semiparametric transformation models for semicompeting survival data semicompeting risk outcome data e g time to disease progression and time to death are commonly collected in clinical trials however analysis of these data is often hampered by a scarcity of available statistical tools as such we propose a novel semiparametric transformation model that improves the existing models in the following two ways first it estimates regression coefficients and association parameters simultaneously second the measure of surrogacy for example the proportion of the treatment effect that is mediated by the surrogate and the ratio of the overall treatment effect on the true endpoint over that on the surrogate endpoint can be directly obtained we propose an estimation procedure for inference and show that the proposed estimator is consistent and asymptotically normal extensive simulations demonstrate the valid usage of our method we apply the method to a multiple myeloma trial to study the impact of several biomarkers on patients semicompeting outcomes namely time to progression and time to death

spectral theory for the periodic sine gordon equation a concrete viewpoint a summary of the spectral theory for quasiperiodic sine and sinh gordon equations is given analogies with whole line solitons and scattering theory motivates the discussion the relation between the ingredients in the inverse spectral solution of the periodic sine gordon equation and physical characteristics of sine gordon waves is emphasized the explicit topics covered are summarized in the table of contents in the introduction

maximum principles for some quasilinear elliptic systems abstract we give maximum principles for solutions u r n to a class of quasilinear elliptic systems whose prototype is i 1 n x i 1 n j 1 n a i j x u x u x j x 0 x where 1 n is the equation index and is an open bounded subset of r n we assume that coefficients a i j x y are measurable with respect to x continuous with respect to y r n bounded and elliptic in vectorial problems when trying to bound the solution by means of the boundary data we need to bypass de giorgi s counterexample by means of some additional structure assumptions on the coefficients a i j x y in this paper we assume that off diagonal coefficients a i j have support in some staircase set along the diagonal in the y y plane

backlund transformations for nonlinear sigma models with values in riemannian symmetric spaces this work deals with backlund transformations for the principal sl n sigma model together with all reduced models with values in riemannian symmetric spaces first the dressing method of zakharov mikhailov and shabat is shown for the case of a meromorphic dressing matrix to be equivalent to a backlund transformation for an associated linearly extended system comparison of this multi backlund transformation with the composition of ordinary ones leads to a new proof of the permutability theorem a new method of solution for such multi backlund transformations mbt is developed by the introduction of a soliton correlation matrix which satisfies a riccati system equivalent to the mbt using the geometric structure of this system a linearization is achieved leading to a nonlinear superposition formula expressing the solution explicitly in terms of solutions of a single backlund transformation through purely linear algebraic relations a systematic study of all reductions of the system by involutive automorphisms is made thereby defining the multi backlund transformations and their solution for all riemannian symmetric spaces

on the τ function of the painleve equations abstract concerning the hamiltonian structure associated with painleve equations we define the function related to a hamiltonian and show that the correlation function given in the study of the two dimensional ising model is a function for the third painleve equation the list of the hamiltonians which are polynomials in the two canonical variables is given and we prove that the function related to each of them is holomorphic

a semiparametric method for estimating population size for capture recapture experiments with random covariates in continuous time a semiparametric estimation procedure is proposed to model capture recapture data with the aim of estimating the population size for a closed population individuals covariates are possibly time dependent and missing at noncaptured times and may be measured with error a set of estimating equations ees based on covariate process and capture recapture data is constructed to estimate the relevant parameters and the population size these ees can be solved by an algorithm similar to an em algorithm simulation results show that the proposed procedures work better than the naive estimate in some cases they are even better than ideal estimates for which the true values of covariates are available for all captured subjects over the entire experimental period we apply the method to a capture recapture experiment on the bird species prinia flaviventris in hong kong

consecutive rosochatius deformations of the neumann system consecutive rosochatius deformations of the neumann system are investigated it is first shown that different realizations of a classical sl 2 gaudin magnet model yield different integrable hamiltonian systems then an algorithm of constructing infinitely many symplectic realizations of sl 2 algebra from a known one is presented and thus the neumann system can be deformed consecutively the second rosochatius deformation of the neumann system is taken as an illustrative example to show that the deformed systems admit separations of variables and may be linearized on the jacobi variety

the c neumann problem as a completely integrable system on an adjoint orbit it is shown by purely lie algebraic methods that the c neumann problem the motion of a material point on a sphere under the influence of a quadratic potential is a completely integrable system of euler poisson equations on a minimal dimensional orbit of a semidirect product of lie algebras 1 the c neumann problem the motion of a point on the sphere s 1 under the influence of a quadratic potential u x ax x x e r a diag al an is a completely integrable hamiltonian system for n 3 this has been shown by c neumann in 1859 12 and for arbitrary n by k uhlenbeck 16 r devaney 3 j moser 10 11 m adler and p van moerbeke 2 in this paper we show how this problem fits naturally in the framework of euler poisson equations 41 5 14 17 proving that the c neumann problem is a hamiltonian system on a minimaldimensional adjoint orbit in a semidirect product of lie algebras thus its complete integrability will follow entirely from lie algebraic considerations the equations of motion are i ax1 axx i 1 n 1 1 where the lagrange multiplier a ax x 11x112 is chosen such that x e sn i during the motion set x y and get the equivalent system to 1 1 xi yi yi a1xi ax x 11y112 xi llxll 1 x y 0 1 2 the following crucial remark that motivated the present investigation is due to k uhlenbeck and can be verified without any difficulties lemma 1 1 put x xixj p yixj xiyj system 1 2 is equivalent to x p x p x a lixl 1 x y o 1 3 remark that if one replaces x and a by x id n and a tr a id n respectively where id is the n x n identity matrix equations 1 3 remain unchanged from now on we shall assume that in 1 3 this change has been made so that x p a e sl n the next section gives a lie algebraic interpretation to these equations received by the editors march 12 1980 1980 mathematics subject classification primary 58f07 70h05 secondary 53c15 17b99

missing data methods for generalized linear models a comparative review missing data is a major issue in many applied problems especially in the biomedical sciences we review four common approaches for inference in generalized linear models glms with missing covariate data maximum likelihood ml multiple imputation mi fully bayesian fb and weighted estimating equations wees there is considerable interest in how these four methodologies are related the properties of each approach the advantages and disadvantages of each methodology and computational implementation we examine data that are missing at random and nonignorable missing for ml we focus on techniques using the em algorithm and in particular discuss the em by the method of weights and related procedures as discussed by ibrahim for mi we examine the techniques developed by rubin for fb we review approaches considered by ibrahim et al for wee we focus on the techniques developed by robins et al we use a real dataset and a detailed simulation study to compare the four methods

on the existence of weak solutions to a class of nonlinear elliptic systems with drift term abstract we study the existence of a weak solution u of the following nonlinear vectorial dirichlet problem u w 0 1 2 r n i 1 n d i a i x u d u i 1 n d i j 1 n e i j x u j f x x where is a bounded subset of r n n 3 u and f for any 1 2 n are the th components of the vectors u and f respectively and the tensors a x s and e x satisfy suitable structural assumptions

the kowalewski and henon heiles motions as manakov geodesic flows on so 4 a two dimensional family of lax pairs the invariant surfaces for the kowalewski top the henon heiles system and the manakov geodesic flow onso 4 complete into abelian surfacesa by adjoining in each case a divisord of arithmetic genus 9 these divisors belong to the same linear system ona and they each define a polarization 2 4 therefore there are rational maps transforming the kowalewski top and the henon heiles system into manakov s geodesic flow onso 4 this paper deals with the precise geometric relationship between these three problems it is based on the splitting of the 8 dimensional space of sections ofd theta functions into an even and an odd part and also on a normal form for the six quadrics describinga as embedded in 7 as a byproduct we get a 2 dimensional family of lax pairs for both the kowalewski top and the henon heiles system

survival analysis with heterogeneous covariate measurement error this article is motivated by a time to event analysis where the covariate of interest was measured at the wrong time we show that the problem can be formulated as a special case of survival analysis with heterogeneous covariate measurement error and develop a general analytic framework we study the asymptotic behavior of the naive partial likelihood estimates and analytically demonstrate that under the heterogeneous measurement error structure and the assumption that all components of the covariate vector and the measurement error vector combined are mutually independent these naive estimates will shrink toward 0 and that the degree of attenuation increases as the measurement error increases we also give counterexamples for reverse attenuation when the independence conditions are violated we use our analytical results to derive a simple bias correcting estimator that performs well in simulations for small and moderate amounts of measurement error our framework can be used to provide insight into th

proportional hazards regression with missing covariates abstract nonparametric maximum likelihood npml is used to estimate regression parameters in a proportional hazards regression model with missing covariates the npml estimator is shown to be consistent and asymptotically normally distributed under some conditions em type algorithms are applied to solve the maximization problem variance estimates of the regression parameters are obtained by a profile likelihood approach that uses em aided numerical differentiation simulation results indicate that the npml estimates of the regression parameters are more efficient than the approximate partial likelihood estimates and estimates from complete case analysis when missing covariates are missing completely at random and that the proposed method corrects for bias when the missing covariates are missing at random

isomonodromic deformations of a rational differential system and reconstruction with the topological recursion the sl2 case in this paper we show that it is always possible to deform a differential equation x x l x x with l x sl2 c x by introducing a small formal parameter in such a way that it satisfies the topological type properties of bergere borot and eynard annales henri poincare 16 12 2713 2782 2015 this is obtained by including the former differential equation in an isomonodromic system and using some homogeneity conditions to introduce the topological recursion is then proved to provide a formal series expansion of the corresponding tau function whose coefficients can thus be expressed in terms of intersections of tautological classes in the deligne mumford compactification of the moduli space of surfaces we present a few examples including any fuchsian system of sl2 c x as well as some elements of painleve hierarchies

dual isomonodromic deformations and moment maps to loop algebras the hamiltonian structure of the monodromy preserving deformation equations of jimboet al jmms is explained in terms of parameter dependent pairs of moment maps from a symplectic vector space to the dual spaces of two different loop algebras the nonautonomous hamiltonian systems generating the deformations are obtained by pulling back spectral invariants on poisson subspaces consisting of elements that are rational in the loop parameter and identifying the deformation parameters with those determining the moment maps this construction is shown to lead to dual pairs of matrix differential operators whose monodromy is preserved under the same family of deformations as illustrative examples involving discrete and continuous reductions a higher rank generalization of the hamiltonian equations governing the correlation functions for an impenetrable bose gas is obtained as well as dual pairs of isomonodromy representations for the equations of the painleve transcendentspv andvi

reweighting estimators for cox regression with missing covariates missingness in covariates is a common problem in survival data in this article we propose a reweighting method for estimating the regression parameters in the cox model with missing covariates we also consider the augmented reweighting method by subtracting the projection term onto the nuisance tangent space the proposed method provides consistent and asymptotically normally distributed estimators when the missing data mechanism depends on the outcome variables as well as on the observed covariates with either monotone or arbitrary nonmonotone missingness patterns simulation results indicate that in most situations the proposed reweighting estimators are more efficient than the inverse probability weighting estimators for the regression coefficients of the missing covariates and are as efficient as or more efficient than the inverse probability weighting estimators for the regression coefficients of the completely observed covariates the simple reweighting estimators can be easily implemented in st

hyperelliptic quasi periodic and soliton solutions of the nonlinear schrodinger equation on considere la construction de solutions par des methodes de geometrie algebriques et en particulier par les fonctions theta hyperelliptiques

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

kac moody lie algebras and soliton equations iii stationary equations associated with a1 1 abstract the hamiltonian structure of stationary soliton equations associated with the akns eigenvalue problem is derived in two ways first it is shown to arise from the kostant kirillov symplectic structure on a coadjoint orbit in an infinite dimensional lie algebra second it is obtained as the restriction to a finite dimensional manifold of the infinite dimensional hamiltonian structure associated with a certain eigenvalue problem polynomial in the eigenvalue parameter

double semiparametric method for missing covariates in cox regression models the problem of nuisance covariate model specification is considered in cox regression where the maximum semiparametric likelihood method is used to handle the missing covariates a component of the covariates is modeled nonparametrically to achieve robustness against covariate model misspecification and to reduce the number of possibly intractable integrations involved in the parametric modeling of the covariates the statistical properties of the proposed method are examined it is found that in some important situations the maximum semiparametric likelihood can be applied without making any additional parametric model assumptions on covariates the proposed method can yield a more efficient estimator than the nonparametric imputation methods and does not require specification of the missingness mechanism when compared with the inverse probability weighting method a real data example is analyzed to demonstrate use of the proposed method

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

eeboost a general method for prediction and variable selection based on estimating equations the modern statistical literature is replete with methods for performing variable selection and prediction in standard regression problems however simple models may misspecify or fail to capture important aspects of the data generating process such as missingness correlation and over underdispersion in this article we describe eeboost a strategy for variable selection and prediction which can be applied in high dimensional settings where inference for low dimensional parameters would typically be based on estimating equations the method is simple flexible and easily implemented using existing software the eeboost algorithm is obtained as a modification of the standard boosting or functional gradient descent technique we show that eeboost is closely related to a class of l1 constrained projected likelihood ratio minimizations and therefore produces similar variable selection paths to penalized methods without the need to apply constrained optimization algorithms the flexibility of eeboost is

isospectral hamiltonian flows in finite and infinite dimensions the approach to isospectral hamiltonian flow introduced in part i is further developed to include integration of flows with singular spectral curves the flow on finite dimensional ad invariant poisson submanifolds of the dual widetilde gl r of the positive part of the loop algebra widetilde gl r is obtained through a generalization of the standard method of linearization on the jacobi variety of the invariant spectral curves these curves are embedded in the total space of a line bundlet p1 c allowing an explicit analysis of singularities arising from the structure of the image of a moment map tilde j r m n r times m n r to widetilde gl r from the space of rank r deformations of a fixedn n matrixa it is shown how the linear flow of line bundles e t to tilde s over a suitably desingularized curve tilde s may be used to determine both the flow of matricial polynomialsl and the hamiltonian flow in the spacemn r mn r in terms of functions the resulting flows are proved to be completely integrable the reductions to subalgebras developed in part i are shown to correspond to invariance of the spectral curves and line bundles e t to tilde s under certain linear or anti linear involutions the integration of two examples from part i is given to illustrate the method the rosochatius system and the cnls coupled non linear schrodinger equation

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

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

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

reweighting estimators for cox regression with missing covariate data analysis of insulin resistance and risk of stroke in the northern manhattan study incomplete covariates often obscure analysis results from a cox regression in an analysis of the northern manhattan study nomas to determine the influence of insulin resistance on the incidence of stroke in non diabetic individuals insulin level is unknown for 34 1 of the subjects the available data suggest that the missingness mechanism depends on outcome variables which may generate biases in estimating the parameters of interest if only using the complete observations this article aimed to introduce practical strategies to analyze the nomas data and present sensitivity analyses by using the reweighting method in standard statistical packages when the data set structure is in counting process style the reweighting estimates can be obtained by built in procedures with variance estimated by the jackknife method simulation results indicate that the jackknife variance estimate provides reasonable coverage probability in moderate sample sizes we subsequently conducted sensitivity analyses for the nomas data showing that the risk estimates are robust to a variety of missingness mechanisms at the end of this article we present the core sas and r programs used in the analysis

cox regression with survival time dependent missing covariate values analysis with time to event data in clinical and epidemiological studies often encounters missing covariate values and the missing at random assumption is commonly adopted which assumes that missingness depends on the observed data including the observed outcome which is the minimum of survival and censoring time however it is conceivable that in certain settings missingness of covariate values is related to the survival time but not to the censoring time this is especially so when covariate missingness is related to an unmeasured variable affected by the patient s illness and prognosis factors at baseline if this is the case then the covariate missingness is not at random as the survival time is censored and it creates a challenge in data analysis in this article we propose an approach to deal with such survival time dependent covariate missingness based on the well known cox proportional hazard model our method is based on inverse propensity weighting with the propensity estimated by nonparametric kernel regression our estimators are consistent and asymptotically normal and their finite sample performance is examined through simulation an application to a real data example is included for illustration

sieve maximum likelihood estimation for regression models with covariates missing at random missing covariates are common in regression problems we propose a new semiparametric method based on a fully nonparametric distribution for the missing covariates that are assumed to be missing at random the method of sieve maximum likelihood estimation is used to obtain the estimators of the regression coefficients these estimators are shown to be consistent and asymptotically normal with their asymptotic covariance matrix that achieves the semiparametric efficiency bound a bootstrap approach is used to estimate the asymptotic covariance matrix some practical modeling approaches for high dimensional covariates are proposed extensive simulation studies are conducted to examine the finite sample properties of the estimates and a real data set from a liver cancer clinical trial is analyzed using the proposed method

on using the cox proportional hazards model with missing covariates summary we propose two methods for handling missing covariates in using the cox proportional hazards model the maximum partial likelihood estimator based only on study subjects having complete covariates does not utilise all available information also it is biased when the probability of missingness depends on the failure or censoring time our suggestion is to impute the conditional expectation of the statistic involving missing covariates given the available information the proposed method provides a consistent regression parameter estimator when the probability of missingness depends on the failure or censoring time as well as on the observed covariates also the proposed estimator is more efficient than the estimator suggested previously by lin ying 1993 when data are missing completely at random

r matrix construction of electromagnetic models for the painleve transcendents the painleve transcendents pi pv and their representations as isomonodromic deformation equations are derived as nonautonomous hamiltonian systems from the classical r matrix poisson bracket structure on the dual space slr 2 of the loop algebra slr 2 the hamiltonians are obtained by composing elements of the poisson commuting ring of spectral invariant functions on slr 2 with a time dependent family of poisson maps whose images are four dimensional rational coadjoint orbits in slr 2 each system may be interpreted as describing a particle moving on a surface of zero curvature in the presence of a time varying electromagnetic field the painleve equations follow from reduction of these systems by the hamiltonian flow generated by a second commuting element in the ring of spectral invariants 1995 american institute of physics

smallness and cancellation in some elliptic systems with measure data abstract in a bounded open subset r n we study dirichlet problems with elliptic systems involving a finite radon measure on r n with values into r n defined by div a x u x d u x in u 0 on where a i x y 1 n j 1 n a i j x y j with 1 n the equation index we prove the existence of a distributional solution u r n obtained as the limit of approximations by assuming i that coefficients a i j are bounded caratheodory functions ii ellipticity of the diagonal coefficients a i j and iii smallness of the quadratic form associated to the off diagonal coefficients a i j i e verifying a r staircase support condition with r 0 such a smallness condition is satisfied for instance in each one of these cases a a i j a j i skew symmetry b a i j is small c a i j may be decomposed into two parts the first enjoying skew symmetry and the second being small in absolute value we give an example that satisfies our hypotheses but does not satisfy assumptions introduced in previous works a brezis s type nonexistence result is also given for general smooth elliptic hyperbolic systems

quasilinear elliptic systems with measure data abstract we study the existence of solutions of quasilinear elliptic systems involving n equations and a measure on the right hand side with the form i 1 n x i 1 n j 1 n a i j x u x j u in u 0 on where 1 n is the equation index is an open bounded subset of r n u r n and is a finite randon measure on r n with values in r n existence of a solution is proved for two different sets of assumptions on a examples are provided that satisfy our conditions but do not satisfy conditions required on previous works on this matter

isospectral hamiltonian flows in finite and infinite dimensions i generalized moser systems and moment maps into loop algebras a moment map jr jia gl r is constructed from the poisson manifold j a of rank r perturbations of a fixed n xn matrix a to the dual r f e positive part of the formal loop algebra i r g r c 1 the adler kostant symes theorem is used to give hamiltonians which generate commutative isospectral flows on g r the pull back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in j a the latter may be identified with flows on finite dimensional coadjoint orbits in g and linearized on the jacobi variety of an invariant spectral curve xr which generically is an r sheeted riemann surface reductions of j a are derived corresponding to subalgebras of gl r c and sl r c determined as the fixed point set of automorphism groupes generated by involutions i e jdl the classical algebras as well as reductions to twisted subalgebras of s r c the theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of pde s

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

variable selection in the cox regression model with covariates missing at random summary we consider variable selection in the cox regression model cox 1975 biometrika 362 269 276 with covariates missing at random we investigate the smoothly clipped absolute deviation penalty and adaptive least absolute shrinkage and selection operator lasso penalty and propose a unified model selection and estimation procedure a computationally attractive algorithm is developed which simultaneously optimizes the penalized likelihood function and penalty parameters we also optimize a model selection criterion called the icq statistic ibrahim zhu and tang 2008 journal of the american statistical association 103 1648 1658 to estimate the penalty parameters and show that it consistently selects all important covariates simulations are performed to evaluate the finite sample performance of the penalty estimates also two lung cancer data sets are analyzed to demonstrate the proposed methodology

the soliton correlation matrix and the reduction problem for integrable systems integrable 1 1 dimensional systems associated to linear first order matrix equations meromorphic in a complex parameter as formulated by zakharov mikhailov and shabat 1 3 zms are analyzed by a new method based upon the soliton correlation matrix m matrix the multi backlund transformation which is equivalent to the introduction of an arbitrary number of poles in the zms dressing matrix is expressed by a pair of matrix riccati equations for them matrix through a geometrical interpretation based upon group actions on grassman manifolds the solution of this system is explicitly determined in terms of the solutions to the zms linear system reductions of the system corresponding to invariance under finite groups of automorphisms are also solved by reducing them matrix suitably so as to preserve the class of invariant solutions

multi hamiltonian structures for r matrix systems for the rational elliptic and trigonometric r matrices we exhibit the links between three levels of poisson spaces a some finite dimensional spaces of matrix valued meromorphic functions on the complex line b spaces of spectral curves and sheaves supported on them and c symmetric products of a surface we have at each level a linear space of compatible poisson structures and the maps relating the levels are poisson this leads in a natural way to the nijenhuis coordinates for these spaces at level b there are hamiltonian systems on these spaces which are integrable for each poisson structure in the family and which are such that the lagrangian leaves are the intersections of the symplectic leaves over the poisson structures in the family specific examples include many of the well known integrable systems

discrete time analogues of some nonlinear oscillators in the inverse square potential we propose a family of symplectic maps providing finite difference approximations for the wojciechowski and rosochatius systems the lax pair representations are found and complete integrability is proved

fitting semiparametric transformation regression models to data from a modified case cohort design summary we consider the problem of fitting semiparametric transformation regression models to data from a modified case cohort study in which the censoring times of all the censored subjects in the cohort are observed we propose to maximise a conditional profile likelihood to obtain the estimator of the regression parameter under the assumption that the censoring is independent of the covariates the estimator is shown to be consistent and asymptotically normally distributed numerical studies suggest that the relative efficiency of the estimator is very high and that the estimator is often less biased than the estimator from the complete case analysis and more accurate than the pseudolikelihood estimator

auxiliary covariate data in failure time regression summary we consider the problem of missing covariate data in the context of censored failure time relative risk regression auxiliary covariate data which are considered informative about the missing data but which are not explicitly part of the relative risk regression model may be available full covariate information is available for a validation set an estimated partial likelihood method is proposed for estimating relative risk parameters this method is an extension of the estimated likelihood regression analysis method for uncensored data pepe 1992 pepe fleming 1991 a key feature of the method is that it is nonparametric with respect to the association between the missing and observed including auxiliary covariate components asymptotic distribution theory is derived for the proposed estimated partial likelihood estimator in the case where the auxiliary or mismeasured covariates are categorical asymptotic efficiencies are calculated for exponential failure times using an exponential relative risk model the estimated partial likelihood estimator compares favourably with a fully parametric maximum likelihood analysis comparisons are also made with a standard partial likelihood analysis which ignores the incomplete observations important efficiency gains can be made with the estimated partial likelihood method small sample properties are investigated through simulation studies

kac moody lie algebras and soliton equations ii lax equations associated with a1 1 the soliton equations associated with sl 2 eigenvalue problems polynomial in the eigenvalue parameter are given a unified treatment they are shown to be generated by a single family of commuting hamiltonians on a subalgebra of the loop algebra of sl 2 the conserved densities and fluxes of the usual anks hierarchy are identified with conserved densities and fluxes for the polynomial eigenvalue problems the hamiltonian structures of the soliton equations associated with the polynomial eigenvalue problems are given a unified treatment

abelian integrals and the reduction method for an integrable hamiltonian system a classical finite dimensional integrable hamiltonian system corresponding to the motion of a particle constrained to an n dimensional sphere n 0 x2 1 with the hamiltonian h 1 2 y2 u2 x2 e x2 where u and e are constants and y are the momenta conjugate to x is integrated using several different methods these are the following 1 the projection of geodesic free flow on a larger space namely the sphere s2n 1 for e 0 the flow is obtained in terms of elementary functions 2 separation of variables in the hamilton jacobi equation in elliptic coordinates or alternatively the use of a complete set of integrals of motion in involution to reduce hamilton s equations to quadratures the flow is obtained in terms of abelian integrals which are then inverted in terms of generalized functions the relation between the different methods and results is clarified using methods of algebraic geometry in particular the geometry of quadrics

nonparametric maximum likelihood estimators of time dependent accuracy measures for survival outcome under two stage sampling designs large prospective cohort studies of rare chronic diseases require thoughtful planning of study designs especially for biomarker studies when measurements are based on stored tissue or blood specim

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

algebraic integrability of the confluent neumann system in this paper we study the neumann system which describes the harmonic oscillator of arbitrary dimension constrained to the sphere in particular we will consider the confluent case where two eigenvalues of the potential coincide which implies that the system has s1 symmetry we will prove complete algebraic integrability of the confluent neumann system and show that its flow can be linearized on the generalized jacobian torus of some singular algebraic curve the symplectic reduction of s1 action will be described and we will show that the general rosochatius system is a symplectic quotient of the confluent neumann system where all the eigenvalues of the potential are double

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f