reversible watermark using the difference expansion of a generalized integer transform a reversible watermarking algorithm with very high data hiding capacity has been developed for color images the algorithm allows the watermarking process to be reversed which restores the exact original image the algorithm hides several bits in the difference expansion of vectors of adjacent pixels the required general reversible integer transform and the necessary conditions to avoid underflow and overflow are derived for any vector of arbitrary length also the potential payload size that can be embedded into a host image is discussed and a feedback system for controlling this size is developed in addition to maximize the amount of data that can be hidden into an image the embedding algorithm can be applied recursively across the color components simulation results using spatial triplets spatial quads cross color triplets and cross color quads are presented and compared with the existing reversible watermarking algorithms these results indicate that the spatial quad based algorithm allows for hiding the largest payload at the highest signal to noise ratio

semiparametric mixed effects models for clustered failure time data the cox proportional hazards model with a random effect has been proposed for the analysis of data which consist of a large number of small clusters of correlated failure time observations the class of linear transformation models provides many useful alternatives to the cox model for analyzing univariate failure time data in this article we generalize these models by incorporating random effects which generate the dependence among the failure times within the cluster to handle correlated data inference and prediction procedures for such random effects models are proposed they are relatively simple compared with the methods based on the nonparametric maximum likelihood estimators for the cox frailty model in the literature our proposals are illustrated with a data set from a well known eye study extensive numerical studies are conducted to evaluate various robustness properties of the new procedures

generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

likelihood based inference using signed ranks for matched pairs summary exact and approximate inference based on the marginal likelihood which results from the signed ranks of the within pair differences of independent matched pairs is con sidered inference is made using bayesian ideas a quickly computed approximate analysis is introduced and this is shown to be extremely good when the within pair differences are assumed to have a normal distribution numerical comparisons are also made when the differences have a logistic distribution but for this case the approxi mation is not as good the approximations involve the wilcoxon signed rank statistic and the half normal scores signed rank statistic the approximation is extended to consider regression models for matched pairs data an application is given illustrating the ideas in this paper we consider exact and approximate inference based on the marginal rank sign likelihood which results from independent matched pairs data it is assumed that the within pair differences are independent and symmetrically distributed inference is made using bayesian ideas suppose that d1 1dn are observable differences which result from a matched pairs experiment and that it is possible to transform the dj s giving yj sign dj h idj 1 where h is an unknown increasing and differentiable function on 0 oo and h o 0 it is assumed that the y1 s are independent and symmetrically distribtuted about 0 with a known density under such circumstances the signs of the dj s and the ranks of the absolute values of the dj s remain invariant under the transformation and these are given by the signs and ranks of the y1 s in non parametric statistics inference can be made for 0 using the signs of the differences the sign test and also by utilizing between pair comparisons the ranks of the absolute differences giving the signed rank test of wilcoxon or the half normal scores test lehmann 1975 chapter 5 gives an account of non parametric tests based on signed ranks using matched pairs data in this paper we consider the marginal likelihood p r s i 0 of the dj s based on their signs s and the ranks r of their absolute values the idea of a marginal rank likelihood was proposed by kalbfleisch and prentice 1973 and the likelihood p r s i 0 for matched pairs data was considered by woolson and lachenbruch 1980 who developed test statistics for the hypothesis h 0 0 with censored data we use the marginal likelihood p r s i 0 to make inferences about 0 from a bayesian point of view in particular when the prior density for 0 is chosen to be locally uniform the posterior density of 0 is given by the standardized likelihood

on the cox model with time varying regression coefficients in the analysis of censored failure time observations the standard cox proportional hazards model assumes that the regression coefficients are time invariant often these parameters vary over time and the temporal covariate effects on the failure time are of great interest in this article following previous work of cai and sun we propose a simple estimation procedure for the cox model with time varying coefficients based on a kernel weighted partial likelihood approach we construct pointwise and simultaneous confidence intervals for the regression parameters over a properly chosen time interval via a simple resampling technique we derive a prediction method for future patients survival with any specific set of covariates building on the estimates for the time varying coefficients we also consider the mixed case and present an estimation procedure for time independent parameters in the model furthermore we show how to use an integrated function of the estimate for a specific regression coeffic

a lossless robust data hiding scheme this paper presents a lossless robust data hiding scheme the original cover image can be recovered without any distortion after the hidden data have been extracted if the stego image remains intact and on the other hand the hidden data can still be extracted correctly if the stego image goes through jpeg compression to some extent the proposed scheme divides a cover image into a number of non overlapping blocks and calculates the arithmetic difference of each block bits are embedded into blocks by shifting the arithmetic difference values the shift quantity and shifting rule are fixed for all blocks and reversibility is achieved furthermore owing to the separation of bit 0 zone and bit 1 zone as well as the particularity of arithmetic difference minor alteration applying to the stego image generated by non malicious attacks such as jpeg compression will not cause the bit 0 zone and the bit 1 zone to overlap and robustness is achieved experimental results show that compared with previous works the performance of the proposed scheme is significantly improved

wilcoxon type generalized bayesian information criterion we develop a generalized bayesian information criterion for regression model selection the new criterion relaxes the usually strong distributional assumption associated with schwarz s bic by adopting a wilcoxon type dispersion function and appropriately adjusting the penalty term we establish that the wilcoxon type generalized bic preserves the consistency of schwarz s bic without the need to assume a parametric likelihood we also show that it outperforms schwarz s bic with heavier tailed data in the sense that asymptotically it can yield substantially smaller l 2 risk on the other hand when the data are normally distributed both criteria have similar l 2 risk the new criterion function is convex and can be conveniently computed using existing statistical software our proposal provides a flexible yet highly efficient alternative to schwarz s bic at the same time it broadens the scope of wilcoxon inference which has played a fundamental role in classical nonparametric analysis

alternative variance and efficiency calculations for the case cohort design summary we define a bootstrap sampling plan for the case cohort design and present bootstrap variance estimates and confidence intervals for the log relative hazard the coverages of these confidence intervals are found to be near nominal levels in simulations a simple null variance calculation based on a superpopulation model is shown to provide good estimates of the power and efficiency of the case cohort design

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

efficient estimation of the partly linear additive cox model the partly linear additive cox model is an extension of the linear cox model and allows flexible modeling of covariate effects semiparametrically we study asymptotic properties of the maximum partial likelihood estimator of this model with right censored data using polynomial splines we show that with a range of choices of the smoothing parameter the number of spline basis functions required for estimation of the nonparametric components the estimator of the finite dimensional regression parameter is root n consistent asymptotically normal and achieves the semiparametric information bound rates of convergence for the estimators of the nonparametric components are obtained they are comparable to the rates in nonparametric regression implementation of the estimation approach can be done easily and is illustrated by using a simulated example

a simple resampling method by perturbing the minimand suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a u process structure the covariance matrix of the estimator is generally a function of the underlying density function which may be difficult to estimate well by conventional methods in this paper we present a simple resampling method by perturbing the objective function repeatedly inferences of the parameters can then be made based on a large collection of the resulting optimisers we illustrate our proposal by three examples with a heteroscedastic regression model

reversible data hiding based on block median preservation this paper proposes a reversible data hiding scheme for gray level images it exploits the high correlation among image block pixels to produce a difference histogram secret data is embedded based on a multi level histogram shifting mechanism with reference to the integer median of each block the image blocks are divided into four categories due to four corresponding embedding strategies aiming at preserving the medians during data embedding in decoder the median pixels are retrieved first followed by the hidden data extraction and the host image can be accurately recovered via an inverse histogram shifting mechanism after removing the secret data from the marked image experimental results validate the effectiveness of our scheme and demonstrate that it outperforms several previous methods in terms of capacity and marked image s quality

analysing competing risks data with transformation models we present a flexible class of marginal models for the cumulative incidence function the semiparametric transformation model is utilized in a decomposition for the marginal failure probabilities which extends previous work on farewell s cure model novel estimation inference and prediction procedures are developed with large sample properties derived from the theory of martingales and u statistics a small simulation study demonstrates that the methods are appropriate for practical use the methods are illustrated with a thorough analysis of a prostate cancer clinical trial simple graphical displays are used to check for the goodness of fit

posterior probabilities for a change point using ranks summary simple approximate methods of analysis are given for change point models using ranked observations the models can be applied to continuous observations providing a robust analysis in this case for ranked observations the models provide analyses for association numerical examples involving continuous and ranked observations are given

model free feature screening for ultrahigh dimensional data with the recent explosion of scientific data of unprecedented size and complexity feature ranking and screening are playing an increasingly important role in many scientific studies in this article we propose a novel feature screening procedure under a unified model framework which covers a wide variety of commonly used parametric and semiparametric models the new method does not require imposing a specific model structure on regression functions and thus is particularly appealing to ultrahigh dimensional regressions where there are a huge number of candidate predictors but little information about the actual model forms we demonstrate that with the number of predictors growing at an exponential rate of the sample size the proposed procedure possesses consistency in ranking which is both useful in its own right and can lead to consistency in selection the new procedure is computationally efficient and simple and exhibits a competent empirical performance in our intensive simulations and real

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

maximum likelihood estimation in the proportional odds model abstract we consider maximum likelihood estimation of the parameters in the proportional odds model with right censored data the estimator of the regression coefficient is shown to be asymptotically normal with efficient variance the maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent a likelihood ratio test for the regression coefficient is also considered

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

penalized log likelihood estimation for partly linear transformation models with current status data we consider partly linear transformation models applied to current status data the unknown quantities are the transformation function a linear regression parameter and a nonparametric regression effect it is shown that the penalized mle for the regression parameter is asymptotically normal and efficient and converges at the parametric rate although the penalized mle for the transformation function and nonparametric regression effect are only n 1 3 consistent inference for the regression parameter based on a block jack knife is investigated we also study computational issues and demonstrate the proposed methodology with a simulation study the transformation models and partly linear regression terms coupled with new estimation and inference techniques provide flexible alternatives to the cox model for current status data analysis

efficient estimation of semiparametric transformation models for counting processes summary a class of semiparametric transformation models is proposed to characterise the effects of possibly time varying covariates on the intensity functions of counting processes the class includes the proportional intensity model and linear transformation models as special cases nonparametric maximum likelihood estimators are developed for the regression parameters and cumulative intensity functions of these models based on censored data the estimators are shown to be consistent and asymptotically normal the limiting variances for the estimators of the regression parameters achieve the semi parametric efficient bounds and can be consistently estimated the limiting variances for the estimators of smooth functionals of the cumulative intensity function can also be consistently estimated simulation studies reveal that the proposed inference procedures perform well in practical settings two medical studies are provided

inference under right censoring for transformation models with a change point based on a covariate threshold we consider linear transformation models applied to right censored survival data with a change point in the regression coefficient based on a covariate threshold we establish consistency and weak convergence of the nonparametric maximum likelihood estimators the change point parameter is shown to be n consistent while the remaining parameters are shown to have the expected root n consistency we show that the procedure is adaptive in the sense that the nonthreshold parameters are estimable with the same precision as if the true threshold value were known we also develop monte carlo methods of inference for model parameters and score tests for the existence of a change point a key difficulty here is that some of the model parameters are not identifiable under the null hypothesis of no change point simulation studies establish the validity of the proposed score tests for finite sample sizes

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

estimating the real parameter in a two sample proportional odds model this paper considers efficient estimation of the euclidean parameter 0 in the proportional odds model g 1 g l f 1 f 1 when two independent i i d samples with distributions f and g respectively are observed the fisher information 1 0 is calculated based on the solution of a pair of integral equations which are derived from a class of more general semiparametric models a one step estimate is constructed using an initial n consistent estimate and shown to be asymptotically efficient in the sense that its asymptotic risk achieves the corresponding minimax lower bound

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

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

reversible data embedding into images using wavelet techniques and sorting the proliferation of digital information in our society has enticed a lot of research into data embedding techniques that add information to digital content like images audio and video in this paper we investigate high capacity lossless data embedding methods that allow one to embed large amounts of data into digital images or video in such a way that the original image can be reconstructed from the watermarked image we present two new techniques one based on least significant bit prediction and sweldens lifting scheme and another that is an improvement of tian s technique of difference expansion the new techniques are then compared with various existing embedding methods by looking at capacity distortion behavior and capacity control

weighted estimating equations for semiparametric transformation models with censored data from a case cohort design summary in a case cohort design introduced by prentice 1986 covariates are assembled only for a subcohort randomly selected from the entire cohort and any additional cases outside the subcohort semiparametric transformation models are considered here for failure time data from the case cohort design weighted estimating equations are proposed for esti mation of the regression parameters the estimation procedure of survival probability at given covariate levels is also provided asymptotic properties are derived for the estimators using finite population sampling theory u statistics theory and martingale convergence results the finite sample properties of the proposed estimators as well as the efficiency relative to the full cohort estimators are assessed via simulation studies a case cohort dataset from the atherosclerosis risk in communities study is used to illustrate the estimating procedure

semiparametric inference in the proportional odds regression model abstract for fitting the proportional odds regression model with right censored survival times we introduce some weighted empirical odds functions these functions are solutions of some self consistency equations and have a nice martingale representation from these functions several classes of new regression estimators such as the pseudo maximum likelihood estimator martingale residual based estimators and minimum distance estimators are derived these estimators have desirable properties such as easy computation asymptotic normality via a martingale analysis and reliable asymptotic covariance estimation in closed form extensive numerical studies show that the minimum l 2 distance estimators have very good finite sample behaviors compared to existing methods results of some simulation studies and applications to a real dataset are given the weighted odds function based approach also provides inference on the baseline odds function and some measures for lack of fit analysis

regression to the mean for nonnormal populations summary regression to the mean is the term used to describe the effect by which individuals selected on the basis of an initial measurement which is particularly high or low compared with other members of the population have upon remeasurement values nearer to the population mean for the normal distribution simple expressions for estimates of the magnitude of this effect are available many biological variables however are not normally distributed estimates for regression to the mean for nonnormal data are given based on edgeworth series and saddlepoint approximations

semiparametric regression analysis for clustered failure time data inference procedures based on the partial likelihood function for the cox proportional hazards model have been generalised to the case in which the data consist of a large number of independent small groups of correlated failure time observations lee wei amato 1992 liang self chang 1993 cai prentice 1997 however the cox model may not fit the data well a class of linear transformation models which includes the proportional hazards and odds models as special cases has been studied extensively for univariate event times in this paper statistical methods to analyse such correlated observations are proposed for these models we use the data from a recent study of the genetic aetiology of alcoholism to illustrate the new procedures for estimation prediction and model selection

a reversible data hiding scheme using complementary embedding strategy obtaining good visual quality and high hiding capacity with reversible data hiding systems is a technically challenging problem in this paper we propose a simple reversible data hiding scheme that uses a complementary hiding strategy the proposed method embeds one secret bit horizontally and vertically into one cover pixel of a grayscale cover image by decreasing odd valued pixels and increasing even valued pixels by one experimental results show that the hiding capacity measured by bit per pixel bpp of the proposed scheme is at least 1 21bpp with a psnr peak signal to noise ratio value greater than 52db for all standard test images especially in the case of four layer embedding the psnr value of the proposed method is still greater than 51db at a hiding capacity of about 5bpp for all standard test images in addition the proposed method is quite simple because it primarily uses additions and subtractions these results indicate that the proposed scheme is superior to many existing reversible data hiding schemes introduced in the literature

an extension of partial likelihood methods for proportional hazard models to general transformation models on utilise un schema de reechantillonnage appele echantillonneur de vraisemblance pour calculer la vraisemblance partielle et les estimateurs de vraisemblance partielle maximum

semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure summary we consider the problem of estimating the regression coefficients in a competing risks model where the relationship between the cause specific hazard for the cause of interest and covariates is described using linear transformation models and when cause of failure is missing at random for a subset of individuals using the theory of robins et al 1994 for missing data problems and the approach of chen et al 2002 for estimating regression coefficients for linear transformation models we derive augmented inverse probability weighted complete case estimators for the regression coefficients that are doubly robust simulations demonstrate the relevance of the theory in finite samples

robust inference for univariate proportional hazards frailty regression models we consider a class of semiparametric regression models which are one parameter extensions of the cox j roy statist soc ser b 34 1972 187 220 model for right censored univariate failure times these models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty the frailty is assumed to have mean 1 within a known one parameter family of distributions inference is based on a nonparametric likelihood the behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified the joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo value maximizing the asymptotic limit of the likelihood appropriately standardized the estimator converges weakly to a gaussian process when the model is correctly specified the procedure is semiparametric efficient achieving the semiparametric information bound for all parameter components it is also proved that the bootstrap gives valid inferences for all parameters even under misspecification we demonstrate analytically the importance of the robust inference in several examples in a randomized clinical trial a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified under certain conditions on the covariates the ratios of the regression parameters are still identifiable the practical utility of the procedure is illustrated on a non hodgkin s lymphoma dataset

local estimating equations abstract estimating equations have found wide popularity recently in parametric problems yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula motivated by a problem in nutritional epidemiology we use estimating equations to derive nonparametric estimators of a parameter depending on a predictor the nonparametric component is estimated via local polynomials with loess or kernel weighting asymptotic theory is derived for the latter in keeping with the estimating equation paradigm variances of the nonparametric function estimate are estimated using the sandwich method in an automatic fashion without the need typical in the literature to derive asymptotic formulas and plug in an estimate of a density function the same philosophy is used in estimating the bias of the nonparametric function that is an empirical method is used without deriving asymptotic theory on a case by case basis the methods are applied to a series of examples the applicatio

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

weighted breslow type and maximum likelihood estimation in semiparametric transformation models a semiparametric transformation model comprises a parametric component for covariate effects and a nonparametric component for the baseline hazard intensity the breslow type estimator has been proposed for estimating the nonparametric component in some inefficient estimation procedures we show that introducing weights into this estimator leads to nonparametric maximum likelihood estimation with the weights depending on the martingale residuals the weighted breslow type estimator suggests an iterative reweighting algorithm for nonparametric maximum likelihood estimation which can be implemented by a weighted variant of the existing algorithms for inefficient estimation and can be computationally more efficient than an em type algorithm the weighting idea is further extended to semiparametric transformation models with mismeasured covariates

semiparametric analysis of transformation models with censored data summary a unified estimation procedure is proposed for the analysis of censored data using linear transformation models which include the proportional hazards model and the proportional odds model as special cases this procedure is easily implemented numerically and its validity does not rely on the assumption of independence between the covariates and the censoring variable the estimator is the same as the cox partial likelihood estimator in the case of the proportional hazards model moreover the asymptotic variance of the proposed estimator has a closed form and its variance estimator is easily obtained by plug in rules the method is illustrated by simulation and is applied to the veterans administration lung cancer data

methods for assessing whether change depends on initial value statistical analysis of whether the change in a variable depends on its initial value in clinical trials and other studies is complicated by the phenomenon of regression to the mean we review this problem and examine some approaches for handling it macgregor s log log plot fails to correct for the regression effect while oldham s method of plotting the change against the average of initial and final values is shown to give misleading results when the effect of treatment varies between subjects or when subjects are selected for study if their initial observations fall above or below a specified cut off point these results are illustrated by computer simulations we prefer the use of blomqvist s method of correcting the association between change and initial value to allow for the regression effect

on the linear transformation model for censored data recently cheng wei ying 1995 1997 proposed a class of estimation procedures for semi parametric linear transformation models with censored observations when the support of the censoring variable is shorter than that of the failure time the estimators are asymptotically biased in this paper we present a simple modification of cheng s estimation procedures for the regression parameters through extensive numerical studies with practical sample sizes we find that the new proposals perform well but the original interval estimators may not have correct coverage probabilities when censoring is heavy prediction procedures for the survival probabilities of future subjects are also modified accordingly

general saddlepoint approximations with applications to l statistics abstract saddlepoint approximations are extended to general statistics the technique is applied to derive approximations to the density of linear combinations of order statistics including trimmed means a comparison with exact results shows the accuracy of these approximations even in very small sample sizes

proportional odds regression and sieve maximum likelihood estimation summary this paper introduces under a censoring mechanism an estimation procedure for the baseline function and the regression parameters in the proportional odds model based on the sieve maximum likelihood method the procedure uses monotone splines of variable orders and knots as approximations for the baseline function and an approximately unbiased estimator of the comparative kullback leibler risk to select the best approximation the procedure adapts to various unknown structures of the baseline function such as spatial structures and smoothness of an unknown degree the proposed procedure is implemented for right censored and so called case 2 interval censored data the estimated regression parameters are shown to be asymptotically normal and efficient the small sample operating characteristics of the proposed procedure are examined via simulations and are illustrated on a dataset from a study of breast cancer patients

estimates for a regression parameter using ranks on considere une technique de reechantillonnage de monte carlo due a doksum et plusieurs modifications de celle ci

a semiparametric estimate of treatment effects with censored data summary a semiparametric estimate of an average regression effect with right censored failure time data has recently been proposed under the cox type model where the regression effect t is allowed to vary with time in this article we derive a simple algebraic relationship between this average regression effect and a measurement of group differences in k sample transformation models when the random error belongs to the gp family of harrington and fleming 1982 biometrika69 553 566 the latter being equivalent to the conditional regression effect in a gamma frailty model the models considered here are suitable for the attenuating hazard ratios that often arise in practice the results reveal an interesting connection among the above three classes of models as alternatives to the proportional hazards assumption and add to our understanding of the behavior of the partial likelihood estimate under nonproportional hazards the algebraic relationship provides a simple estimator under the transformation model we develop a variance estimator based on the empirical influence function that is much easier to compute than the previously suggested resampling methods when there is truncation in the right tail of the failure times we propose a method of bias correction to improve the coverage properties of the confidence intervals the estimate its estimated variance and the bias correction term can all be calculated with minor modifications to standard software for proportional hazards regression

nonparametric regression to the mean available data may reflect a true but unknown random variable of interest plus an additive error which is a nuisance the problem in predicting the unknown random variable arises in many applied situations where measurements are contaminated with errors it is known as the regression to the mean problem there exists a well known solution when both the distributions of the true underlying random variable and the contaminating errors are normal this solution is given by the classical regression to the mean formula which has a data shrinkage interpretation we discuss the extension of this solution to cases where one or both of these distributions are unknown and demonstrate that the fully nonparametric case can be solved for the case of small contaminating errors the resulting nonparametric regression to the mean paradigm can be implemented by a straightforward data sharpening algorithm that is based on local sample means asymptotic justifications and practical illustrations are provided

tied grouped continuous and ordered categorical data a comparison of two models summary likelihood ratio tests for no regression effect are considered when a linear model is used to explain the sample outcome where the observations are tied grouped continuous or ordered categorical data two likelihoods are considered one is an adaptation of a likelihood based on ranks modified for ties and the second is a likelihood for grouped continuous data the two likelihoods give asymptotically equivalent test statistics provided that the number of tied values or categories does not increase too quickly with n the total number of observations approximate estimation procedures are proposed based on average rank scores and two examples are given in this paper we examine models for the analysis of grouped continuous data and ordered categorical data the first model considers a likelihood function based on ranks which is adapted to deal with ties prentice 1978 pettitt 1982 the second model is the grouped continuous model recently considered by mccullagh 1980 where further extensive references can be found in this paper we consider a likelihood ratio statistic to test for no regression effect when the sample outcome is explained in terms of a linear regression model this statistic is calculated for both model likelihoods and it is found to be asymptotically the same for both models provided that the number of categories or tied values k increases with n the total number of observations at a rate slower than n as n oo for a faster increase in k the likelihood based on ranks provides a more efficient analysis this analysis also suggests that approximate estimates and standard errors for regression parameters can be derived from the rank likelihood and these can be compared with estimates for the grouped continuous model two numerical examples are given the first involves grouped continuous data and a two sample problem the second involves ordered categorical data and a regression problem analyses based on the rank model and the grouped continuous model are found to give very similar results the rank analysis might be preferred to the grouped continuous model for moderate to large numbers of categories and small to moderate sample sizes

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

rank regression with log gamma residuals summary a robust analysis for field data is proposed using a stratified rank regression model that analysis follows pettitt 1982 alternatively a new technique is described where residuals are log gamma random variables the log gamma distribution is approximately normal when the shape parameter is large and this parameter is taken as an integer which is either preselected or estimated by a simple grid search algorithms for estimating location parameters by maximizing the likelihood based on within stratum rank information are described and illustrated using a small data set

proportional hazards tests and diagnostics based on weighted residuals summary nonproportional hazards can often be expressed by extending the cox model to include time varying coefficients e g for a single covariate the hazard function for subject i is modelled as exp fl t zi t a common example is a treatment effect that decreases with time we show that the function 3 t can be directly visualized by smoothing an appropriate residual plot also many tests of proportional hazards including those of cox 1972 gill schumacher 1987 harrell 1986 lin 1991 moreau o quigley mesbah 1985 nagelkerke oosting hart 1984 o quigley pessione 1989 schoenfeld 1980 and wei 1984 are related to time weighted score tests of the proportional hazards hypothesis and can be visualized as a weighted least squares line fitted to the residual plot

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

the product limit estimator and the bootstrap some asymptotic representations the product limit estimator and its quantile process are represented as i i d mean processes with a remainder of ordern 3 4 logn 3 4 a s corresponding bootstrap versions of these representations are given which can help one visualize how the bootstrap procedure operates in this set up

a lossless data hiding scheme based on three pixel block differences this paper proposes a data hiding scheme that losslessly embeds a message into a cover image using the two differences between the first and the second pixel as well as between the second and the third pixel in a three pixel block in the cover image an absolute difference between a pair of pixels is selected to embed the message if the number of pixel pairs with the difference in the image is the largest to embed a bit 1 or 0 the selected difference is increased by 1 or left unchanged respectively in the best case a three pixel block can embed two bits 11 and only the central pixel needs to be increased or decreased by 1 the average payload capacity among the test images can be up to 2 08 bits per pixel bpp

robust variance estimation for the case cohort design large cohort studies of rare outcomes require extensive data collection often for many relatively uninformative subjects sampling schemes have been proposed that oversample certain groups for example the case cohort design of prentice 1986 biometrika 73 1 11 provides an efficient method of analysis of failure time data however the variance estimate must explicitly correct for correlated score contributions a simple robust variance estimator is proposed that allows for more complicated sampling mechanisms the variance estimate uses a jackknife estimate of the variance of the individual influence function and is shown to be equivalent to a robust variance estimator proposed by lin and wei 1989 journal of the american statistical association 84 1074 1078 for the standard cox model simulation results indicate excellent agreement with corrected asymptotic estimates and appropriate test size the technique is illustrated with data evaluating the efficacy of mammography screening in reducing breast cancer mortality

ordinal data ordered scale points and order statistics this paper concerns ordinal responses an ordered dirichlet distribution describes prior and posterior beliefs about the cumulative probabilities of response categories associating the response categories with intervals of a latent random variable then induces a distribution on the order statistics of that variable the psychometrician can use the asymptotic theory of order statistics to learn how distributional assumptions about the latent variable effect inference an example relates the skewness of a latent variable to the proportional odds and proportional hazards models of mccullagh 1980

weighted semiparametric likelihood method for fitting a proportional odds regression model to data from the case cohort design the problem of fitting a proportional odds regression model to data from the case cohort design proposed by prentice is considered a weighted semiparametric likelihood method is proposed under the proportional odds model the maximum weighted semiparametric likelihood estimators of both the regression parameter and the transformation function are shown to be consistent and normally distributed the applicability of the weighted semiparametric likelihood method to the semiparametric transformation regression models is also discussed in particular when the proportional hazards regression model is fitted estimators proposed by chen and lo can be generated by the weighted semiparametric likelihood method under different weighting schemes a simulation study suggests that the case cohort design is also useful under the proportional odds regression model and the proposed method performs well with practical finite sample sizes

variable selection for proportional odds model in this paper we study the problem of variable selection for the proportional odds model which is a useful alternative to the proportional hazards model and might be appropriate when the proportional hazards assumption is not satisfied we propose to fit the proportional odds model by maximizing the marginal likelihood subject to a shrinkage type penalty which encourages sparse solutions and hence facilitates the process of variable selection two types of shrinkage penalties are considered the lasso and the adaptive lasso alasso penalty in the alasso penalty different weights are imposed on different coefficients such that important variables are more protectively retained in the final model while unimportant ones are more likely to be shrunk to zeros we further provide an efficient computation algorithm to implement the proposed methods and demonstrate their performance through simulation studies and an application to real data numerical results indicate that both methods can produce accurate and interpretable models and the alasso tends to work better than the usual lasso

steganalysis and payload estimation of embedding in pixel differences using neural networks in this paper a steganalysis technique is proposed for pixel value differencing method this steganographic method which is immune against conventional attacks performs the embedding in the difference of the values of pixel pairs therefore the histogram of the differences of an embedded image is different as compared with a cover image a number of characteristics are identified in the difference histogram that show meaningful alterations when an image is embedded five distinct multilayer perceptrons neural networks are trained to detect different levels of embedding every image is fed to all networks and a voting system categorizes the image as stego or cover the implementation results indicate 88 6 success in correct categorization of the test images that contained more than 20 embedding furthermore using a neural network an estimator is presented which gives an estimate of the amount of the mpvd embedding in an image implementation of the estimator showed an average accuracy of 88 3 in the estimation of the amount of embedding

information bounds for the conditional hazard ratio in a nested family of regression models information bounds are obtained for a parametric treatment effect in a nested family of models for the conditional distribution of survival given confounding variables the family extends from the fully parametric weibull model to a completely nonparametric model for right censored data and includes the cox model and the stratified version of it it is shown that in certain special cases there is no loss of information about the treatment effect when going from a fully parametric to a nonparametric specification of the conditional hazard function

proper likelihoods for bayesian analysis summary the validity of posterior probability statements follows from probability calculus when the likelihood is the density of the observations to investigate other cases a second more intuitive definition of validity is introduced based on coverage of posterior sets this notion of validity suggests that the likelihood must be the density of a statistic not necessarily sufficient for posterior probability statements to be valid a convenient numerical method is proposed to invalidate the use of certain likelihoods for bayesian analysis integrated marginal and conditional likelihoods derived to avoid nuisance parameters are also discussed

sample size power calculation for stratified case cohort design the case cohort cc study design usually has been used for risk factor assessment in epidemiologic studies or disease prevention trials for rare diseases the sample size power calculation for a stratified cc scc design has not been addressed before this article derives such result based on a stratified test statistic simulation studies show that the proposed test for the scc design utilizing small sub cohort sampling fractions is valid and efficient for situations where the disease rate is low furthermore optimization of sampling in the scc design is discussed and compared with proportional and balanced sampling techniques an epidemiological study is provided to illustrate the sample size calculation under the scc design

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

approximate methods using ranks for regression with censored data summary an approximation to marginal rank likelihoods is given and used to make inferences for the linear regression model with censored data the approximations involve linear rank statistics adapted for censored data and estimates of their variance various explicit scores are given for right censored data and logistic scores for doubly censored data inferences using the approximate rank analysis are compared with inferences using fully and partially parametric techniques on two data sets

analysis of survival data by the proportional odds model a model is presented for the analysis of lifetime data in which the rates of mortality for separate groups of patients converge with time a non parametric estimate is given for the survivor function the theoretical basis for the model assumes that prognostic factors have a multiplicative effect on the odds against survival beyond any given time the model is fitted to data using maximum likelihood estimation and an example of its use in the analysis of a lung cancer trial is given

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

semiparametric transformation models for survival data with a cure fraction we propose a class of transformation models for survival data with a cure fraction the class of transformation models is motivated by biological considerations and includes both the proportional hazards and the proportional odds cure models as two special cases an efficient recursive algorithm is proposed to calculate the maximum likelihood estimators mles furthermore the mles for the regression coefficients are shown to be consistent and asymptotically normal and their asymptotic variances attain the semiparametric efficiency bound simulation studies are conducted to examine the finite sample properties of the proposed estimators the method is illustrated on data from a clinical trial involving the treatment of melanoma

bayesian bootstrap multivariate regression a bayesian bootstrap multivariate regression bbmr procedure is presented that allows robust bayesian analysis of multivariate regression models bbmr does not require a parametric specification for the likelihood function and instead uses a bootstrapped likelihood based on the sampling distribution of location and scale estimators a mixing algorithm for implementing the procedure automatically incorporates the scale invariant ignorance prior on the covariance matrix bbmr can be implemented as a generic algorithm in standard statistical software independently of the actual choice of prior distribution monte carlo evidence is provided showing accuracy and robustness of the approach in representing posterior distributions

retrospective likelihood based methods for analyzing case cohort genetic association studies summary the case cohort cch design is a cost effective design for assessing genetic susceptibility with time to event data especially when the event rate is low in this work we propose a powerful pseudo score test for assessing the association between a single nucleotide polymorphism snp and the event time under the cch design the pseudo score is derived from a pseudo likelihood which is an estimated retrospective likelihood that treats the snp genotype as the dependent variable and time to event outcome and other covariates as independent variables it exploits the fact that the genetic variable is often distributed independent of covariates or only related to a low dimensional subset estimates of hazard ratio parameters for association can be obtained by maximizing the pseudo likelihood a unique advantage of our method is that it allows the censoring distribution to depend on covariates that are only measured for the cch sample while not requiring the knowledge of follow up or covariate information on subjects not selected into the cch sample in addition to these flexibilities the proposed method has high relative efficiency compared with commonly used alternative approaches we study large sample properties of this method and assess its finite sample performance using both simulated and real data examples