shared frailty models for recurrent events and a terminal event there has been an increasing interest in the analysis of recurrent event data cook and lawless 2002 statistical methods in medical research 11 141 166 in many situations a terminating event such as death can happen during the follow up period to preclude further occurrence of the recurrent events furthermore the death time may be dependent on the recurrent event history in this article we consider frailty proportional hazards models for the recurrent and terminal event processes the dependence is modeled by conditioning on a shared frailty that is included in both hazard functions covariate effects can be taken into account in the model as well maximum likelihood estimation and inference are carried out through a monte carlo em algorithm with metropolis hastings sampler in the e step an analysis of hospitalization and death data for waitlisted dialysis patients is presented to illustrate the proposed methods methods to check the validity of the proposed model are also demonstrated this model avoids the difficulties encountered in alternative approaches which attempt to specify a dependent joint distribution with marginal proportional hazards and yields an estimate of the degree of dependence

a two unit general parallel system with n 2 cold standbys analytic and simulation approach abstract a parallel 2 n 2 system is investigated here where two units start their operation simultaneously and any one of them is replaced instantaneously upon its failure by one of the n 2 cold standbys we assume availability of n non identical non repairable units for replacement or support the system reliability is evaluated by recursive relations with unit lifetimes t i i 1 n that have a general joint distribution function f t on the basis of the derived expression simulation techniques have been developed for the evaluation of the system reliability and the mean time to failure useful when dealing with large systems or correlated unit lifetimes and less mathematically manageable distributions simulation results are presented for various lifetime distributions and comparisons are made with derived analytic results for some special distributions and moderate values of n

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

a joint model of recurrent events and a terminal event with a nonparametric covariate function we extend the shared frailty model of recurrent events and a dependent terminal event to allow for a nonparametric covariate function we include a gaussian random effect frailty in the intensity functions of both the recurrent and terminal events to capture correlation between the two processes we employ the penalized cubic spline method to describe the nonparametric covariate function in the recurrent events model we use laplace approximation to evaluate the marginal penalized partial likelihood without a closed form we also propose the variance estimates for regression coefficients numerical analysis results show that the proposed estimates perform well for both the nonparametric and parametric components we apply this method to analyze the hospitalization rate of patients with heart failure in the presence of death

semiparametric estimation of random effects using the cox model based on the em algorithm consider a survival experiment where individuals within a certain subset of the population share a common unobservable random frailty such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households suppose that if the frailty omega is known the cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate assuming tht the random frailties follow a gamma distribution estimates of the fixed and random effects are obtained by using an em algorithm based on a profile likelihood construction the method developed is applied to the framingham heart study to examine the risks of smoking and cholesterol levels adjusting for potential random effects

a note on gauss hermite quadrature summary for gauss hermite quadrature we consider a systematic method for transforming the variable of integration so that the integrand is sampled in an appropriate region the effectiveness of the quadrature then depends on the ratio of the integrand to some gaussian density being a smooth function well approximated by a low order polynomial it is pointed out that in this approach order one gauss hermite quadrature becomes the laplace approximation thus the quadrature as implemented here can be thought of as a higher order laplace approximation

nonlinearization of the lax pairs for discrete ablowitz ladik hierarchy abstract the discrete ablowitz ladik hierarchy with four potentials and the hamiltonian structures are derived under a constraint between the potentials and eigenfunctions the nonlinearization of the lax pairs associated with the discrete ablowitz ladik hierarchy leads to a new symplectic map and a class of finite dimensional hamiltonian systems the generating function of the integrals of motion is presented by which the symplectic map and these finite dimensional hamiltonian systems are further proved to be completely integrable in the liouville sense each member in the discrete ablowitz ladik hierarchy is decomposed into a hamiltonian system of ordinary differential equations plus the discrete flow generated by the symplectic map

coping with time and space in modelling malaria incidence a comparison of survival and count regression models to study the effect of a mega hydropower dam in southwest ethiopia on malaria incidence we have set up a longitudinal study to gain insight in temporal and spatial aspects that is in time period year season combination and location village we need models that account for these effects the frailty model with periodwise constant baseline hazard a constant value for each period and a frailty term that models the clustering in villages provides an appropriate tool for the analysis of such incidence data count data can be obtained by aggregating for each period events at the village level the mixed poisson regression model can be used to model the count data we show the similarities between the two models the risk factor in both models is the distance to the dam and we study the effect of the risk factor on malaria incidence in the frailty model each subject has its own risk factor whereas in the poisson regression model we also need to average the risk factors of all subjects contributing to a particular count the power loss caused by using village averaged distance instead of individual distance is studied and quantified the loss in the malaria data example is rather small in such a setting it might be advantageous to use less labor intensive sampling schemes than the weekly individual follow up scheme used in this study the proposed alternative sampling schemes might also avoid community fatigue a typical problem in such research projects

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

the positive and negative camassa holm γ hierarchies zero curvature representations bi hamiltonian structures and algebro geometric solutions in this paper we extend the camassa holm ch equation to two different hierarchies of nonlinear evolution equations by resorting to two lenard recursion sequences one is of positive order ch hierarchy including a harry dym type equation while the other is of negative order ch hierarchy of integrodifferential equations with nonzero integration constants including the ch equation we provide the zero curvature representations for both hierarchies by solving a key matrix equation moreover the lenard sequences are used to construct a lax matrix that satisfies a stationary zero curvature equation which enables us to establish bi hamiltonian structures for both hierarchies by applying trace identity in addition the lenard sequence and lax pair are used to systematically derive the its matveev trace formula and the dubrovin type equations associated with the ch equation the hyperelliptic curve and abel jacobi coordinates are then introduced to linearize the associated flow from which the algebro geometric solutions to the ch equation are constructed by using standard jacobi inversion technique in this paper we extend the camassa holm ch equation to two different hierarchies of nonlinear evolution equations by resorting to two lenard recursion sequences one is of positive order ch hierarchy including a harry dym type equation while the other is of negative order ch hierarchy of integrodifferential equations with nonzero integration constants including the ch equation we provide the zero curvature representations for both hierarchies by solving a key matrix equation moreover the lenard sequences are used to construct a lax matrix that satisfies a stationary zero curvature equation which enables us to establish bi hamiltonian structures for both hierarchies by applying trace identity in addition the lenard sequence and lax pair are used to systematically derive the its matveev trace formula and the dubrovin type equations associated with the ch equation the hyperelliptic curve and abel jacobi coordinates are then introduced to linearize the associated flow from which the a

the use of gaussian quadrature for estimation in frailty proportional hazards models in this paper we propose a novel gaussian quadrature estimation method in various frailty proportional hazards models we approximate the unspecified baseline hazard by a piecewise constant one resulting in a parametric model that can be fitted conveniently by gaussian quadrature tools in standard software such as sas proc nlmixed we first apply our method to simple frailty models for correlated survival data e g recurrent or clustered failure times then to joint frailty models for correlated failure times with informative dropout or a dependent terminal event such as death simulation studies show that our method compares favorably with the well received penalized partial likelihood method and the monte carlo em mcem method for both normal and gamma frailty models we apply our method to three real data examples 1 the time to blindness of both eyes in a diabetic retinopathy study 2 the joint analysis of recurrent opportunistic diseases in the presence of death for hiv infected patients and 3 the joint modeling of local distant tumor recurrences and patients survival in a soft tissue sarcoma study the proposed method greatly simplifies the implementation of the joint frailty models and makes them much more accessible to general statistical practitioners

quasiperiodic waves and asymptotic behavior for bogoyavlenskii s breaking soliton equation in 2 1 dimensions based on a multidimensional riemann theta function the hirota bilinear method is extended to explicitly construct multiperiodic quasiperiodic wave solutions for the 2 1 dimensional bogoyavlenskii breaking soliton equation among these periodic waves the one periodic waves are well known cnoidal waves their surface pattern is one dimensional and often they are used as one dimensional models of periodic waves in shallow water the two periodic biperiodic waves are a direct generalization of one periodic waves their surface pattern is two dimensional that is they have two independent spatial periods in two independent horizontal directions the two periodic waves may be considered to represent periodic waves in shallow water without the assumption of one dimensionality a limiting procedure is presented to analyze asymptotic behavior of the one and two periodic waves in details the exact relations between the periodic wave solutions and the well known soliton solutions are established it is rigorously shown that the periodic wave solutions tend to the soliton solutions under a small amplitude limit

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

interval reliability of typical systems with partially known probabilities abstract most probabilistic methods of the system reliability analysis assume that the component lifetime distributions are known precisely and the system components are independent the paper considers reliability analysis of typical systems when the above assumptions are violated and there is only some partial information about the component lifetime distributions the analysis is based on considering sets of possible probability distributions consistent with available information all resulting expressions are obtained in the explicit form the impact of incompleteness of initial data on the resulting system reliability measures is illustrated by a numerical example

from the special 2 1 toda lattice to the kadomtsev petviashvili equation the nonlinearization of the eigenvalue problems associated with the toda hierarchy and the coupled korteweg de vries kdv hierarchy leads to an integrable symplectic map s and an integrable hamiltonian system h0 respectively it is proved that s and h0 have the same integrals hk the quasi periodic solution of the 2 1 dimensional kadomtsev petviashvili equation is split into three hamiltonian systems h0 h1 h2 while that of the special 2 1 dimensional toda equation is separated into h0 h1 plus the discrete flow generated by the symplectic map s a clear evolution picture of various flows is given through the window of abel jacobi coordinates the explicit theta function solutions are obtained by resorting to this separation technique

a positive stable frailty model for clustered failure time data with covariate dependent frailty summary in this article we propose a positive stable shared frailty cox model for clustered failure time data where the frailty distribution varies with cluster level covariates the proposed model accounts for covariate dependent intracluster correlation and permits both conditional and marginal inferences we obtain marginal inference directly from a marginal model then use a stratified cox type pseudo partial likelihood approach to estimate the regression coefficient for the frailty parameter the proposed estimators are consistent and asymptotically normal and a consistent estimator of the covariance matrix is provided simulation studies show that the proposed estimation procedure is appropriate for practical use with a realistic number of clusters finally we present an application of the proposed method to kidney transplantation data from the scientific registry of transplant recipients

integrable decompositions of a symmetric matrix kaup newell equation and a symmetric matrix derivative nonlinear schrodinger equation it is shown that the reduction conditions in the spectral problems of soliton equations can be replaced by more equations of eigenfunctions based on this the method of nonlinearization of spectral problem is extended to soliton equations with reduction conditions integrable decompositions of a symmetric matrix kaup newell equation and a symmetric matrix derivative nonlinear schrodinger equation are constructed

integrable rosochatius deformations of the restricted soliton flows a method to construct integrable rosochatius deformations of the restricted soliton flows in the setup of lax formulation is presented the integrable rosochatius deformations of the restricted soliton flows such as the restricted ablowitz kaup newell segur flow the restricted tu meng flow the restricted tu flow with neumann type constraints and the restricted modified korteweg de vries flow together with their lax representations are presented in addition a lax representation of the jacobi rosochatius system is obtained

quasiperiodic solutions of jaulent miodek equations with a negative flow a hierarchy of new nonlinear evolution equations is proposed which are composed of the positive and negative jaulent miodek flows based on the theory of algebraic curve the corresponding flows are straightened under the abel jacobi coordinates the meromorphic function the baker akhiezer vector and the hyperelliptic curve kn are introduced by which quasiperiodic solutions of the first two nonlinear evolution equations in the hierarchy are constructed according to the asymptotic properties and the algebro geometric characters of and kn

hierarchical likelihood approach for frailty models systematic likelihood inference for frailty models is possible using lee nelder s 1996 hierarchical likelihood we develop an inferential method for frailty models via hierarchical likelihood which gives a simple unified framework and a numerically efficient algorithm simulations and practical examples are presented to illustrate the new method

quasi periodic solution of the 2 1 dimensional boussinesq burgers soliton equation abstract a 2 1 dimensional bossinesq burgers soliton equation is proposed which has a affinitive connection with the boussinesq burgers soliton hierarchy through a natural nonlinearization of the boussinesq burgers s eigenvalue problems a finite dimensional hamiltonian system is obtained and is proved to be completely integrable in liouville sense the abel jacobi coordinates are constructed to straighten out the hamiltonian flows from which the quasi periodic solutions of the 2 1 dimensional boussinesq burgers equation are derived by resorting to the riemann theta functions

semiparametric transformation models with random effects for recurrent events in this article we study a class of semiparametric transformation models with random effects for the intensity function of the counting process these models provide considerable flexibility in formulating the effects of possibly time dependent covariates on the developments of recurrent events while accounting for the dependence of the recurrent event times within the same subject we show that the nonparametric maximum likelihood estimators npmles for the parameters of these models are consistent and asymptotically normal the limiting covariance matrices for the estimators of the regression parameters achieve the semiparametric efficiency bounds and can be consistently estimated the limiting covariance function for the estimator of any smooth functional of the cumulative intensity function also can be consistently estimated we develop a simple and stable em algorithm to compute the npmles as well as the variance and covariance estimators simulation studies demonstrate that the proposed methods per

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

negative order korteweg de vries equations in this paper based on the regular korteweg de vries kdv system we study negative order kdv nkdv equations particularly their hamiltonian structures lax pairs conservation laws and explicit multisoliton and multikink wave solutions thorough bilinear backlund transformations the nkdv equations studied in our paper are differential and actually derived from the first member in the negative order kdv hierarchy the nkdv equations are not only gauge equivalent to the camassa holm equation through reciprocal transformations but also closely related to the ermakov pinney systems and the kupershmidt deformation the bi hamiltonian structures and a darboux transformation of the nkdv equations are constructed with the aid of trace identity and their lax pairs respectively the single and double kink wave and bell soliton solutions are given in an explicit formula through the darboux transformation the one kink wave solution is expressed in the form of tanh while the one bell soliton is in the form of sech and both forms are very standard the collisions of two kink wave and two bell soliton solutions are analyzed in detail and this singular interaction differs from the regular kdv equation multidimensional binary bell polynomials are employed to find bilinear formulation and backlund transformations which produce n soliton solutions a direct and unifying scheme is proposed for explicitly building up quasiperiodic wave solutions of the nkdv equations furthermore the relations between quasiperiodic wave solutions and soliton solutions are clearly described finally we show the quasiperiodic wave solution convergent to the soliton solution under some limit conditions

the deduction of the lax representation for constrained flows from the adjoint representation for x and tn finite dimensional hamiltonian systems obtained from the decompositions of zero curvature equations it is shown that their lax representations can be deduced directly from the adjoint representations of the auxiliary linear problems as a consequence the zero curvature representation for soliton hierarchy with source is presented

separation of variables in the classical integrable sl 3 magnetic chain there are two fundamental problems studied by the theory of hamiltonian integrable systems integration of equations of motion and construction of action angle variables a third problem however should be added to the list separation of variables though much simpler thant the two others it has important relations to quantum integrability separation of variables is constructed for thesl 3 magnetic chain an example of an integrable model associated to a nonhyperelliptic algebraic curve

algebro geometric solution of the 2 1 dimensional burgers equation with a discrete variable the quasiperiodic solution of the 2 1 dimensional burgers equation with a discrete variable is obtained through three steps a decomposition into a symplectic map plus two finite dimensional hamiltonian systems b straightening out of both the discrete and the continuous flows in the jacobian variety c inversion into the original variables inner relation with the modified kadomtsev petviashvili equation is presented the explicit theta function solutions for these two 2 1 integrable models are given

from integrable to superintegrable it is shown that the presence of multiple eigenvalue parameters may result in the superintegrability of the restricted soliton flows the restricted akns flow the neumann system and the restricted mkdv flow with an eigenvalue parameter whose multiplicity is greater than two are demonstrated to be superintegrable

nonparametric predictive reliability of series of voting systems abstract nonparametric predictive inference npi for system reliability reflects the dependence of reliabilities of similar components due to limited knowledge from testing npi has recently been presented for reliability of a single voting system consisting of multiple types of components the components are all assumed to play the same role within the system but with regard to their reliability components of different types are assumed to be independent the information from tests is available per type of component this paper presents npi for systems with subsystems in a series structure where all subsystems are voting systems and components of the same type can be in different subsystems as npi uses only few modelling assumptions system reliability is quantified by lower and upper probabilities reflecting the limited information in the test data the results are illustrated by examples which also illustrate important aspects of redundancy and diversity for system reliability

a generalized g g expansion method and its applications to nonlinear evolution equations in this paper a generalized g g expansion method and its algorithm are proposed by studying wang s g g expansion method and constructing a first order nonlinear ordinary differential equation with a third degree nonlinear term being concise and straightforward the method is applied to combined kdv mkdv equation and coupled jaulent miodek equation as a result some new exact travelling wave solutions are obtained which include solitary wave solutions triangular periodic wave solutions exponential solutions complex travelling solutions and rational solutions this method can also be applied to other nonlinear evolution equations in mathematical physics

generalized survival models for correlated time to event data our aim is to develop a rich and coherent framework for modeling correlated time to event data including 1 survival regression models with different links and 2 flexible modeling for time dependent and nonlinear effects with rich postestimation we extend the class of generalized survival models which expresses a transformed survival in terms of a linear predictor by incorporating a shared frailty or random effects for correlated survival data the proposed approach can include parametric or penalized smooth functions for time time dependent effects nonlinear effects and their interactions the maximum penalized marginal likelihood method is used to estimate the regression coefficients and the variance for the frailty or random effects the optimal smoothing parameters for the penalized marginal likelihood estimation can be automatically selected by a likelihood based cross validation criterion for models with normal random effects gauss hermite quadrature can be used to obtain the cluster level marginal likelihoods the akaike information criterion can be used to compare models and select the link function we have implemented these methods in the r package rstpm2 simulating for both small and larger clusters we find that this approach performs well through 2 applications we demonstrate 1 a comparison of proportional hazards and proportional odds models with random effects for clustered survival data and 2 the estimation of time varying effects on the log time scale age varying effects for a specific treatment and two dimensional splines for time and age

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

some algebro geometric solutions for the coupled modified kadomtsev petviashvili equations arising from the neumann type systems a treatment is described for getting some algebro geometric solutions of the coupled modified kadomtsev petviashvili cmkp equations and a hierarchy of 1 1 dimensional integrable nonlinear evolution equations inlees by using the neumann type systems through three steps i according to the nonlinearization of lax pair the cmkp equations and the 1 1 dimensional inlees are reduced to a family of compatible neumann type systems on a symplectic submanifold whose involutive solutions give rise to the finite parametric solutions of the inlees in both 2 1 and 1 1 dimensions ii from the holomorphic differentials and the abel map on a hyperelliptic curve of riemman surface the abel jacobi variables are introduced to straighten out the neumann type flows the 1 1 and 2 1 dimensional flows giving the abel jacobi solutions iii based on the riemann theorem and the trace formulas the jacobi inversion is applied to the straightened flows for getting some new algebro geometric solutions of the cmkp equations and the 1 1 dimensional integrable hierarchy

dunnett type inference in the frailty cox model with covariates a frequent objective in medical research is the investigation of differences in patient survival between several experimental treatments and one standard treatment in order to assess these differences statistically we have to apply adjustments for multiple comparisons to prevent an increased number of false positive findings the most prominent procedure of this type is the bonferroni correction which maintains the error level but leads to conservative results on the basis of a general statistical framework for simultaneous inference we propose a new statistical procedure for many to one comparisons of treatments with adjustment for covariates for clustered survival data modeled by a frailty cox model in contrast to the bonferroni method dependencies between estimated effects are taken into account the resulting simultaneous confidence intervals for the hazard ratios of the experimental treatments compared with a control can be interpreted in terms of both statistical significance and clinical importance the quality of the new procedure is judged by the coverage probability for the simultaneous confidence intervals simulation results show an acceptable performance in balanced and various unbalanced designs the practical merits are demonstrated by a reanalysis of a chronic myelogeneous leukemia clinical trial the procedure presented here works well for multiple comparisons with a control with adjustment for covariates for survival data from multicenter clinical trials

finite gap solutions of 2 1 dimensional integrable nonlinear evolution equations generated by the neumann systems each soliton equation in the korteweg de vries kdv hierarchy the 2 1 dimensional breaking soliton equation and the 2 1 dimensional caudrey dodd gibbon kotera sawada cdgks equation are reduced to two or three neumann systems on the tangent bundle tsn 1 of the unit sphere sn 1 the lax moser matrix for the neumann systems of degree n 1 is deduced in view of the mckean trubowitz identity and a bilinear generating function whose favorite characteristic accounts for the problem of the genus of riemann surface matching to the number of elliptic variables from the lax moser matrix the constrained hamiltonians in the sense of dirac poisson bracket for all the neumann systems are written down in a uniform recursively determined by integrals of motion the involution of integrals of motion and constrained hamiltonians is completed on tsn 1 by using a lax equation and their functional independence is displayed over a dense open subset of tsn 1 by a direct calculation which contribute to the liouville integ

frequency of recurrent events at failure time modeling and inference recurrent events arise in many longitudinal medical studies where time to a terminal event or failure is the primary endpoint with incomplete follow up data the analysis of recurrent events is a challenge owing to their association with the failure one specific quantity of interest rarely addressed in the statistical literature is the recurrence frequency at the failure time an example is hospitalization frequency which is often used as a rough measure of lifetime medical cost in this article we show that a marginal model e g the log linear model of the recurrence frequency although desirable is typically not identifiable for this reason we advocate modeling the recurrent events and the failure time jointly and propose an approach to forming semiparametric joint models from prespecified marginal ones we suggest two conceptually simple and nested regression models aiming at the recurrence frequency as a mark of the failure and at the process of recurrent events we formulate monotone estima

the finite band solution of the jaulent miodek equation a method to construct the finite band solution to the soliton equation is presented we take the jaulent miodek equation as an example with the use of the nonlinearization of lax pair the jaulent miodek equation is decomposed into two finite dimensional integrable systems whose properties are studied from the view of an r matrix then through solving these finite dimensional integrable systems the finite band solution of the jaulent miodek equation is obtained

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

a likelihood reformulation method in non normal random effects models in this paper we propose a practical computational method to obtain the maximum likelihood estimates mle for mixed models with non normal random effects by simply multiplying and dividing a standard normal density we reformulate the likelihood conditional on the non normal random effects to that conditional on the normal random effects gaussian quadrature technique conveniently implemented in sas proc nlmixed can then be used to carry out the estimation process our method substantially reduces computational time while yielding similar estimates to the probability integral transformation method j comput graphical stat 2006 15 39 57 furthermore our method can be applied to more general situations e g finite mixture random effects or correlated random effects from clayton copula simulations and applications are presented to illustrate our method

estimation of variance in cox s regression model with shared gamma frailties the cox regression model with a shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times estimation in this model when the frailties are assumed to follow a gamma distribution is reviewed and we address the problem of obtaining variance estimates for regression coefficients frailty parameter and cumulative baseline hazards using the observed nonparametric information matrix a number of examples are given comparing this approach with fully parametric inference in models with piecewise constant baseline hazards

1 soliton solution and conservation laws for the jaulent miodekequation with power law nonlinearity abstract this paper obtains the 1 soliton solution of the jaulent miodek equation with power law nonlinearity the solitary wave ansatz is used to obtain the soliton solution to this equation subsequently the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the euler lagrange operator annihilates the total divergence

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

the quasi periodic solutions of mixed kdv equations the quasi periodic solutions of mixed kdv equations are constructed to derive the solutions we introduce the mixed finite dimensional integrable hamiltonian systems fdihs which are linearized on the jacobi variety of the associated hyperelliptic curve a relation between the fdihs and the mixed kdv equations is revealed based on this relation we construct the quasi periodic solutions for the mixed kdv equations with aid of the riemann theta function the quasi periodic solutions for the kdv6 equation and the negative order kdv equation are obtained as special members of the mixed kdv equations

quasi periodic solutions of the modified kadomtsev petviashvili equation the 2 1 dimensional modified kadomtsev petviashvili equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of lax pairs abel jacobi coordinates are introduced to straighten the flows from which quasi periodic solutions of the modified kadomtsev petviashvili equation are obtained in terms of riemann theta functions

quasi periodic wave solution and asymptotic behavior for the 2 1 dimensional toda lattice equation abstract one and two periodic wave solutions for the 2 1 dimensional toda lattice equation are presented based on the hirota bilinear method and the riemann theta function the asymptotic behaviors of these two solutions are considered and the rigorous proof is given that the periodic wave solutions tend to the soliton solutions in an appropriate limiting procedure

algebro geometric solutions for the gerdjikov ivanov hierarchy this paper is dedicated to provide theta function representations of algebro geometric solutions and related crucial quantities for the gerdjikov ivanov gi hierarchy our main tools include the polynomial recursive formalism the hyperelliptic curve with finite number of genus the baker akhiezer functions the meromorphic function the dubrovin type equations for auxiliary divisors and the associated trace formulas with the help of these tools the explicit representations of the baker akhiezer functions the meromorphic function and the algebro geometric solutions are obtained for the entire gi hierarchy