connection coefficients between boas buck polynomial sets abstract in this paper a general method to express explicitly connection coefficients between two boas buck polynomial sets is presented as application we consider some generalized hypergeometric polynomials from which we derive some well known results including duplication and inversion formulas

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

on askey scheme and d orthogonality i a characterization theorem this is the first in a series of papers dealing with generalized hypergeometric d orthogonal polynomials extending the polynomial families in the askey scheme in this paper we give a characterization theorem to introduce new examples of generalized hypergeometricd orthogonal polynomials to be studied in the forthcoming works for d 1 we obtain an unification of some known characterization theorems in the orthogonal polynomials theory

building 3 d statistical shape models by direct optimization statistical shape models are powerful tools for image interpretation and shape analysis a simple yet effective way of building such models is to capture the statistics of sampled point coordinates over a training set of example shapes however a major drawback of this approach is the need to establish a correspondence across the training set in 2 d a correspondence is often defined using a set of manually placed landmarks and linear interpolation to sample the shape in between such annotation is however time consuming and subjective particularly when extended to 3 d in this paper we show that it is possible to establish a dense correspondence across the whole training set automatically by treating correspondence as an optimization problem the objective function we use for the optimization is based on the minimum description length principle which we argue is a criterion that leads to models with good compactness specificity and generalization ability we manipulate correspondence by reparameterizing each training shape we describe an explicit representation of reparameterization for surfaces in 3 d that makes it impossible to generate an illegal i e not one to one correspondence we also describe several large scale optimization strategies for model building and perform a detailed analysis of each approach finally we derive quantitative measures of model quality allowing meaningful comparison between models built using different methods results are given for several different training sets of 3 d shapes which show that the minimum description length models perform significantly better than other approaches

a riemannian framework for tensor computing tensors are nowadays a common source of geometric information in this paper we propose to endow the tensor space with an affine invariant riemannian metric we demonstrate that it leads to strong theoretical properties the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries null eigenvalues are at the infinity the geodesic between two tensors and the mean of a set of tensors are uniquely defined etc we have previously shown that the riemannian metric provides a powerful framework for generalizing statistics to manifolds in this paper we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation filtering diffusion and restoration of missing data for instance most interpolation and gaussian filtering schemes can be tackled efficiently through a weighted mean computation linear and anisotropic diffusion schemes can be adapted to our riemannian framework through partial differential evolution equations provided that the metric of the tensor space is taken into account for that purpose we provide intrinsic numerical schemes to compute the gradient and laplace beltrami operators finally to enforce the fidelity to the data either sparsely distributed tensors or complete tensors fields we propose least squares criteria based on our invariant riemannian distance which are particularly simple and efficient to solve

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

d orthogonality of little q laguerre type polynomials abstract in this paper we solve a characterization problem in the context of the d orthogonality that allows us on one hand to provide a q analog for the d orthogonal polynomials of laguerre type introduced by the first author and douak and on the other hand to derive new l q classical d orthogonal polynomials generalizing the little q laguerre polynomials various properties of the resulting basic hypergeometric polynomials are singled out for d 1 we obtain a characterization theorem involving as far as we know new l q classical orthogonal polynomials for which we give the recurrence relation and the difference equation

linear regression analysis based on buckley james estimating equation in this note we consider the problem of drawing inference about the regression parameters in a linear model with survival data a simple procedure based on the buckley james 1979 biometrika 66 429 436 estimating equation is proposed and illustrated with an example

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

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

on d symmetric classical d orthogonal polynomials abstract the d symmetric classical d orthogonal polynomials are an extension of the standard symmetric classical polynomials according to the hahn property in this work we give some characteristic properties for these polynomials related to generating functions and recurrence differential equations as applications we characterize the d symmetric classical d orthogonal polynomials of boas buck type we construct a d 1 order linear differential equation with polynomial coefficients satisfied by each polynomial of a d symmetric classical d orthogonal set and we show that the d symmetric classical d orthogonal property is preserved by the derivative operator some of the obtained properties appear to be new even for the case d 1

d orthogonality of hermite type polynomials abstract in this paper we state a characterization theorem for d orthogonal polynomials of hermite type as application we solve two characterization problems related to gould hopper polynomials and charlier type polynomials various properties of the resulting generalized hypergeometric polynomials are singled out in particularly we derive the d dimensional functional vectors ensuring the d orthogonality of these polynomials the obtained weight functions are reduced to the well known weight functions of charlier and hermite polynomials for d 1 we also explicitly express the d dimensional functional vector associated with polynomials of laguerre type which are related to the obtained hermite type polynomials

predicting survival probabilities with semiparametric transformation models abstract prediction of survival probabilities for future patients is one of the main goals of fitting survival data with regression models in this article we consider a large class of semiparametric transformation models which includes the well known proportional hazards and proportional odds models for the analysis of failure time data specifically we propose pointwise and simultaneous confidence interval procedures for the survival probability of future patients with specific covariates these procedures can be easily implemented through simulation and are illustrated with the data from two well known clinical studies

multiple orthogonal polynomials for classical weights a new set of special functions which has a wide range of applications from number theory to integrability of nonlinear dynamical systems is described we study multiple orthogonal polynomials with respect to p 1 weights satisfying pearson s equation in particular we give a classification of multiple orthogonal polynomials with respect to classical weights which is based on properties of the corresponding rodrigues operators we show that the multiple orthogonal polynomials in our classification satisfy a linear differential equation of order p 1 we also obtain explicit formulas and recurrence relations for these polynomials

estimating subject specific survival functions under the accelerated failure time model summary we use the semiparametric accelerated failure time model to predict the survival function and its related quantities for future subjects with a given set of covariates we derive the large sample distribution for the subject specific cumulative hazard function estimate we then propose a simple resampling technique for constructing pointwise confidence intervals and simultaneous bands for the corresponding survival function and its quantile function over a properly selected time interval the new proposals are illustrated with the mayo primary biliary cirrhosis data

infarct localization from myocardial deformation prediction and uncertainty quantification by regression from a low dimensional space diagnosing and localizing myocardial infarct is crucial for early patient management and therapy planning we propose a new method for predicting the location of myocardial infarct from local wall deformation which has value for risk stratification from routine examinations such as 3d echocardiography the pipeline combines non linear dimensionality reduction of deformation patterns and two multi scale kernel regressions confidence in the diagnosis is assessed by a map of local uncertainties which integrates plausible infarct locations generated from the space of reduced dimensionality these concepts were tested on 500 synthetic cases generated from a realistic cardiac electromechanical model and 108 pairs of 3d echocardiographic sequences and delayed enhancement magnetic resonance images from real cases infarct prediction is made at a spatial resolution around 4 mm more than 10 times smaller than the current diagnosis made regionally our method is accurate and significantly outperforms the clinically used thresholding of the deformation patterns on real data sensitivity specificity of 0 828 0 804 area under the curve 0 909 versus 0 742 for the most predictive strain component uncertainty adds value to refine the diagnosis and eventually re examine suspicious cases

a note on the uncertainty of a survival probability estimated from cox s regression model a partir d un modele de cox pour des donnees de survie censurees il est possible d estimer la probabilite de survie a l annee t pour un individu de covariables z 0

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

d orthogonality of humbert and jacobi type polynomials in this paper we treat three questions related to the d orthogonality of the humbert polynomials the first one consists to determinate the explicit expression of the d dimensional functional vector for which the d orthogonality holds the second one is the investigation of the components of humbert polynomial sequence that allows us to introduce as far as we know new d orthogonal polynomials generalizing the classical jacobi ones the third one consists to solve a characterization problem related to a generalized hypergeometric representation of the humbert polynomials

prediction of survival probability based on a linear regression model summary after fitting survival data with a linear regression model it is important to know how to use the results to make prediction of the t year survival probability or median failure time for future patients with certain covariates we propose some simple prediction procedures without using complicated and unstable nonparametric functional estimates the new methods are illustrated with the stanford heart transplant data

vector orthogonal relations vector qd algorithm vector pade approximants to a function f f 1 f d from to d have been defined uniquely without any auxiliary choice than the degrees of the numerator and the denominator the same for all the components f i as in the scalar case 1 5 the denominators are associated to polynomials p r s which are given by vector orthogonal properties r and which satisfy for each s recurrence relations of order d 1 i e with d 2 terms called relations d we study here consequences of r and d first we prove an algorithm similar to the generalized mna al gorithm then we define a vector qd algorithm which links two diagonals p r s r and p r s 1 r conversely if a family p r s r 0 verifying d is given it is possible to build p r s r 0 s 0 and d linear functionals c a a 1 d such that p r 0 p r and p r s verify the orthogonal relations r with respect to the c a

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

d orthogonality via generating functions in this paper starting from a suitable generating function of a polynomial set we show how to decide whether the considered polynomial set is d orthogonal and if it is so how to determine the corresponding d dimensional functional vector then we apply the obtained results to some known and new d orthogonal polynomial sets for the known ones we give new proofs for some already obtained results

some discrete d orthogonal polynomial sets in this paper we characterize all polynomial sets which are at the same time d orthogonal and appell the resulting polynomials reduce to charlier polynomials for d 1 1 various properties of the obtained polynomials are singled out generating function recurrence relation of order d 1 and a difference equation of order d 1 we also explicitly express the d dimensional functional for which the d orthogonality holds