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

an analytical solution for the free vibration analysis of rectangular plates resting on symmetrically distributed point supports abstract a general analytical solution is obtained for the free vibration of rectangular plates supported on their lateral surface by symmetrically distributed point supports highly accurate eigenvalues are provided for a square plate supported at various points along the diagonal results are compared with earlier findings obtained by a finite element method it is shown that the method may be extended to solve various other problems the tabulation of eigenvalues appears to be the most comprehensive yet made for a square plate with point supports on the diagonals

local full likelihood estimation for the proportional hazards model summary in this paper a new approach to local likelihood estimation for censored data is proposed this method employs the full likelihood and alternates between estimating the baseline hazard and estimating the covariate effect the proposed methodology incorporates multidimensional data via additive models some results regarding inference for the covariate effect are also presented in this paper we propose new methodology for estimating a general covariate effect when the data arise from a proportional hazards model the methodology uses the full likelihood rather than the partial likelihood and is iterative in nature we note that techniques relying on the partial likelihood do not agree with the modeling assumptions and hence may be less desirable to begin some notation is introduced the data are observed as independent identically distributed triples ti bi zi where t is the minimum of the true failure time and the true censoring time 6 is an indicator of failure and z is a covariate that may be vector valued the true possibly unobserved failure time is assumed to have distribution function f the survivor function is denoted x the hazard x t and the integrated hazard a t further it is assumed that the data arise from a proportional hazards model that is the hazard x t z is assumed to be the product of a baseline hazard xo t and a covariate effect v z

partially linear hazard regression with varying coefficients for multivariate survival data summary the paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data a profile pseudo partial likelihood estimation method is proposed the estimation of the parameters of the linear part is accomplished via maximization of the profile pseudo partial likelihood whereas the varying coefficient functions are considered as nuisance parameters that are profiled out of the likelihood it is shown that the estimators of the parameters are root n consistent and the estimators of the non parametric coefficient func tions achieve optimal convergence rates asymptotic normality is obtained for the estimators of the finite parameters and varying coefficient functions consistent estimators of the asymptotic variances are derived and empirically tested which facilitate inference for the model we prove that the varying coefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent simulations are con ducted to demonstrate the performance of the estimators proposed a real data set is analysed to illustrate the methodology proposed

theory of partial likelihood a general asymptotic theory is developed for the maximum likelihood estimator based on a partial likelihood conditions are given for consistency and asymptotic normality and a method is provided for the calculation of the asymptotic efficiency of the estimator the implications of the general theory are examined in special cases such as inference in stochastic processes cox regression models and ar processes with missing segments

local em estimation of the hazard function for interval censored data summary we propose a smooth hazard estimator for interval censored survival data using the method of local likelihood the model is fit using a local em algorithm the estimator is more descriptive than traditional empirical estimates in regions of concentrated information and takes on a parametric flavor in regions of sparse information we derive two different standard error estimates for the smooth curve one based on asymptotic theory and the other on the bootstrap we illustrate the local em method for times to breast cosmesis deterioration finkelstein 1986 biometrics42 845 854 and for times to hiv 1 infection for individuals with hemophilia kroner et al 1994 journal of aids7 279 286 our hazard estimates for each of these data sets show interesting structures that would not be found using a standard parametric hazard model or empirical survivorship estimates

nonparametric regression using local kernel estimating equations for correlated failure time data we study nonparametric regression for correlated failure time data kernel estimating equations are used to estimate nonparametric covariate effects independent and weighted kernel estimating equations are studied the derivative of the nonparametric function is first estimated and the nonparametric function is then estimated by integrating the derivative estimator we show that the nonparametric kernel estimator is consistent for any arbitrary working correlation matrix and that its asymptotic variance is minimized by assuming working independence we evaluate the performance of the proposed kernel estimator using simulation studies and apply the proposed method to the western kenya parasitaemia data

global partial likelihood for nonparametric proportional hazards models as an alternative to the local partial likelihood method of tibshirani and hastie and fan gijbels and king a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model t x exp x 0 t the estimator x reduces to the cox partial likelihood estimator if the covariate is discrete the estimator is shown to be consistent and semiparametrically efficient for linear functionals of x moreover breslow type estimation of the cumulative baseline hazard function using the proposed estimator x is proved to be efficient the asymptotic bias and variance are derived under regularity conditions computation of the estimator involves an iterative but simple algorithm extensive simulation studies provide evidence supporting the theory the method is illustrated with the stanford heart transplant data set the proposed global approach is also extended to a partially linear proportional hazards model and found to provide efficien

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

on use of the dirac delta function in the vibration analysis of elastic structures the dirac delta function has often been employed to represent the amplitude of concentrated harmonic forces in the analysis of vibration of elastic structures such as beams and plates it is known that this function as represented by a truncated fourier series does not provide a true representation of a concentrated force nevertheless it is frequently employed and good convergence is usually though not always encountered in solutions thereby obtained in this paper the nature of the function is discussed and for illustrative purposes it is used to obtain series solutions for some selected beam and plate free vibration problems in some cases problems are chosen for which exact solutions are already obtainable by analytical means this permits powerful checks to be made on rates of convergence experienced when the series solutions are investigated rates of convergence are discussed in detail and it is explained why convergence is to be expected when analyzing certain families of problems when employing this function and a lack of convergence is to be expected in others

local partial likelihood estimation in proportional hazards regression fan gijbels and king ann statist 25 1997 1661 1690 considered the estimation of the risk function x in the proportional hazards model their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood they proved the large sample properties of the derivative function but the large sample properties of the estimator for the risk function itself were not established in this paper we consider direct estimation of the relative risk function x 2 x 1 for any location normalization point x 1 the main novelty in our approach is that we select observations in shrinking neighborhoods of both x 1 and x 2 when constructing a local version of the partial likelihood whereas fan gijbels and king ann statist 25 1997 1661 1690 only concentrated on a single neighborhood resulting in the cancellation of the risk function in the local likelihood function the asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated the idea behind our approach is extended to estimate the differences between groups a simulation study is carried out

on estimation of partially linear transformation models we study a general class of partially linear transformation models which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis a new martingale based estimating equation approach consisting of both global and kernel weighted local estimation equations is developed for estimating the parametric and nonparametric covariate effects in a unified manner we show that with a proper choice of the kernel bandwidth parameter one can obtain the consistent and asymptotically normal parameter estimates for the linear effects asymptotic properties of the estimated nonlinear effects are established as well we further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness to facilitate the implementation of the new procedure an iterative algorithm is developed numerical examples are given to illustrate the finite sample performance of the procedure supplementary materials are available online

a local likelihood proportional hazards model for interval censored data we discuss the use of local likelihood methods to fit proportional hazards regression models to right and interval censored data the assumed model allows for an arbitrary smoothed baseline hazard on which a vector of covariates operates in a proportional manner and thus produces an interpretable baseline hazard function along with estimates of global covariate effects for estimation we extend the modified em algorithm suggested by betensky lindsey ryan and wand we illustrate the method with data on times to deterioration of breast cosmeses and hiv 1 infection rates among haemophiliacs

hazard rate estimation under random censoring with varying kernels and bandwidths we discuss the estimation of hazard rates under random censoring with the kernel method two practically relevant problems that occur when applying unmodified kernel estimators are boundary effects near the endpoints of the support of the hazard rate and a substantial increase in the variance from left to right over the range of abscissae where the hazard rate is estimated a new class of boundary kernels is proposed for the first problem explicit formulas for these kernels are developed and it is shown that this boundary correction works well in practice a data adaptive varying bandwidth selection procedure is proposed for the second problem this procedure generally will lead to increasing bandwidths near the left endpoint and toward the right endpoint and will lead to smaller integrated mean squared error of the hazard rate estimator as compared to a fixed bandwidth method a practically feasible method incorporating the new boundary kernels and local bandwidth choices is implemented and illustrated with survival data from a leukemia study

bending of a rectangular plate with rotationally restrained edges under a concentrated force the bending problem of a rectangular plate with rotationally restrained edges under a concentrated force is studied an emphasis is placed on the determination of the corner forces and deflection the problem is solved by superposition of classical navier s and levy s solutions analytic solutions in terms of series are obtained for rsss rrss and rsrs plates respectively where r and s stand for rotational restraint and simple support respectively some important design parameters such as maximum deflection and corner force are evaluated the effect of edge restraint on these parameters is illustrated

efficient estimation for the cox model with varying coefficients summary a proportional hazards model with varying coefficients allows one to examine the extent to which covariates interact nonlinearly with an exposure variable a global partial likelihood method in contrast with the local partial likelihood method of fan et al 2006 is proposed for estimation of varying coefficient functions the proposed estimators are proved to be consistent and asymptotically normal semiparametric efficiency of the estimators is demonstrated in terms of their linear functionals evidence in support of the superiority of the method is presented in numerical studies and real examples

relative risk regression models with inverse polynomials the proportional hazards model assumes that the log hazard ratio is a linear function of parameters in the current paper we model the log relative risk as an inverse polynomial which is particularly suitable for modeling bounded and asymmetric functions the parameters estimated by maximizing the partial likelihood are consistent and asymptotically normal the advantages of the inverse polynomial model over the ordinary polynomial model and the fractional polynomial model for fitting various asymmetric log relative risk functions are shown by simulation the utility of the method is further supported by analyzing two real data sets addressing the specific question of the location of the minimum risk threshold

partially linear additive hazards regression with varying coefficients please see the supplementary materials for a correction to this article to explore the nonlinear interactions between some covariates and an exposure variable we propose the partially linear additive hazards model for survival data in a semiparametric setting we construct a local pseudoscore function to estimate the varying and constant coefficients and establish the asymptotic normality of the proposed estimators moreover we develop the weak convergence property for the local estimator of the baseline cumulative hazard function we conduct simulation studies to empirically examine the finite sample performance of the proposed methods and use real data from a breast cancer study for illustration

inference for continuous semimartingales observed at high frequency the econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy of volatility and related quantities we here study this local constancy approximation as a general approach to estimation in such data we show that the technique yields asymptotic properties consistency normality that are correct subject to an ex post adjustment involving asymptotic likelihood ratios these adjustments are derived and documented several examples of estimation are provided powers of volatility leverage effect and integrated betas the first order approximations based on local constancy can be over the period of one observation or over blocks of successive observations it has the advantage of gaining in transparency in defining and analyzing estimators the theory relies heavily on the interplay between stable convergence and measure change and on asymptotic expansions for martingales

local likelihood and local partial likelihood in hazard regression in survival analysis the relationship between a survival time and a covariate is conveniently modeled with the proportional hazards regression model this model usually assumes that the covariate has a log linear effect on the hazard function in this paper we consider the proportional hazards regression model with a nonparametric risk effect we discuss estimation of the risk function and its derivatives in two cases when the baseline hazard function is parametrized and when it is not parametrized in the case of a parametric baseline hazard function inference is based on a local version of the likelihood function while in the case of a nonparametric baseline hazard we use a local version of the partial likelihood this results in maximum local likelihood estimators and maximum local partial likelihood estimators respectively we establish the asymptotic normality of the estimators it turns out that both methods have the same asymptotic bias and variance in a common situation even though the local likelihood method uses information about the baseline hazard function

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

hazard models with varying coefficients for multivariate failure time data statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis a local pseudo partial likelihood procedure is proposed for estimating the unknown coefficient functions a weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator the consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested to reduce the computational burden of the maximum local pseudo partial likelihood estimator a simple and useful one step estimator is proposed statistical properties of the one step estimator are established and simulation studies are conducted to compare the performance of the one step estimator to that of the maximum local pseudo partial likelihood estimator the results show that the one step estimator can save computational cost without compromising performance both asymptotically and empirically and that an optimal weighted average estimator is more efficient than the maximum local pseudo partial likelihood estimator a data set from the busselton population health surveys is analyzed to illustrate our proposed methodology

on products of two involutions in the orthogonal group of a vector space let v be a finite dimentional vector space over a commutative field of characteristic distinct from 2 let v carry a symmetric nondegenerate bilinear form results a let where o v and are involutions there exists an orthogonal decomposition of v into orthogonally indecomposable modules which are simultaneously invariant under and b let o v one can find involutions o v such that and b b b holds if and only if an orthogonal decomposition of v into orthogonally indecomposable modules does not contain a term whose minimum polynomial is x 1 where is even

partially linear hazard regression for multivariate survival data this article studies estimation of partially linear hazard regression models for multivariate survival data a profile pseudo partial likelihood estimation method is proposed under the marginal hazard model framework the estimation on the parameters for the linear part is accomplished by maximization of a pseudo partial likelihood profiled over the nonparametric part this enables us to obtain consistent estimators of the parametric component asymptotic normality is obtained for the estimates of both the linear and nonlinear parts the new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit an algorithm of fast implementation of our proposed method is presented consistent standard error estimates using sandwich type ideas are also developed which facilitates inferences for the model it is shown that the nonparametric component can be estimated as well as if the parametric components were known and the

a semi nonparametric estimator of regression discontinuity design with discrete duration outcomes abstract we consider the regression discontinuity rd design with the duration outcome which has discrete support the parameters of policy interest are treatment effects on unconditional duration effect and conditional hazard effect exiting probabilities for each discrete level we propose a novel semi nonparametric estimator which exploits a flexible separability structure of the underlying continuous time duration process simultaneous inference over discrete levels is nonstandard since the asymptotic variance matrix is singular with unknown rank the peculiarity is delivered by the nature of the rd estimand and we provide solutions random censoring and competing risks can also be allowed in our framework

local partial likelihood estimation for lifetime data this paper considers a proportional hazards model which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable for analysis of lifetime data a local partial likelihood technique is proposed to estimate nonlinear interactions asymptotic normality of the proposed estimator is established the baseline hazard function the bias and the variance of the local likelihood estimator are consistently estimated in addition a one step local partial likelihood estimator is presented to facilitate the computation of the proposed procedure and is demonstrated to be as efficient as the fully iterated local partial likelihood estimator furthermore a penalized local likelihood estimator is proposed to select important risk variables in the model numerical examples are used to illustrate the effectiveness of the proposed procedures

partially linear structure selection in cox models with varying coefficients summary to explore the nonlinear interactions between covariates and an index variable partially linear proportional hazards models have been proposed for censored survival data however specification of the partially linear structure was usually carried out in an ad hoc manner by first fitting a full varying coefficient model and visually examining the resulting fit to identify the linear part in this article we consider the problem of coefficient estimation and constant coefficient identification based on a double shrinkage approach variable selection is also considered in a coherent estimation framework resulting in a double penalization procedure under the mild assumptions we establish asymptotic properties for the procedure such as consistency sparesistency constansistency and asymptotic normality we evaluate the performance of the proposed method by numerical simulations and demonstrate its application using a breast cancer data set

sufficient dimension reduction on the mean and rate functions of recurrent events the counting process with a cox type intensity function has been extensively applied to analyze recurrent event data which assume that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative or additive effects on the mean and rate functions of the counting process the existing statistical inference however often encounters difficulties due to high dimensional covariates such as in gene expression and single nucleotide polymorphism data that have revolutionized our understanding of cancer recurrence and other diseases in this paper a technique of sufficient dimension reduction is applied to the mean and rate function for the number of occurrences of events over time a two step procedure is proposed to estimate the model components first a nonparametric estimator is proposed for the baseline and then the basis of the central subspace and its dimension are estimated through a modified slicing inverse regression on the basis of the estimated structural dimension and on the basis of the central subspace we can estimate the regression function by using the local linear regression a simulation is performed to confirm and assess the theoretical findings and an application is demonstrated on a set of chronic granulomatous disease data copyright 2014 john wiley sons ltd

free in plane vibration analysis of rectangular plates by the method of superposition abstract the superposition method is introduced as a means for obtaining analytical type solutions for free in plane vibration of rectangular plates the governing differential equations and boundary conditions are expressed in dimensionless form the problem of free in plane vibration of the completely free rectangular plate is resolved for illustrative purposes convergence is found to be rapid and excellent agreement between computed results and those obtained by previous authors utilizing the rayleigh ritz energy method is obtained it is pointed out that following procedures analogous to those utilized in resolving lateral plate vibration problems in plane free vibration problems related to point supported plates plates with in plane elastic boundary support etc are now amenable to solution by this method

semiparametric frailty models for clustered failure time data summary we consider frailty models with additive semiparametric covariate effects for clustered failure time data we propose a doubly penalized partial likelihood dppl procedure to estimate the nonparametric functions using smoothing splines we show that the dppl estimators could be obtained from fitting an augmented working frailty model with parametric covariate effects whereas the nonparametric functions being estimated as linear combinations of fixed and random effects and the smoothing parameters being estimated as extra variance components this approach allows us to conveniently estimate all model components within a unified frailty model framework we evaluate the finite sample performance of the proposed method via a simulation study and apply the method to analyze data from a study of sexually transmitted infections sti

structure adaptive approach for dimension reduction we propose a new method of effective dimension reduction for a multiindex model which is based on iterative improvement of the family of average derivative estimates the procedure is computationally straightforward and does not require any prior information about the structure of the underlying model we show that in the case when the effective dimension m of the index space does not exceed 3 this space can be estimated with the rate n 1 2 under rather mild assumptions on the model