monotone iterative technique for the initial value problem for differential equations with non instantaneous impulses an algorithm for constructing two monotone sequences of upper and lower solutions of the initial value problem for a scalar nonnlinear differential equation with non instantaneous impulses is given the impulses start abruptly at some points and their action continue on given finite intervals we prove that the functional sequences are convergent and their limits are minimal and maximal solutions of the considered problem an example is given to illustrate the results

modelling neuromotor ratings with floor effects associated movements ams are a classical diagnostic tool to assess differences between normal children and children with some motor dysfunction this paper presents a methodology to produce age and gender dependent reference curves for ams of normal children for various tasks of a test battery data available consist of separate ratings of duration and extent of ams which are ordinal quantities with few levels other problems are severe age and gender dependent floor effects as well as some ceiling effects leaving little information for analysis at older ages to get a better scale we combined the two ordinal ratings into one meaningful and quasi continuous quantity referred to as intensity of ams in order to solve problems due to floor effects ceiling effects and discreteness we assumed left right and interval censored values respectively we considered a censored regression problem and postulated a truncated normal distribution for the non censored values after an appropriate transformation of the data using wei and tanner s poor man s data augmentation algorithm together with the technique of linear mixed effects modelling useful reference curves could be produced in contrast to the cumulative probabilities approach for ordinal data our methodology allows the calculation of individual age and gender standardized values which puts us in a position to investigate numerous scientific questions

motivic rigidity of severi brauer varieties let d be a central division algebra over a field f we study in this note the rigidity of the motivic decompositions of the severi brauer varieties of d with respect to the ring of coefficients and to the base field we first show that if the ring of coefficient is a field these decompositions only depend on its characteristic in a second part we show that if d remains division over a field extension e f the motivic decompositions of several severi brauer varieties of d remain the same when extending the scalars to e

a variety associated to an algebra with involution abstract a variety iv a is canonically associated to a central simple algebra a with orthogonal involution of the first kind the properties of this variety are the main topic of this paper the paper is divided into two parts we first define this variety to be the subvariety of the grassmannian of the n dimensional subspaces of the n2 dimensional vector space a consisting of all the n dimensional right ideals i of a such that i i 0 the geometric properties of iv a are investigated in particular the generic property of this variety is identified further the kernel of the scalar extension map br f br k where k is the function field of iv a is also computed lastly a criterion on the embeddability of the field k into the function field of the brauer severi variety of a is given in the second part the quillen k theory of iv a is computed the k theory result then leads to an index reduction formula for the function field k

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

approximate bayesian analysis of censored survival data summary the bayesian analysis of data arising from a location scale regression model and which may include a number of right censored observations is considered the posterior distributions of the suitably normalized precision parameter and regression coefficient vector are shown to be well approximated by x2 and multivariate t distributions respectively the ideas are illustrated using some clinical survival data

the index of a brauer class on a brauer severi variety let d and e be central division algebras over k let k be the generic splitting field of e we show that the index of d k k is the minimum of the indices of d e i as i varies we use this to calculate the index of d under related central extensions and to construct division algebras with special properties

posterior computations for censored regression data abstract this article describes the computation of and sampling from the posterior density for censored regression problems with normal and generalized log gamma errors the data augmentation algorithm tanner and wong 1987 is facilitated in the normal error case because of the form of the augmented posterior in the generalized log gamma context this simplicity is absent the work of sweeting 1981 is used as a motivation to develop an importance sampling scheme to sample from an augmented posterior it is shown how the predictive distribution for a new observation may be computed and sampled from the methodology is illustrated with two examples

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

iterative techniques for the initial value problem for caputo fractional differential equations with non instantaneous impulses abstract two types of algorithms for constructing monotone successive approximations for solutions to initial value problems for a scalar nonlinear caputo fractional differential equation with non instantaneous impulses are given the impulses start abruptly at some points and their action continue on given finite intervals both algorithms are based on the application of lower and upper solutions to the problem the first one is a generalization of the monotone iterative technique and it requires an application of the mittag leffler function with one and two parameters the second one is easier from a practical point of view and is applicable when the right hand sides of the equation are monotone we prove that the functional sequences are convergent and their limits are minimal and maximal solutions of the problem an example is given to illustrate the results

applications of multiple imputation to the analysis of censored regression data the first part of the article reviews the data augmentation algorithm and presents two approximations to the data augmentation algorithm for the analysis of missing data problems the poor man s data augmentation algorithm and the asymptotic data augmentation algorithm these two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology the performances of the censored regression algorithms are examined in a simulation study it is found up to the precision of the study that the bias of both the poor man s and asymptotic data augmentation estimators as well as the buckley james estimator does not appear to differ from zero however with regard to mean squared error over a wide range of settings examined in this simulation study the two data augmentation estimators have a smaller mean squared error than does the buckley james estimator in addition associated with the two data augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters it is shown how this device can be used to estimate the standard error of either data augmentation estimate of any parameter e g the correlation coefficient associated with the model in the simulation study the estimated standard error of the asymptotic data augmentation estimate of the regression parameter is found to be congruent with the monte carlo standard deviation of the corresponding parameter estimate the algorithms are illustrated using the updated stanford heart transplant data set

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

an application of imputation to an estimation problem in grouped lifetime analysis tanner and wang in press have introduced the data augmentation algorithm for the analysis of parametric missing data problems in this article this paradigm is used to develop an algorithm for the nonparametric estimation of the hazard function from grouped and censored lifetime data this algorithm makes use of the notions of cross validation and multiple imputation to prescribe the appropriate degree of smoothing for the nonparametric hazard estimate a procedure for estimating the variance of the estimator is also proposed the nonparametric hazard estimate and corresponding variance formula are shown to perform well in a simulation study the algorithm is illustrated with a numerical example

the method of quasilinearization for the periodic boundary value problem for systems of impulsive differential equations an algorithm for constructing two monotone sequences of upper and lower solutions of the periodic boundary value problem for a system of impulsive differential equations is given it is proved that both sequences are semi quadratically convergent to the unique solution of the considered problem in the case of scalar equation quadratic convergence is proved

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

a note on the analysis of censored regression data by multiple imputation wei and tanner 1991 biometrics 47 1297 1309 considered two approximations to the data augmentation algorithm for the analysis of semiparametric linear regression models with censored response and unspecified residual distribution on the basis of a simulation study they concluded that the approximations have smaller mean squared errors than the buckley james estimator over a range of settings we show that these conclusions result from the particular choice of censoring mechanism starting value and stopping rule for the iterations and that they do not appear to hold in general even in the cases considered by wei and tanner one appears to do at least as well with the same starting values and stopping rule using the buckley james iterations

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

correlating two viral load assays with known detection limits summary a timely objective common to many hiv studies involves assessing the correlation between two different measures of viral load obtained from each of a sample of patients this correlation has scientific utility in a number of contexts including those aimed at a comparison of competing assays for quantifying virus and those aimed at determining the level of association between viral loads in two different reservoirs using the same assay a complication for the analyst seeking valid point and interval estimates of such a correlation is the fact that both variables may be subject to left censoring due to values below assay detection limits we address this problem using a bivariate normal likelihood that accounts for left censoring of two variables that may have different detection limits we provide simulation results to evaluate sampling properties of the resulting correlation estimator and compare it with ad hoc estimators in the presence of nondetects in an effort to obtain improved confidence interval properties relative to the wald approach we evaluate and compare profile likelihood based intervals we apply the methods to hiv viral load data on women and infants from a trial in bangkok thailand and we discuss an extension of the original model to accommodate interval censoring arising due to the study design

bounds for the representation of quadratic forms abstract we prove first that for fixed integers n m 1 there is a uniform bound on the number of pfister forms of degree n over any pythagorean field f necessary to represent in the witt ring of f any form of dimension m as a linear combination of such forms with non zero coefficients in f uniform means that the bound does not depend either on the form or on the field f it is given by a recursive function f of n and m similar results hold for the reduced special groups arising from preordered fields and from fields whose pythagoras number is bounded by a fixed integer we single out a large class of pythagorean fields and more generally of reduced special groups cf 4 for which f has a simply exponential bound of the form cmn 1 c a constant such a class is closed under certain possibly infinitary operations which preserve marshall s signature conjecture in the case of groups of finite stability index s we obtain an upper bound for f which is quadratic on m 2n where c depends on s

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

a mixed model procedure for analyzing ordered categorical data a mixed model procedure is developed for predicting the value of an ordered categorical response from knowledge of various predictor variables this procedure resembles the best linear unbiased procedure of henderson 1975 biometrics 31 423 447 for predicting the value of a quantitative response the approach is based on a mixed model version of the threshold model in which it is assumed that the observed category is determined by the value of an underlying unobservable continuous response that follows a mixed linear model the results are illustrated by an application to the problem of predicting the degree of difficulty that will be experienced by a dairy cow in the birth of her calf

on the dimensions of anisotropic quadratic forms in i4 let wf denote the witt ring of a field f of characteristic 2 and let i n f denote the n th power of the ideal if of even dimensional forms in wf the arason pfister hauptsatz states that if 0 i n f is anisotropic then dim 2 n pfister also showed that if i 3 f is anisotropic and dim 8 then dim 12 we extend this result to i 4 f and show that if i 4 f is anisotropic and dim 16 then dim 24 and we provide some results on anisotropic 24 dimensional forms in i 4 f

some new examples in the theory of quadratic forms we construct a 6 dimensional anisotropic quadratic form phi and a 4 dimensional quadratic form psi over some fieldf such that phi becomes isotropic over the function field f psi but every proper subform of phi is still anisotropic over f psi it is an example of non standard isotropy with respect to some standard conditions of isotropy for 6 dimensional forms over function fields of quadrics known previously besides of that we produce an 8 dimensional quadratic form phi with trivial determinant such that the index of the clifford invariant of phi is 4 but phi can not be represented as a sum of two 4 dimensional forms with trivial determinants using this we find a 14 dimensional quadratic form with trivial discriminant and clifford invariant which is not similar to a difference of two 3 fold pfister forms the proofs are based on computations of the topological filtration on the grothendieck group of certain projective homogeneous varieties to do these computations we develop several methods covering a wide class of varieties and being to our mind of independent interest

random effects in censored ordinal regression latent structure and bayesian approach this paper discusses random effects in censored ordinal regression and presents a gibbs sampling approach to fit the regression model a latent structure and its corresponding bayesian formulation are introduced to effectively deal with heterogeneous and censored ordinal observations this work is motivated by the need to analyze interval censored ordinal data from multiple studies in toxicological risk assessment application of our methodology to the data offers further support to the conclusions developed earlier using gee methods yet provides additional insight into the uncertainty levels of the risk estimates

isotropy of six dimensional quadratic forms over function fields of quadrics abstract letfbe a field of characteristic different from 2 and let be an anisotropic six dimensional quadratic form overf we study the last open cases in the problem of describing the quadratic forms such that becomes isotropic over the function fieldf

integral motives relative krull schmidt principle and maranda type theorems in the present article we investigate properties of the category of integral grothendieck chow motives over a field we discuss the krull schmidt principle for integral motives provide a complete list of generalized severi brauer varieties with indecomposable integral motive and exploit a relation between the category of motives of twisted flag varieties and integral p adic representations of finite groups

motivic decomposition of a compactification of a merkurjev suslin variety we provide a motivic decomposition of a twisted form of a smooth hyperplane section of gr 3 6 this twisted form is a norm variety corresponding to a symbol in the milnor k theory k3 3 as an application we construct a torsion element in the chow group of this variety msc2000 20g15 14f43

around 16 dimensional quadratic forms in i 3_q we determine the indexes of all orthogonal grassmannians of a generic 16 dimensional quadratic form in i 3 q this is applied to show that the 3 pfister number of the form is ge 4 other consequences are a new and characteristic free proof of a recent result by chernousov merkurjev on proper subforms in i 2 q originally available in characteristic 0 as well as a new and characteristic free proof of an old result by hoffmann tignol and izhboldin karpenko on 14 dimensional quadratic forms in i 3 q originally available in characteristic ne 2 we also suggest an extension of the method based on investigation of the topological filtration on the grothendieck ring of a maximal orthogonal grassmanian which applies to quadratic forms of dimension higher than 16

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea