diagnostic measures for the cox regression model with missing covariates this paper investigates diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for the cox regression model our diagnostics include case deletion measures conditional martingale residuals and score residuals the q distance is proposed to examine the effects of deleting individual observations on the estimates of finite dimensional and infinite dimensional parameters conditional martingale residuals are used to construct goodness of fit statistics for testing possible misspecification of the model assumptions a resampling method is developed to approximate the p values of the goodness of fit statistics simulation studies are conducted to evaluate our methods and a real data set is analyzed to illustrate their use

leverage local influence and curvature in nonlinear regression summary the connections between measures of leverage statistical curvature and the local influence of a mean shift perturbation are explored in nonlinear regression models the circumstances under which the jacobian leverage reduces to a commonly used linear approximation are found to be connected to the effective residual curvature of the nonlinear model the local influence of a mean shift perturbation in the model function is seen to be closely related to the jacobian leverage

jackknife based estimators and confidence regions in nonlinear regression the properties of several jackknife based estimators are investigated in the context of the nonlinear regression model these estimators are suggested to overcome lack of balance of the design and the nonlinearity of the model it is shown that a reweighted estimator combined with a modified variance estimate provides a technique that is reasonably robust with respect to outliers leverage points and curvature effects several examples are presented to illustrate these properties

cross validation in survival analysis the predictive value of a statistical model is conceptually different from the explained variation in this paper we construct a measure of the predictive value of the cox proportional hazards model computed from the leave one out regression coefficients these coefficients can also be used to calculate a shrinkage factor which can be applied to improve the predictions and that can be used in r2 type measures of the proportion of explained variation our methods are illustrated by a study of chemotherapy for advanced ovarian cancer

adjusted qmle for the spatial autoregressive parameter abstract one simple and often very effective way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter we apply this general principle to the quasi maximum likelihood estimator qmle of the autoregressive parameter in a spatial autoregression the resulting estimator for has better finite sample properties compared to the qmle for especially in the presence of a large number of covariates it can also solve the incidental parameter problem that arises for example in social interaction models with network fixed effects however spatial autoregressions present specific challenges for this type of adjustment because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for conditions for this to happen are given and implications are discussed for inference we propose confidence intervals based on a lugannani rice approximation to the distribution of the adjusted qmle of based on our simulations the coverage properties of these intervals are excellent even in models with a large number of covariates

curvature measures for multiresponse regression models a multiresponse model presented in this study is two fold first a nonuniformity measure is developed to measure the validity of the approximation of the determinant contours by generalised least squares contours secondly curvature measures similar to those of bates watts are calculated for the generalised least squares model to evaluate the validity of the linear approximation of the model functions in a neighbourhood of the parameter estimates

a note on parameter effects curvature abstract the parameter effects curvature measure proposed by bates and watts 1980 is examined for a growth model and the fieller creasy problem exact confidence regions are constructed and compared to linear approximation regions for the growth model the agreement between the regions is good despite high curvature in the fieller creasy problem it is shown that the agreement can be quite poor despite low curvature

parameter transformations for improved approximate confidence regions in nonlinear least squares in a previous paper it was shown that parameter effects nonlinearities of a nonlinear regression model experimental design parameterization combination can be quantified by means of a parameter effects curvature array a based on second derivatives of the model function in this paper the individual terms of a are interpreted and local compensation methods are suggested a method of computing the parameter effects array corresponding to a transformed set of parameters is given and we discuss how this result could be used to determine reparameterizations which have zero local parameter effects nonlinearity

smoothing spline nonlinear nonparametric regression models almost all of the current nonparametric regression methods such as smoothing splines generalized additive models and varyingcoefficients models assume a linear relationship when nonparametric functions are regarded as parameters in this article we propose a general class of smoothing spline nonlinear nonparametric models that allow nonparametric functions to act nonlinearly they arise in many fields as either theoretical or empirical models our new estimation methods are based on an extension of the gauss newton method to infinite dimensional spaces and the backfitting procedure we extend the generalized cross validation and generalized maximum likelihood methods to estimate smoothing parameters we establish connections between some nonlinear nonparametric models and nonlinear mixed effects models we derive approximate bayesian confidence intervals for inference we illustrate the methods with an application to term structure of interest rates and conduct simulations to evaluate the finite sampl

the graphical evaluation of explanatory variables in proportional hazard regression models summary a graphical technique for assessing explanatory variables in cox s proportional hazards regression model is examined the method arises from consideration of the cumulative hazard transformation and the partial likelihood score function and consists of permuting the observed rank statistic to account for the effects of explanatory variables fitted to the model an example is provided

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

rich families and projectional skeletons in asplund wcg spaces abstract we show a way of constructing projectional skeletons using the concept of rich families in banach spaces which admit a projectional generator our next result is that a banach space x is asplund and weakly compactly generated if and only if there exists a commutative 1 projectional skeleton q on x such that q is a commutative 1 projectional skeleton on x we consider both real and also complex banach spaces

power transformations and reparameterizations in nonlinear regression models a two stage procedure is proposed to achieve normality and homoscedasticity of the classical error assumptions and to remove nonlinearity of the regression function this systematic approach involves power transformations and reparameterization test statistics are obtained to assess the necessity of power transformations and the validity of homoscedasticity of the errors in addition nonlinearity measures are provided to diagnose the accuracy of linearization based approximate confidence regions for parameters numerical illustrations of the two stage procedure arc presented

more about transformations and influential cases in regression we extend the diagnostic method of cook and wang 1983 for assessing case influence to regression models in which both response and linear predictor are transformed we also suggest a possible improvement of cook and wang s method

comparison of case deletion diagnostic methods for cox regression case deletion diagnostics are a routine component of regression analysis since they identify unusual observations that substantially affect parameter estimates the exact approach is to compute the change in each regression parameter by dropping that individual and refitting the model repeating a cox regression for the removal of each individual is very time consuming and therefore not done in practice the two methods commonly used to approximate the exact case deletion change for cox regression are the empirical influence function approach and the covariate vector augmentation approach this paper reports the results of a simulation study on how well these methods estimate the exact change in a parameter estimate when deleting a known outlier or a known non outlier additionally we investigate how well these methods correctly identify outliers and non outliers the covariate augmentation approach clearly outperformed the influence function approach in these simulations

inference and sequential design summary if an experiment is designed sequentially repeated sampling inference may not necessarily be made using distributional results that are valid for fixed designs a few simple illustrative examples and alternative approaches are given sometimes the sequential nature of design can be ignored asymptotically links are forged with inference for stochastic processes and missing data problems

an ordering for positive dependence on introduit une relation d ordre partiel pour des distributions bivariables dependantes positives appelees plus associees

approximate case influence for the proportional hazards regression model with censored data a method is presented for approximating the influence of individual cases upon regression coefficient estimates obtained from the cox proportional hazards model observations can thus be identified which may greatly influence statistical inferences regarding the effects of prognostic factors upon survival time an example from a cancer clinical trial is given

on prediction and the power transformation family summary the power transformation family is often used for transforming to a normal linear model the variance of the regression parameter estimators can be much larger when the transformation parameter is unknown and must be estimated compared to when the transformation parameter is known we consider prediction of future untransformed observations when the data can be transformed to a linear model when the transformation must be estimated the prediction error is not much larger than when the parameter is known

confidence regions for parameter subsets in nonlinear regression on utilise la methode a deux niveaux proposee par hamilton watts et bates 1982 pour obtenir des approximations ameliorees des regions de confiance

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

simultaneous projectional skeletons abstract we prove the existence of a simultaneous projectional skeleton for certain subspaces of c k spaces this generalizes a result on simultaneous projectional resolutions of identity proved by m valdivia we collect some consequences of this result in particular we give a new characterization of asplund spaces using the notion of projectional skeleton

natural examples of valdivia compact spaces abstract we collect examples of valdivia compact spaces their continuous images and associated classes of banach spaces which appear naturally in various branches of mathematics we focus on topological constructions generating valdivia compact spaces linearly ordered compact spaces compact groups l 1 spaces banach lattices and noncommutative l 1 spaces

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

nonlinear experiments optimal design and inference based on likelihood abstract nonlinear experiments involve response and regressors that are connected through a nonlinear regression type structure examples of nonlinear models include standard nonlinear regression logistic regression probit regression poisson regression gamma regression inverse gaussian regression and so on the fisher information associated with a nonlinear experiment is typically a complex nonlinear function of the unknown parameter of interest as a result we face an awkward situation designing an efficient experiment will require knowledge of the parameter but the purpose of the experiment is to generate data to yield parameter estimates our principal objective here is to investigate proper designing of nonlinear experiments that will let us construct efficient estimates of parameters we focus our attention on a very general nonlinear setup that includes many models commonly encountered in practice the experiments considered have two fundamental stages a static design in the initial stage

geometry of nonlinear least squares with applications to sloppy models and optimization parameter estimation by nonlinear least squares minimization is a common problem that has an elegant geometric interpretation the possible parameter values of a model induce a manifold within the space of data predictions the minimization problem is then to find the point on the manifold closest to the experimental data we show that the model manifolds of a large class of models known as sloppy models have many universal features they are characterized by a geometric series of widths extrinsic curvatures and parameter effect curvatures which we describe as a hyper ribbon a number of common difficulties in optimizing least squares problems are due to this common geometric structure first algorithms tend to run into the boundaries of the model manifold causing parameters to diverge or become unphysical before they have been optimized we introduce the model graph as an extension of the model manifold to remedy this problem we argue that appropriate priors can remove the boundaries and further improve the convergence rates we show that typical fits will have many evaporated parameters unless the data are very accurately known second bare model parameters are usually ill suited to describing model behavior cost contours in parameter space tend to form hierarchies of plateaus and long narrow canyons geometrically we understand this inconvenient parametrization as an extremely skewed coordinate basis and show that it induces a large parameter effect curvature on the manifold by constructing alternative coordinates based on geodesic motion we show that these long narrow canyons are transformed in many cases into a single quadratic isotropic basin we interpret the modified gauss newton and levenberg marquardt fitting algorithms as an euler approximation to geodesic motion in these natural coordinates on the model manifold and the model graph respectively by adding a geodesic acceleration adjustment to these algorithms we alleviate the difficulties from parameter effect curvature improving both efficiency and success rates at finding good fits

bounds on distributional treatment effect parameters using panel data with an application on job displacement abstract this paper develops new techniques to bound distributional treatment effect parameters that depend on the joint distribution of potential outcomes an object not identified by standard identifying assumptions such as selection on observables or even when treatment is randomly assigned i show that panel data and an additional assumption on the dependence between untreated potential outcomes for the treated group over time i provide more identifying power for distributional treatment effect parameters than existing bounds and ii provide a more plausible set of conditions than existing methods that obtain point identification i apply these bounds to study heterogeneity in the effect of job displacement during the great recession using standard techniques i find that workers who were displaced during the great recession lost on average 34 of their earnings relative to their counterfactual earnings had they not been displaced using the methods developed in the current paper i also show that the average effect masks substantial heterogeneity across workers

influence functions for iteratively defined statistics summary hampel s influence function and its finite sample counterparts are the basis for a number of diagnostic statistics these diagnostics can be expensive to compute in the natural way when the estimation calculations are iterative as they frequently are when maximum likelihood or robust methods are used we show how the influence function can be calculated in these situations by implicit differentiation of the fixed point equation satisfied by the limit of the iterative procesb we consider in particular the cases of newton s method and iteratively reweighted least squares where interesting analytic results are available as an application we consider the generalization of pregibon s 1981 logistic regression diagnostics to cover generalized linear models with noncanonical link functions such as probit regression

maximum weighted partial likelihood estimators for the cox model new estimators for cox regression that maximize a weighted version of the partial likelihood are considered their asymptotic properties on the model are sketched estimators with bounded influence curves are identified and shown to have good asymptotic relative efficiency the results of a small simulation study are included the estimators are applied to a well known data set the possible influence of an outlying observation on the cox estimator can be of any magnitude individuals who survive longest have a high potential of being influential in analogy with weighted linear rank tests we introduce estimators of the regression coefficients that maximize a weighted partial likelihood for instance by using weights proportional to the number at risk one obtains a wilcoxon type estimator this estimator has bounded influence provided the covariate space is compact and in a wide variety of situations its asymptotic relative efficiency is at least as good as that of the wilcoxon test asymptotic prop

a simple method for the adjustment of profile likelihoods summary we propose a simple adjustment for profile likelihoods the aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods such as bias inconsistency and overoptimistic variance estimates the adjustment is applied to the profile loglikelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function for cases in which explicit calculation of the adjustments is difficult we give two methods to simplify their computation an automatic simulation method that requires as input only the profile loglikelihood and its first few derivatives first order asymptotic expressions some examples are provided and a comparison is made with the conditional profile log likelihood of cox and reid

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

a quadratic design criterion for precise estimation in nonlinear regression models d optimal experimental designs for precise estimation in nonlinear regression models are obtained by minimizing the determinant of the approximate variance covariance matrix of the parameter estimates this determinant may not give a true indication of the volume of a joint inference region for the parameters however because of intrinsic and parameter effects nonlinearity in this article we investigate experimental designs that minimize a second order volume approximation unlike d optimal designs these designs depend on the noise and confidence levels and on the parameterization used and when used sequentially quadratic designs depend on the residuals from previous experiments and on the type of inference quadratic designs appear to be less sensitive to variations in initial parameter values used for design

a diagnostic for cox regression and general conditional likelihoods abstract diagnostics for changes in the maximum likelihood estimate of due to deletion of single observations in linear and logistic regression models are equivalent to diagnostics obtained from fitting augmented regression models for the cox proportional hazards model and in conditional models for arbitrarily matched or stratified data diagnostics derived from augmented regression models are again useful and easy to compute these diagnostics are applicable to different formulations for the multiplicative covariable effects over time or over strata an exact or approximate treatment of tied failure times or multiple case matching and time dependent covariates

residuals in nonlinear regression abstract the authors employ a quadratic expansion to investigate the behavior of the ordinary residuals in nonlinear regression in particular they derive quadratic approximations for the mean and variance of the ordinary residuals and the covariances between the ordinary residuals and the fitted values this investigation leads to the conclusion that the ordinary residuals can produce misleading results when used in diagnostic methods analogous to those for linear regression consequently a new type of residual that overcomes many of the potential shortcomings of the ordinary residuals is suggested author

leverage and superleverage in nonlinear regression abstract several measures of the leverage of an observation in a nonlinear regression model are defined and developed in contrast to the upper bound on the leverage in a linear model it is found that in a nonlinear model the leverage of an observation may exceed 1 such a case is said to exhibit superleverage relationships between the leverage measures are explored and several examples are developed to illustrate the proposed methodology

asplund spaces characterized by rich families and separable reduction of frechet subdifferentiability abstract asplund property of a banach space x is characterized by the existence of a rich family in the product x x consisting of some carefully chosen separable subspaces this structural result is then used to add a lot of precision and simplicity to the known separable reductions of frechet subdifferentials

assessing the accuracy of normal approximations abstract the widespread applicability and use of normal approximations creates a need for methods for assessing their accuracy in an operational fashion in this article two new methods are proposed and exemplified these new methods are based on a comparison of the level curves of an exact likelihood with the level curves of the usual normal approximation to it and on a comparison of selected line integrals of an exact density and a normal approximation to it the operational usefulness of these methods is compared with the operational usefulness of two well known existing approaches to assessing the accuracy of approximations namely convergence rates and the curvature methods of bates and watts 1980 as an example the second method is applied to the lee geisser 1972 1975 approximation to the predictive distribution of dental measurements on girls at the ages of 8 10 12 and 14 years in this application the method shows that the 50 central predictive probability region has actual predicti

decompositions of preduals of jbw and jbw algebras abstract we prove that the predual of any jbw algebra is a complex 1 plichko space and the predual of any jbw algebra is a real 1 plichko space i e any such space has a countably 1 norming markushevich basis or equivalently a commutative 1 projectional skeleton this extends recent results of the authors who proved the same for preduals of von neumann algebras and their self adjoint parts however the more general setting of jordan algebras turned to be much more complicated we use in the proof a set theoretical method of elementary submodels as a byproduct we obtain a result on amalgamation of projectional skeletons

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

accounting for intrinsic nonlinearity in nonlinear regression parameter inference regions joint confidence and likelihood regions for the parameters in nonlinear regression models can be defined using the geometric concepts of sample space and solution locus using a quadratic approximation to the solution locus instead of the usual linear approximation it is shown that these inference regions correspond to ellipsoids on the tangent plane at the least squares point accurate approximate inference regions can be obtained by mapping these ellipsoids into the parameter space and measures of the effect of intrinsic nonlinearity on inference can be based on the difference between the tangent plane ellipsoids and the sphere which would be obtained using a linear approximation

smooth goodness of fit tests for the baseline hazard in cox s proportional hazards model abstract for the cox proportional hazards model the goodness of fit problem of testing whether the baseline hazard rate function equals some specified hazard rate function 0 in the presence of incomplete data is considered extending neyman s idea the goodness of fit tests are score tests obtained by embedding in a larger family of hazard rate functions developed through smooth and possibly random transformations of 0 but whereas their smooth alternatives were formulated through the density function my formulation is through the hazard rate function which is more natural in failure time models where model specification is now done through hazard rates furthermore my smooth alternatives are allowed to be data driven or dynamic through this machinery classes of omnibus as well as directional goodness of fit tests are obtained moreover this machinery provides a theoretically sound method for combining varied directional goodness of fit tests into omnibus tests some of the resul

transformations and influential cases in regression we describe a diagnostic method for assessing the degree to which individual cases and groups of cases influence the box cox likelihood estimate of the transformation parameter for the response variable in linear regression models we compare the method to a method proposed by atkinson 1982 and sketch the extension to explanatory variables we present two examples

maximum likelihood estimation and large sample inference for generalized linear and nonlinear regression models summary the class of generalized linear models is extended to allow for correlated observations nonlinear models and error distributions not of the exponential family form the extended class of models include a number of important examples particularly of the composite transformational type large sample inference and maximum likelihood estimation for the extended class of generalized linear models are discussed and the analysis of deviance is generalized to the extended class of models calculation of the maximum likelihood estimate for a general likelihood by fisher s scoring method and a related method is considered and the relation with the gauss newton method is discussed

likelihood calculations for matched case control studies and survival studies with tied death times summary a recursion is presented which permits rapid computation of a conditional likelihood function which arises in matched case control studies and survival studies with tied death times an example with seven parameters and ten large strata the largest of which contains 29 cases and 52 controls illustrates the feasibility of the conditional maximum likelihood solution these methods may be specialized to permit rapid calculation of the conditional maximum likelihood estimate of the common odds ratio for several 2 x 2 tables

bivariate distributions with nonmonotone dependence structure a new ordering for nonmonotone dependence is proposed and a method is presented for describing parametric families of bivariate distributions with fixed marginals and specified dependence structures the method is easy to use and allows for arbitrary marginals and arbitrary dependence structures e g structures of nonmonotone dependence any parametric family of bivariate distributions is ordered by the nonmonotone dependence ordering constructed from the desirable dependence structure the construction is based on a generalization of the copula of distribution functions to a copula of probability measures on product spaces examples are shown for various bivariate distributions

monotone retractability and retractional skeletons abstract we prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton in particular a compact space is monotonically retractable if and only if it is corson this gives an answer to a question of r rojas hernandez and v v tkachuk further we apply this result to characterize retractional skeleton using a topology on the space of continuous functions answering thus a question of the first author and a related question of w kubi

a monotone version of the sokolov property and monotone retractability in function spaces abstract we introduce the monotone sokolov property and show that it is dual to monotone retractability in the sense that x is monotonically retractable if and only if c p x is monotonically sokolov besides a space x is monotonically sokolov if and only if c p x is monotonically retractable monotone retractability and monotone sokolov property are shown to be preserved by r quotient images and f subspaces furthermore every monotonically retractable space is sokolov so it is collectionwise normal and has countable extent we also establish that if x and c p x are lindelof spaces then they are both monotonically retractable and have the monotone sokolov property an example is given of a space x such that c p x has the lindelof property but neither x nor c p x is monotonically retractable we also establish that every lindelof space with a unique non isolated point is monotonically retractable on the other hand each lindelof space with a unique non isolated point is monotonically sokolov

diagnostics in transformation and weighted regression we describe a diagnostic method for assessing the influence of an individual case on the transformation power estimator in the box cox regression model and transform both sides regression model carroll and ruppert 1988 we compare the method to those proposed by cook and wang 1983 and hinkley and wang 1988 the new method takes into account the deletion effect on the jacobian of the variable s transformation it provides a more accurate and reliable transformation power estimator we also extend this method to analyze the case influence on the weighted parameter estimators in both the weighted regression model and the transformed and weighted regression model several examples are used to illustrate the results

diagnostic plots in cox s regression model two diagnostic plots are presented for validating the fitting of a cox proportional hazards model the added variable plot is developed to assess the effect of adding a covariate to the model the constructed variable plot is applied to detect nonlinearity of a fitted covariate both plots are also useful for identifying influential observations on the issues of interest the methods are illustrated on examples of multiple myeloma and lung cancer data

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

normal approximation diagnostics for the cox model summary we discuss two diagnostic methods for assessing the accuracy of the normal approximated confidence region to the likelihood based confidence region for the cox proportional hazards model with censored data the proposed diagnostic methods are extensions of the contour measures of hodges 1987 journal of the american statistical association82 149 154 and cook and tsai 1990 journal of the american statistical association85 770 777 and the curvature measures of jennings 1986 journal of the american statistical association81 471 476 and cook and tsai 1990 these methods are also illustrated in a study of hepatocyte growth factor in patients with lung cancer and a mayo clinic randomized study of participants with primary biliary cirrhosis

data analytic methods for matched case control studies the recent introduction of complex multivariate statistical models in matched case control studies is a mixed blessing their use can lead to a better understanding of the way in which many variables contribute to the risk of disease on the other hand these powerful methods can obscure salient features in the data that might have been detected by other less sophisticated methods this shortcoming is due to a lack of support methodology for the routine use of these models satisfactory computation of estimated relative risks and their standard errors is not sufficient justification for the fitted model goodness of fit must be examined if inferences are to be trusted this paper is concerned with the analysis of matched case control studies with logistic models analogies of these models to linear regression models are emphasized in particular basic concepts such as analysis of variance multiple correlation coefficient one degree of freedom tests and residual analysis are discussed the fairly new field of regression diagnostics is also introduced all procedures are illustrated on a study of bladder cancer in males

diagnostics for assessing the accuracy of normal approximations in exponential family nonlinear models abstract diagnostics are investigated for assessing the agreement between likelihood and standard large sample confidence regions for parameters from an exponential family nonlinear model cordeiro and paula 1989 the development connects the contour methods proposed by hodges 1985 1987 with the curvature measures for normal nonlinear regression proposed by bates and watts 1980 and jennings s 1982 1986 diagnostics for logistic regression the proposed methodology is illustrated with several examples

global measures of local influence for proportional hazards regression models cox proportional hazards regression models have been extended to multiple failure times and other situations by using a robust covariance matrix instead of the usual inverse of the information matrix we modify an existing measure of individual influence by substituting the robust covariance matrix for the inverse of the information matrix this provides a scalar measure of influence with known mean and bounded range on the interval 0 1 the measure is applicable to marginal multiple failure time models two examples are presented

a note on jorgensen s iteratively defined statistics summary the newton raphson and fisher scoring iteratively reweighted least squares methods are two fundamental tools for computing parameter estimators and deletion diagnostics jorgensen 1993 proposed a modified method to compute deletion diagnostics in this paper we study the relationship between jorgensen s newton raphson and fisher scoring one step deletion estimators by using the observed and expected fisher information matrices in addition we extend jorgensen s true leverage and approximate leverage from binary regression models to general model settings

case deletion diagnostics for mixed models mixed linear models arise in many areas of application standard estimation methods for mixed models are sensitive to bizarre observations such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions we develop case deletion diagnostics for detecting influential observations in mixed linear models diagnostics for both fixed effects and variance components are proposed computational formulas are given that make the procedures feasible the methods are illustrated using examples

leave k out diagnostics for time series abstract the authors propose diagnostics for arima model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters the use of leave one out diagnostics is a well established tool in regression analysis this document demonstrates the efficacy of observation deletion based diagnostics for arima models addressing issues special to the time diagnostics based on the innovations variance it is shown that the dependency aspect of time series data gives rise to a smearing effect which confounds the diagnostics for the coefficients it is also shown that the diagnostics based on the innovations variance are much clearer and more sensitive than those for the coefficients a leave k out diagnostics approach is proposed to deal with patches of outliers and problems caused by masking are handled by use of iterative deletion an overall strategy for arima model fitting is given and applied to two data sets

a diagnostic for cox regression with discrete failure time models summary changes in maximum likelihood parameter estimates due to deletion of individual observations are useful statistics both for regression diagnostics and for computing robust estimates of covariance for many likelihoods including those in the exponential family these delete one statistics can be approximated analytically from a one step newton raphson iteration on the full maximum likelihood solution but for general conditional likelihoods and the related cox partial likelihood the one step method does not reduce to an analytic solution for these likelihoods an alternative analytic approximation that relies on an appropriately augmented design matrix has been proposed in this paper we extend the augmentation approach to explicitly deal with discrete failure time models in these models an individual subject may contribute information at several time points thereby appearing in multiple risk sets before eventually experiencing a failure or being censored our extension also allows the covariates to be time dependent the new augmentation requires no additional computational resources while improving results

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

diagnostic regression analysis and shifted power transformations diagnostic displays for outlying and influential observations are reviewed in some examples apparent outliers vanish after a power transformation of the data interpretation of the score statistic for transformations as regression on a constructed variable makes diagnostic methods available for detection of the influence of individual observations on the transformation methods for the power transformation are exemplified and extended to the power transformation after a shift in location for which there are two constructed variables the emphasis is on plots as diagnostic tools

the relation between information theory and the differential geometry approach to statistics abstract cencov has shown that the riemannian metric on the probability simplex xi 1 defined by ds 2 dx i 2 x i has an invariance property under certain probabilistically natural mappings no other riemannian metric has the same property the geometry associated with this metric is shown to lead almost automatically to measures of divergence between probability distributions which are associated with kullback bhattacharyya and matusita certain vector fields are associated in a natural way with random variables the integral curves of these vector fields yield the maximum entropy or minimum divergence estimates of probabilities some other consequences of this geometric view are also explored

a note on adjusted profile likelihoods in non linear regression summary the problem of partial non linear regression is used to provide an example of mccullagh and tibshirani s profile likelihood adjustment for more than one parameter of interest where for one linear nuisance parameter an expression for the adjusted profile likelihood can be derived

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

predictive value of statistical models a review is given of different ways of estimating the error rate of a prediction rule based on a statistical model a distinction is drawn between apparent optimum and actual error rates moreover it is shown how cross validation can be used to obtain an adjusted predictor with smaller error rate a detailed discussion is given for ordinary least squares logistic regression and cox regression in survival analysis finally the splitsample approach is discussed and demonstrated on two data sets

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

curvatures for parameter subsets in nonlinear regression on etend les mesures de nonlinearite proposees par bates et watts 1980 a un sous ensemble arbitraire des parametres dans un modele de regression non lineaire normal

banach spaces with projectional skeletons a projectional skeleton in a banach space is a directed family of projections onto separable subspaces covering the entire space the class of banach spaces with projectional skeletons is strictly larger than the class of plichko spaces i e banach spaces with a countably norming markushevich basis we show that every space with a projectional skeleton has a projectional resolution of the identity and has a norming space with similar properties to spaces we characterize the existence of a projectional skeleton in terms of elementary substructures providing simple proofs of known results concerning weakly compactly generated spaces and plichko spaces we prove a preservation result for plichko banach spaces involving transfinite sequences of projections as a corollary we show that a banach space is plichko if and only if it has a commutative projectional skeleton

correction factors for f ratios in nonlinear regression summary multiplicative correction factors are derived for the limiting f distributions of two test statistics for parameter subsets in nonlinear regression the factors depend on the first and second derivatives of the model and are related to measures of intrinsic nonlinearity an example is given for which the correction is substantial a similar factor is obtained for the lack of fit test in nonlinear regression

regression analysis nonlinear or nonnormal simple and accurate p values from likelihood analysis we develop simple approximations for the p values to use with regression models having linear or nonlinear parameter structure and normal or nonnormal error distribution computer iteration then gives confidence intervals both frequentist and bayesian versions are given the approximations are derived from recent developments in likelihood analysis and have third order accuracy also for very small and medium sized samples the accuracy can typically be high the likelihood basis of the procedure seems to provide the grounds for this general accuracy examples are discussed and simulations record the distributional accuracy

a relative off set orthogonality convergence criterion for nonlinear least squares an orthogonality convergence criterion using relative offset is proposed this criterion is compared to currently used criteria and its advantages are discussed