution of this paper is to develop wavelet based approximate internal mar models for stochastic processes this will be done by incorporating a powerful synthesis algorithm for the detail coefficients which complements the usual wavelet reconstruction algorithm for the scaling coefficients taking advantage of the statistical machinery provided by the mar framework we will illustrate the application of our models to sample path generation and estimation from noisy irregular and sparse measurements

a recursive model reduction method for approximate inference in gaussian markov random fields this paper presents recursive cavity modeling a principled tractable approach to approximate near optimal inference for large gauss markov random fields the main idea is to subdivide the random field into smaller subfields constructing cavity models which approximate these subfields each cavity model is a concise yet faithful model for the surface of one subfield sufficient for near optimal inference in adjacent subfields this basic idea leads to a tree structured algorithm which recursively builds a hierarchy of cavity models during an ldquoupward passrdquo and then builds a complementary set of blanket models during a reverse ldquodownward pass rdquo the marginal statistics of individual variables can then be approximated using their blanket models model thinning plays an important role allowing us to develop thinned cavity and blanket models thereby providing tractable approximate inference we develop a maximum entropy approach that exploits certain tractable representations of fisher information on thin chordal graphs given the resulting set of thinned cavity models we also develop a fast preconditioner which provides a simple iterative method to compute optimal estimates thus our overall approach combines recursive inference variational learning and iterative estimation we demonstrate the accuracy and scalability of this approach in several challenging large scale remote sensing problems

dynamic stiffness formulation free vibration and wave motion of helical springs a coil spring can only be treated as a simple massless force element at low frequencies the effects of internal resonances leading to significant dynamic stiffening for an automotive suspension spring this occurs at frequencies as low as about 40 hz this paper presents an efficient method for calculating the dynamic stiffness of a helical coil spring the partial differential equations of motion are used to derive the relation between wavenumber and frequency along with the associated wave shapes by expressing the response in terms of these waves the dynamic stiffness matrix is assembled natural frequencies are obtained from the reduced stiffness matrix allowing for different boundary conditions making use of the wittrick williams algorithm the results of the dynamic stiffness method are compared with those of the transfer matrix method and the finite element method the nature of the wave propagation is also investigated although at low frequencies four wave types propagate above a particular frequency only two propagating waves remain these are composite waves which are excited by both axial and transverse motion for lower values of helix angle an intermediate frequency range exists where six propagating waves can occur

estimation of the survival function for gray s piecewise constant time varying coefficients model gray s extension of cox s proportional hazards ph model for right censored survival data allows for a departure from the ph assumption via introduction of time varying regression coefficients tvc using penalized splines gray s work focused on estimation inference and residual analyses but no estimator for the survival function has been proposed we derive a survival function estimator for one important member of the class of tvc models a piecewise constant time varying coefficients pc tvc model we also derive an estimate for the confidence limits of the survival function accuracy in estimating underlying survival times and survival quantiles is assessed for both cox s and gray s pc tvc model using a simulation study featuring scenarios violating the ph assumption finally an example of the estimated survival functions and the corresponding confidence limits derived from cox s ph and gray s pc tvc model respectively is presented for a liver transplant data set in the second part of the thesis we examine the effect of model misspecification for two classes of regression models for right censored survival data additive and multiplicative models for the conditional hazard rate a particular attention is given to data exhibiting time varying regression coefficients the class of multiplicative models is represented by cox ph model and gray s tvc model respectively and for additive models we use aalen s linear model both gray s tvc model and aalen s linear model incorporate time varying coefficients a simulation study is performed to cross analyze survival data which follows either a multiplicative or an additive model for the conditional hazard rate the effect of misspecifying the true model for the conditional hazard rate is assessed by looking at the power of the individual models to detect an existing effect bias and mean square error observed for each conditional model based estimator of survival we also show that aalen s model formulae is a first order taylor series approximation of that of gray s model which explains the comparably higher flexibility on part of the aalen s model as compared to the cox ph when the gray s tvc model for the data is misspecified

a generalized levinson algorithm for covariance extension with application to multiscale autoregressive modeling efficient computation of extensions of banded partially known covariance matrices is provided by the classical levinson algorithm one contribution of this paper is the introduction of a generalization of this algorithm that is applicable to a substantially broader class of extension problems this generalized algorithm can compute unknown covariance elements in any order that satisfies certain graph theoretic properties which we describe this flexibility which is not provided by the classical levinson algorithm is then harnessed in a second contribution of this paper the identification of a multiscale autoregressive mar model for the maximum entropy me extension of a banded partially known covariance matrix the computational complexity of mar model identification is an order of magnitude below that of explicitly computing a full covariance extension and is comparable to that required to build a standard autoregressive ar model using the classical levinson algorithm

multiscale recursive estimation data fusion and regularization we describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and or noisy measurements which may also be at several scales in particular multiscale signal representations lead naturally to pyramidal or tree like data structures in which each level in the tree corresponds to a particular scale of representation a class of multiscale dynamic models evolving on dyadic trees is introduced the main focus of this paper is on the description analysis and application of an extremely efficient optimal estimation algorithm for this class of models this algorithm consists of a fine to coarse filtering sweep followed by a coarse to fine smoothing step corresponding to the dyadic tree generalization of kalman filtering and rauch tung striebel smoothing the kalman filtering sweep consists of the recursive application of three steps a measurement update step a fine to coarse prediction step and a fusion step we illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of fractal regularizations of ill posed signal and image processing problems encountered

estimation of fractal signals from noisy measurements using wavelets the role of the wavelet transformation as a whitening filter for 1 f processes is exploited to address problems of parameter and signal estimations for 1 f processes embedded in white background noise robust computationally efficient and consistent iterative parameter estimation algorithms are derived based on the method of maximum likelihood and cramer rao bounds are obtained included among these algorithms are optimal fractal dimension estimators for noisy data algorithms for obtaining bayesian minimum mean square signal estimates are also derived together with an explicit formula for the resulting error these smoothing algorithms find application in signal enhancement and restoration the parameter estimation algorithms find application in signal enhancement and restoration the parameter estimation algorithms in addition to solving the spectrum estimation problem and to providing parameters for the smoothing process are useful in problems of signal detection and classification results from simulations are presented to demonstrated the viability of the algorithms

likelihood calculation for a class of multiscale stochastic models with application to texture discrimination a class of multiscale stochastic models based on scale recursive dynamics on trees has previously been introduced theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale e g 1 f processes as well as 1d markov processes and 2d markov random fields moreover efficient optimal estimation algorithms have been developed for these models by exploiting their scale recursive structure the authors exploit this structure in order to develop a computationally efficient and parallelizable algorithm for likelihood calculation they illustrate one possible application to texture discrimination and demonstrate that likelihood based methods using the algorithm achieve performance comparable to that of gaussian markov random field based techniques which in general are prohibitively complex computationally

free vibration analysis of non cylindrical helices with variable cross section by using mixed fem the objective of the study is to present a mixed finite element fe formulation for the free vibration analysis of non cylindrical helices with variable cross section non cylindrical helix geometry was well approximated through the variable arc lengths and linear variations in curvatures via shape functions the mixed fe model for non cylindrical helices was developed by using the exact cylindrical helix geometry and corresponding field equations the element and consistent mass matrices are attained under these assumptions the element matrix is derived based on the timoshenko beam theory and the effects of rotary inertia are involved into the mass matrix although the formulation is quite simple the generated element is capable to provide highly accurate solutions for the conical barrel and hyperboloidal geometries of non cylindrical helices the results of presented fe model based on an approximated geometry approach are in a good agreement with the other studies in the actual literature some original examples were generated and solved for the literature as well

a note on permutation tests for variance components in multilevel generalized linear mixed models in many applications of generalized linear mixed models to multilevel data it is of interest to test whether a random effects variance component is zero it is well known that the usual asymptotic chi square distribution of the likelihood ratio and score statistics under the null does not necessarily hold in this note we propose a permutation test based on randomly permuting the indices associated with a given level of the model that has the correct type i error rate under the null results from a simulation study suggest that it is more powerful than tests based on mixtures of chi square distributions the proposed test is illustrated using data on the familial aggregation of sleep disturbance

functional inference in frailty measurement error models for clustered survival data using the simex approach we consider frailty models for clustered survival data in the presence of measurement errors in covariates we first show that when the measurement error is accounted for in a full likelihood analysis but the distribution of the unobserved covariate is misspecified the maximum likelihood estimators are asymptotically biased especially for the variance component whose bias can be substantial we then discuss making inference using functional estimation via the simex method where no distribution of the unobserved error prone covariate is assumed the simex method is easy to implement by repeatedly fitting standard frailty models we study the asymptotic properties of the simex estimates and show that they are consistent and asymptotically normal in simulation studies we compare the simex method and the likelihood method in terms of efficiency and robustness we also propose a simex score test for the variance component to test for the within cluster correlation and evaluate its performance through simu

generalized coordinate for warping of naturally curved and twisted beams with general cross sectional shapes this paper presents an efficient procedure for analyzing naturally curved and twisted beams with general cross sectional shapes the hypothesis concerning the cross sectional shapes of the beams is abandoned in this analysis and relatively general equations are derived for the analysis of such a structure solving directly such equations for various boundary conditions which take into account the effects of torsion related warping as well as transverse shear deformations can yield the solutions to the problem the solutions can be used to calculate various internal forces stresses strains and displacements of the beams the present theory will be used to investigate the stresses and displacements of a cantilevered curved beam subjected to action of arbitrary load the numerical results are very close to the fem results

on the dynamics of spatially curved and twisted rods a finite element formulation for spatially curved and twisted rods a set of governing equations consisting of equilibrium equations and strain displacement and constitutive relations are derived in terms of three translational and three rotational degrees of freedom by solving the strain displacement relations for constant and zero states of strain the rigid body and constant strain modes of the rod are obtained these displacement modes are then used as basis functions for development of a finite element model to verify the formulation and the elemental matrices three examples are analyzed for free vibrations and in each case the computed results are compared with those obtained experimentally good agreement is found for several modes of vibrations

analytical formulation and evaluation for free vibration of naturally curved and twisted beams abstract an analytical study for free vibration of naturally curved and twisted beams with uniform cross sectional shapes is carried out using spatial curved beam theory based on the washizu s static model in the governing equations of motion of the beams all displacement functions and the generalized warping coordinate are defined at the centroid axis and also the effects of rotary inertia transverse shear deformations and torsion related warping are included in the proposed model explicit analytical expressions are derived for the vibrating mode shapes of a curved bending torsional shearing coupled beam under clamped clamped boundary condition with the help of symbolic computing package mathematica and a process of searching is used to determine the natural frequencies comparisons of the present results with the fem results using beam elements in ansys code show good accuracy in computation and validity of the model further the present model is used for cylindrical helical springs with circular cross section fixed at both ends and the results indicate that the natural frequencies agree well with the theoretical and experimental results available

selecting factors predictive of heterogeneity in multivariate event time data in multivariate survival analysis investigators are often interested in testing for heterogeneity among clusters both overall and within specific classes we represent different hypotheses about the heterogeneity structure using a sequence of gamma frailty models ranging from a null model with no random effects to a full model having random effects for each class following a bayesian approach we define prior distributions for the frailty variances consisting of mixtures of point masses at zero and inverse gamma densities since frailties with zero variance effectively drop out of the model this prior allocates probability to each model in the sequence including the overall null hypothesis of homogeneity using a counting process formulation the conditional posterior distributions of the frailties and proportional hazards regression coefficients have simple forms posterior computation proceeds via a data augmentation gibbs sampling algorithm a single run of which can be used to obtain model averaged estimates of the population parameters and posterior model probabilities for testing hypotheses about the heterogeneity structure the methods are illustrated using data from a lung cancer trial

fractal estimation using models on multiscale trees we estimate the hurst parameter h of fractional brownian motion or by extension the fractal exponent spl phi of stochastic processes having 1 f sup spl phi like spectra by applying a multiresolution framework this framework admits an efficient likelihood function evaluation allowing us to compute the maximum likelihood estimate of this fractal parameter with relative ease in addition to yielding results that compare well with other proposed methods and in contrast with other approaches our method is directly applicable with at most very simple modification in a variety of other contexts including fractal estimation given irregularly sampled data or nonstationary measurement noise and the estimation of fractal parameters for 2 d random fields

free vibration analysis of cylindrical helical springs with noncircular cross sections abstract the free vibration analysis of cylindrical helical springs with noncircular cross sections is carried out by means of an analytical study in the governing equations of motion of a spring all displacement functions and a generalized warping coordinate are defined at the centroidal principal axis the effects of the rotational inertia axial and shear deformations including torsion related warping deformations are also considered in the formulations explicit analytical expressions that give the vibrating mode shapes are derived by rigorous application of the symbolic computing package mathematica and the muller root search method is used to determine the natural frequencies numerical examples are provided for springs with elliptic rectangular and equilateral triangular cross sections and subjected to clamped clamped and clamped free boundary conditions the natural frequencies are presented for a range of geometric parameters in the case of elliptical wires results are presented for the aspect ratio a b ranging from 3 5 to 5 3 the helix pitch angle from 5 to 12 5 the number of active turns n from 6 to 12 and the ratio of cylinder radius to minor axis r 2a ranging from 20 3 to 50 3 validation of the proposed model has been achieved through comparison with a finite element model using three dimensional solid elements and the results available in published literature which in these cases indicates a good correlation

a frailty model for informative censoring to account for the correlation between failure and censoring we propose a new frailty model for clustered data in this model the risk to be censored is affected by the risk of failure this model allows flexibility in the direction and degree of dependence between failure and censoring it includes the traditional frailty model as a special case it allows censoring by some causes to be analyzed as informative while treating censoring by other causes as noninformative it can also analyze data for competing risks to fit the model the em algorithm is used with markov chain monte carlo simulations in the e steps simulation studies and analysis of data for kidney disease patients are provided consequences of incorrectly assuming noninformative censoring are investigated

the power of testing a semi parametric shared gamma frailty parameter in failure time data frailty is usually modeled as an unobserved random variable acting multiplicatively on the baseline hazard function where a shared unobserved quantity in the intensity induces a positive correlation among the observed failure times using the asymptotic properties of the nonparametric maximum likelihood estimator for the gamma frailty model we derive a power function for testing the shared frailty parameter and evaluate the effect of number of groups and number of individuals per groups on the power of the test by simulation studies the results show that choosing between 8 and 25 groups with sample sizes between 200 and 500 individuals will be enough to get a high power

a locally most powerful test for homogeneity with many strata summary a locally most powerful test is proposed for homogeneity of nuisance parameters from many strata in the mixed model setting the test is based on the difference between the square of the score and the observed information about the nuisance parameters all evaluated at the null hypothesis several examples including constant normal mean with possibly different variances and matched case control studies are presented in detail the relative efficiencies of the unstratified estimator of parameter of interest versus the stratified one are calculated two data sets on matched case control studies are used for illustration

multiscale representations of markov random fields recently a framework for multiscale stochastic modeling was introduced based on coarse to fine scale recursive dynamics defined on trees this model class has some attractive characteristics which lead to extremely efficient statistically optimal signal and image processing algorithms the authors show that this model class is also quite rich in particular they describe how 1 d markov processes and 2 d markov random fields mrfs can be represented within this framework the recursive structure of 1 d markov processes makes them simple to analyze and generally leads to computationally efficient algorithms for statistical inference on the other hand 2 d mrfs are well known to be very difficult to analyze due to their noncausal structure and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification in contrast their multiscale representations are based on scale recursive models and thus lead naturally to scale recursive algorithms which can be substantially more efficient computationally than those associated with mrf models in 1 d the multiscale representation is a generalization of the midpoint deflection construction of brownian motion the representation of 2 d mrfs is based on a further generalization to a midline deflection construction the exact representations of 2 d mrfs are used to motivate a class of multiscale approximate mrf models based on one dimensional wavelet transforms they demonstrate the use of these latter models in the context of texture representation and in particular they show how they can be used as approximations for or alternatives to well known mrf texture models

vibrations of rods with general space curvature in this paper the equations of motion for a rod with arbitrary space curvature and cross section geometry are re examined and results showing the effects of curvature torsion and cross section shape on natural frequencies and mode shapes are presented expressions for the kinetic and potential energy functions of a curved and twisted rod are formulated in terms of centerline displacements and cross section rotations these expressions are first used to derive the equations of motion and natural boundary conditions by using hamilton s principle next the kinetic and potential energy functions are used to formulate a rayleigh ritz solution for the mode shapes and natural frequencies of helical rods with fixed fixed and fixed free ends the effects of space curvature and torsion and of cross section out of roundness on frequencies and mode shapes of fixed free helical rods are examined

natural vibration of arbitrary spatially curved rectangular rods with pre twisted angles abstract for the natural vibration of rods of pre twisted rectangular cross sections with its centerline spatially curved and twisted arbitrarily a system of non dimensional ordinary differential equations is obtained in three translation displacements and three rotational angles of the rod the eigenvalue problem is solved for the natural frequencies of various pre twisted angles of the rectangular cross section area aspect ratios slenderness ratio end conditions and functions of varying cross section area along the rods by using a numerical method of runge kutta integration the eigenvalues are determined by the vanishing of a rank six determinant whose column vectors are obtained at the end of six independent numerical integrations the differential equations of the adjoint operator system for the eigenvalue problem with its associated boundary conditions are also derived and solved for the eigenvalues to check with that of the vibration system it is found that the effect of increasing pre twisted angle of the rod is that the lowest natural frequency of an arbitrary curved rod will asymptotically tend to be a constant in spite of slenderness ratio aspect ratio of the rectangular cross section e g ratio types of end conditions or the functions of the cross section area along the rod

efficient multiscale regularization with applications to the computation of optical flow a new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence the solution of the new problem formulation is computed with an efficient multiscale algorithm experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size the new approach also has a number of other important advantages specifically multiresolution flow field estimates are available allowing great flexibility in dealing with the tradeoff between resolution and accuracy multiscale error covariance information is also available which is of considerable use in assessing the accuracy of the estimates in particular these error statistics can be used as the basis for a rational procedure for determining the spatially varying optimal reconstruction resolution furthermore if there are compelling reasons to insist upon a standard smoothness constraint the new algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation finally the usefulness of the approach should extend to a wide variety of ill posed inverse problems in which variational techniques seeking a smooth solution are generally used

fractional brownian motion a maximum likelihood estimator and its application to image texture fractals have been shown to be useful in characterizing texture in a variety of contexts use of this methodology normally involves measurement of a parameter h which is directly related to fractal dimension in this work the basic theory of fractional brownian motion is extended to the discrete case it is shown that the power spectral density of such a discrete process is only approximately proportional to f a instead of in direct proportion as in the continuous case an asymptotic cramer rao bound is derived for the variance of an estimate of h subsequently a maximum likelihood estimator mle is developed to estimate h it is shown that the variance of this estimator nearly achieves the minimum bound a generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the mle when the discrete fractional brownian process is contaminated with additive gaussian noise the results show that even at signal to noise ratios of 30 db significant errors in estimation of h can result when noise is present the mle is then applied to x ray images of the human calcaneus to demonstrate how the line to line formulation can be applied to the two dimensional case these results indicate that it has strong potential for quantifying texture

residuals for relative risk regression summary several possible definitions of residuals are given for relative risk regression with time varying covariates each such residual has a representation as an estimator of a stochastic integral with respect to the martingale arising from a subject s failure time counting process previously proposed residuals for individual study subjects and for specific time points are shown to be special cases of this definition as are previously derived regression diagnostics an illustration and various generalizations are also given able methods are required to detect various departures from modelling assumptions suitably defined residuals may play an important role in such identification however the nonparametric aspect of the model the possibility that modelled regression variables may be varying with follow up time and most importantly the usual presence of right censorship implies that specialized residual definitions are required the class of residuals considered here is most easily formulated using counting process notation for the failure time data let ni t yi t and zi t represent respectively for the ith subject the values of counting censoring and covariate processes at follow up time t i 1 n while ni u yi u zi u 0c u t specifies the corresponding histories for the ith subject prior to time t thus in a typical univariate failure time application ni with right continuous sample paths will take value zero prior to the time of failure on the ith subject and value one thereafter while yi with left continuous sample paths will take value one at times at which the ith subject is at risk for an observed failure and value zero otherwise the counting process ni can be uniquely decomposed so that for all t i

three measures of explained variation for correlated survival data under the proportional hazards mixed effects model measures of explained variation are useful in scientific research as they quantify the amount of variation in an outcome variable of interest that is explained by one or more other variables we develop such measures for correlated survival data under the proportional hazards mixed effects model because different approaches have been studied in the literature outside the classical linear regression model we investigate three measures r 2 rres2 and 2 that quantify three different population coefficients we show that although the three population measures are not the same they reflect similar amounts of variation explained by the predictors among the three measures we show that r 2 which is the simplest to compute is also consistent for the first population measure under the usual asymptotic scenario when the number of clusters tends to infinity the other two measures on the other hand all require that in addition the cluster sizes be large we study the properties of the measures both analytically and through simulation studies we illustrate their different usage on a multi center clinical trial and a recurrent events data set copyright 2016 john wiley sons ltd

the modeling and estimation of statistically self similar processes in a multiresolution framework statistically self similar sss processes can be used to describe a variety of physical phenomena yet modeling these phenomena has proved challenging most of the proposed models for sss and approximately sss processes have power spectra that behave as 1 f sup spl gamma such as fractional brownian motion fbm fractionally differenced noise and wavelet based syntheses the most flexible framework is perhaps that based on wavelets which provides a powerful tool for the synthesis and estimation of 1 f processes but assumes a particular distribution of the measurements an alternative framework is the class of multiresolution processes proposed by chou et al 1994 which has already been shown to be useful for the identification of the parameters of fbm these multiresolution processes are defined by an autoregression in scale that makes them naturally suited to the representation of sss and approximately sss phenomena both stationary and nonstationary also this multiresolution framework is accompanied by an efficient estimator likelihood calculator and conditional simulator that make no assumptions about the distribution of the measurements we show how to use the multiscale framework to represent sss or approximately sss processes such as fbm and fractionally differenced gaussian noise the multiscale models are realized by using canonical correlations cc and by exploiting the self similarity and possible stationarity or stationary increments of the desired process a number of examples are provided to demonstrate the utility of the multiscale framework in simulating and estimating sss processes

multiply rooted multiscale models for large scale estimation divide and conquer or multiscale techniques have become popular for solving large statistical estimation problems the methods rely on defining a state which conditionally decorrelates the large problem into multiple subproblems each more straightforward than the original however this step cannot be carried out for asymptotically large problems since the dimension of the state grows without bound leading to problems of computational complexity and numerical stability in this paper we propose a new approach to hierarchical estimation in which the conditional decorrelation of arbitrarily large regions is avoided and the problem is instead addressed piece by piece the approach possesses promising attributes it is not a local method the estimate at every point is based on all measurements it is numerically stable for problems of arbitrary size and the approach retains the benefits of the multiscale framework on which it is based a broad class of statistical models a stochastic realization theory an algorithm to calculate statistical likelihoods and the ability to fuse local and nonlocal measurements

testing goodness of fit in regression a general approach for specified alternatives when fitting generalized linear models or the cox proportional hazards model it is important to have tools to test for lack of fit because lack of fit comes in all shapes and sizes distinguishing among different types of lack of fit is of practical importance we argue that an adequate diagnosis of lack of fit requires a specified alternative model such specification identifies the type of lack of fit the test is directed against so that if we reject the null hypothesis we know the direction of the departure from the model the goodness of fit approach of this paper allows to treat different types of lack of fit within a unified general framework and to consider many existing tests as special cases connections with penalized likelihood and random effects are discussed and the application of the proposed approach is illustrated with medical examples tailored functions for goodness of fit testing have been implemented in the r package globaltest copyright 2012 john wiley sons ltd

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

a canonical correlations approach to multiscale stochastic realization we develop a realization theory for a class of multiscale stochastic processes having white noise driven scale recursive dynamics that are indexed by the nodes of a tree given the correlation structure of a 1 d or 2 d random process our methods provide a systematic way to realize the given correlation as the finest scale of a multiscale process motivated by akaike s use of canonical correlation analysis to develop both exact and reduced order models for time series we too harness this tool to develop multiscale models we apply our realization scheme to build reduced order multiscale models for two applications namely linear least squares estimation and generation of random field sample paths for the numerical examples considered least squares estimates are obtained having nearly optimal mean square errors even with multiscale models of low order although both field estimates and field sample paths exhibit a visually distracting blockiness this blockiness is not an important issue in many applications for such applications our approach to multiscale stochastic realization holds promise as a valuable general tool

an overlapping tree approach to multiscale stochastic modeling and estimation recently a class of multiscale stochastic models has been introduced in which random processes and fields are described by scale recursive dynamic trees a major advantage of this framework is that it leads to an extremely efficient statistically optimal algorithm for least squares estimation in certain applications however estimates based on the types of multiscale models previously proposed may not be adequate as they have tended to exhibit a visually distracting blockiness we eliminate this blockiness by discarding the standard assumption that distinct nodes on a given level of the multiscale process correspond to disjoint portions of the image domain instead we allow a correspondence to overlapping portions of the image domain we use these so called overlapping tree models for both modeling and estimation in particular we develop an efficient multiscale algorithm for generating sample paths of a random field whose second order statistics match a prespecified covariance structure to any desired degree of fidelity furthermore we demonstrate that under easily satisfied conditions we can lift a random field estimation problem to one defined on an overlapped tree resulting in an estimation algorithm that is computationally efficient directly produces estimation error covariances and eliminates blockiness in the reconstructed imagery without any sacrifice in the resolution of fine scale detail

conditional akaike information under generalized linear and proportional hazards mixed models we study model selection for clustered data when the focus is on cluster specific inference such data are often modelled using random effects and conditional akaike information was proposed in vaida blanchard 2005 and used to derive an information criterion under linear mixed models here we extend the approach to generalized linear and proportional hazards mixed models outside the normal linear mixed models exact calculations are not available and we resort to asymptotic approximations in the presence of nuisance parameters a profile conditional akaike information is proposed bootstrap methods are considered for their potential advantage in finite samples simulations show that the performance of the bootstrap and the analytic criteria are comparable with bootstrap demonstrating some advantages for larger cluster sizes the proposed criteria are applied to two cancer datasets to select models when the cluster specific inference is of interest

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

permutation tests for centre effect on survival endpoints with application in an acute myeloid leukaemia multicentre study when analysing multicentre data it may be of interest to test whether the distribution of the endpoint varies among centres in a mixed effect model testing for such a centre effect consists in testing to zero a random centre effect variance component it has been shown that the usual asymptotic 2 distribution of the likelihood ratio and score statistics under the null does not necessarily hold in the case of censored data mixed effects cox models have been used to account for random effects but few works have concentrated on testing to zero the variance component of the random effects we propose a permutation test using random permutation of the cluster indices to test for a centre effect in multilevel censored data results from a simulation study indicate that the permutation tests have correct type i error rates contrary to standard likelihood ratio tests and are more powerful the proposed tests are illustrated using data of a multicentre clinical trial of induction therapy in acute myeloid leukaemia patients copyright 2014 john wiley sons ltd

wavelet analysis and synthesis of fractional brownian motion fractional brownian motion fbm offers a convenient modeling for nonstationary stochastic processes with long term dependencies and 1 f type spectral behavior over wide ranges of frequencies statistical self similarity is an essential feature of fbm and makes natural the use of wavelets for both its analysis and its synthesis a detailed second order analysis is carried out for wavelet coefficients of fbm it reveals a stationary structure at each scale and a power law behavior of the coefficients variance from which the fractal dimension of fbm can be estimated conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed consequences of discretization are considered and some connections between the wavelet point of view and previous approaches based on length measurements analysis or dyadic interpolation synthesis are briefly pointed out

proportional hazards model with random effects we propose a general proportional hazards model with random effects for handling clustered survival data this generalizes the usual frailty model by allowing a multivariate random effect with arbitrary design matrix in the log relative risk in a way similar to the modelling of random effects in linear generalized linear and non linear mixed models the distribution of the random effects is generally assumed to be multivariate normal but other preferably symmetrical distributions are also possible maximum likelihood estimates of the regression parameters the variance components and the baseline hazard function are obtained via the em algorithm the e step of the algorithm involves computation of the conditional expectations of functions of the random effects for which we use markov chain monte carlo mcmc methods approximate variances of the estimates are computed by louis formula and posterior expectations and variances of the individual random effects can be obtained as a by product of the estimation the inference procedure is exemplified on two data sets

tests for variation over groups in survival data abstract when survival data can be divided into natural groups such as in a clinical trial with patients from a number of different institutions the question arises whether effects are different for the different groups for situations where one is concerned with a random pattern of variation over groups this article proposes testing the null hypothesis of no variation using statistics based on the sums of martingale residuals over subjects within groups these tests are closely related to the locally most powerful tests of liang for testing for variation across a large number of strata the tests are applied to data from a lung cancer trial conducted by the eastern cooperative oncology group