a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

asymptotics for the minimum covariance determinant estimator consistency is shown for the minimum covariance determinant mcd estimators of multivariate location and scale and asymptotic normality is shown for the former the proofs are made possible by showing a separating ellipsoid property for the mcd subset of observations an analogous property is shown for the mcd subset computed from the population distribution

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

linear regression with current status data abstract in survival analysis a linear model often provides an adequate approximation after a suitable transformation of the survival times and possibly of the covariates this article proposes a semiparametric regression method for estimating the regression parameter in the linear model without specifying the distribution of the random error where the response variable is subject to so called case 1 interval censoring the method uses a constructed random sieve likelihood and constraints combining the benefits of semiparametric likelihood with estimating equations the estimation procedure is implemented and the asymptotic distributions for the estimated regression parameter and for the profile likelihood ratio statistic are obtained in addition some model diagnostics aspects are described finally the small sample operating characteristics of the proposed method is examined via simulations and its usefulness is illustrated on datasets from an animal tumorigenicity study and from a hiv study

an algorithm for computing the nonparametric mle of a mixing distribution abstract a fast algorithm for calculating the nonparametric maximum likelihood estimate mle of a mixing distribution g in a mixture model is discussed the literature contains several methods for computing the nonparametric mle of g but these methods are slow in this article we develop an algorithm for maximizing the log likelihood l g over the family of all distribution functions that yields the nonparametric mle of g in some semiparametric problems a structural or fixed parameter is of interest and we are interested in computing profile likelihood sup gl g for a grid of values of the algorithm that we propose is fast enough for this purpose examples illustrate and compare the algorithms one taken from an article by laird the common mean problem and one taken from the literature on optimal experimental design it is also noted that routines from the literature on semi infinite programming may be used to compute the profile log likelihood

detecting features in spatial point processes with clutter via model based clustering abstract we consider the problem of detecting features such as minefields or seismic faults in spatial point processes when there is substantial clutter we use model based clustering based on a mixture model for the process in which features are assumed to generate points according to highly linear multivariate normal densities and the clutter arises according to a spatial poisson process nonlinear features are represented by several densities giving a piecewise linear representation hierarchical model based clustering provides a first estimate of the features and this is then refined using the em algorithm the number of features is estimated from an approximation to its posterior distribution the method gives good results for the minefield and seismic fault problems software to implement it is available on the world wide web

on quantization of simple harmonic oscillators a general framework is presented of quantizing the system of a simple harmonic oscillator various methods of quantization so far proposed are accommodated here in a unified form some remarks are also made on quantization for the case of more than one oscillator

a semiparametric proportional odds regression model for the analysis of current status data abstract an approach to covariate analysis of current status data is described the method is applicable when the logit of the conditional probability of survival given the covariates is some increasing function of time plus a linear combination of the covariates the approach is based on approximating the infinite dimensional nuisance parameter the baseline log odds of failure with a step function and carrying out a maximum likelihood procedure the resulting finite dimensional parameter estimates for the regression parameters are shown to be asymptotically normal and semiparametric efficient numerical studies with small and moderate samples are discussed

a deformation of quantum mechanics on a one dimensional lattice without uniform interval the hermitian conjugation of a q differential operator is discussed then a deformation of quantum mechanics in one dimension is presented as an application the harmonic oscillator is discussed the energy spectrum and the eigenfunctions are shown to depend on an arbitrary deformation function the deformed coherent states are also discussed it is found that the completeness relation of coherent states holds for the case of q coherent states i e the deformation of the heisenberg weyl algebra is a q analogue hopf algebra

application of copulas to improve covariance estimation for partial least squares dimension reduction techniques such as partial least squares are useful for computing summary measures and examining relationships in complex settings partial least squares requires an estimate of the covariance matrix as a first step in the analysis making this estimate critical to the results in addition the covariance matrix also forms the basis for other techniques in multivariate analysis such as principal component analysis and independent component analysis this paper has been motivated by an example from an imaging study in alzheimer s disease where there is complete separation between alzheimer s and control subjects for one of the imaging modalities this separation occurs in one block of variables and does not occur with the second block of variables resulting in inaccurate estimates of the covariance we propose the use of a copula to obtain estimates of the covariance in this setting where one set of variables comes from a mixture distribution simulation studies show that the proposed estimator is an improvement over the standard estimators of covariance the methods are illustrated from the motivating example from a study in the area of alzheimer s disease

exact mean integrated squared error an exact and easily computable expression for the mean integrated squared error mise for the kernel estimator of a general normal mixture density is given for gaussian kernels of arbitrary order this provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis the family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes a number of applications of this method giving important new insights into kernel density estimation are presented among these is the discovery that the usual asymptotic approximations to the mise can be quite inaccurate especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes 1 introduction substantial research has been devoted to kernel density estimation this is because it provides a simple yet appealing context in which to study problems and issues that arise in all types of nonparametric curve estimation this includes regression spectral density and hazard estimation and also a variety of other estimators including histograms splines and orthogonal series three important and useful tools for understanding the behavior of nonparametric curve estimators are asymptotic analysis simulation and numerical calculation of error criteria each of these methods provides many useful insights into the complicated structure present in the study of curve estimation however each has its limitations as well rhe strength of asymptotic analysis is that it frequently allows simultaneous study of many different specific examples through general results applying to entire classes of settings the weakness of asymptotics is that they only describe behavior in the limit this is still very useful in many situations because the asymptotics describe the actual situation quite well however it is less useful when the asymptotics have not yet kicked in that is in studying situations where the asymptotically dominant effect has not taken over yet perhaps the biggest drawback to asymptotics is that it is very difficult to determine in a given situation which of these possibilities is occurring

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

the profile sampler we consider frequentist inference for the parametric component separately from the nuisance parameter in semiparametric models based on sampling from the posterior of the profile likelihood we prove that this procedure gives a first order correct approximation to the maximum likelihood estimator and consistent estimation of the efficient fisher information for without computing derivatives or using complicated numerical approximations an exact bayesian interpretation is established under a certain data dependent prior the sampler is useful in particular when the nuisance parameter is not estimable at the rate where neither bootstrap validity nor general automatic variance estimation has been theoretically justified even when the nuisance parameter is consistent and the bootstrap is known to be valid the proposed markov chain monte carlo procedure can yield computational savings because maximization of the likelihood is not required the theory is verified for three examples the methods are

markov chain marginal bootstrap markov chain marginal bootstrap mcmb is a new method for constructing confidence intervals or regions for maximum likelihood estimators of certain parametric models and for a wide class of m estimators of linear regression the mcmb method distinguishes itself from the usual bootstrap methods in two important aspects it involves solving only one dimensional equations for parameters of any dimension and produces a markov chain rather than a conditionally independent sequence it is designed to alleviate computational burdens often associated with bootstrap in high dimensional problems the validity of mcmb is established through asymptotic analyses and illustrated with empirical and simulation studies for linear regression and generalized linear models

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

a resampling method based on pivotal estimating functions summary suppose that under a semiparametric model setting one is interested in drawing inferences about a finite dimensi onal parameter vector based on an estimating function generally a consistent point estimator j for 0 the true value for j can be easily obtained by finding a root of the corresponding estimating equation to estimate the variance of ft however may involve complicated and subjective nonparametric functional estimates in this paper a general and simple resampling method for inferences about js0 based on pivotal estimating functions is proposed the new procedure is illustrated with the quantile and rank regression models for both cases our proposal can be easily and efficiently implemented with existing statistical software

on the computational complexity of mcmc based estimators in large samples in this paper we examine the implications of the statistical large sample theory for the computational complexity of bayesian and quasi bayesian estimation carried out using metropolis random walks our anal ysis is motivated by the laplace bernstein von mises central limit theo rem which states that in large samples the posterior or quasi posterior approaches a normal density using this observation we establish polyno mial bounds on the computational complexity of general metropolis ran dom walks methods in large samples our analysis covers cases where the underlying log likelihood or extremum criterion function is possibly non concave discontinuous and of increasing dimension however the central limit theorem restricts the deviations from continuity and log concavity of the log likelihood or extremum criterion function in a very specific manner under minimal assumptions for the central limit theorem framework to hold we show that the metropolis algorithm is theoretically efficient even for the canonical gaussian walk which is studied in detail specifically we show that the running time of the algorithm in large samples is bounded in probability by a polynomial in the parameter dimension d and in partic ular is of stochastic order d2 in the leading cases after the burn in period we then give an application to exponential and curved exponential families of increasing dimension

penalized quasi likelihood estimation in partial linear models consider a partial linear model where the expectation of a random variable y depends on covariates x z through f theta 0 x m 0 z with theta 0 an unknown parameter and m 0 an unknown function we apply the theory of empirical processes to derive the asymptotic properties of the penalized quasi likelihood estimator

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

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

a class of simple weight modules over the twisted heisenberg virasoro algebra a class of weight modules m v a over the twisted heisenberg virasoro h are constructed which includes modules of intermediate series where v is an hr d module and a is a complex number we give the necessary and sufficient conditions under which these modules are simple and also determine all the equivalent simple modules in this class moreover we show that simple modules in this class are new finally we construct a class of new simple non weight h modules

computationally simple accelerated failure time regression for interval censored data summary an approach is presented for fitting the accelerated failure time model to interval censored data that does not involve computing the nonparametric maximum likelihood estimate of the distribution function at the residuals the approach involves estimating equations computed with the examination times from the same individual treated as if they had actually been obtained from different individuals the dependence between different measurements obtained from the same individual is then accounted for in the calculation of the standard error of the regression coefficients the approach is applicable to interval censored data in settings in which examinations continue to occur regardless of whether the failure time has occurred simulations are presented to assess the behaviour of the approach and the methodology is illustrated through an application to data from an aids clinical trial

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

a fast algorithm for the minimum covariance determinant estimator the minimum covariance determinant mcd method of rousseeuw is a highly robust estimator of multivariate location and scatter its objective is to find h observations out of n whose covariance matrix has the lowest determinant until now applications of the mcd were hampered by the computation time of existing algorithms which were limited to a few hundred objects in a few dimensions we discuss two important applications of larger size one about a production process at philips with n 677 objects and p 9 variables and a dataset from astronomy with n 137 256 objects and p 27 variables to deal with such problems we have developed a new algorithm for the mcd called fast mcd the basic ideas are an inequality involving order statistics and determinants and techniques which we call selective iteration and nested extensions for small datasets fast mcd typically finds the exact mcd whereas for larger datasets it gives more accurate results than existing algorithms and is faster by orders

on the relation between s estimators and m estimators of multivariate location and covariance we discuss the relation between s estimators and m estimators of multivariate location and covariance as in the case of the estimation of a multiple regression parameter s estimators are shown to satisfy first order conditions of m estimators we show that the influence function if x s f of s functionals exists and is the same as that of corresponding m functionals also we show that s estimators have a limiting normal distribution which is similar to the limiting normal distribution which is similar to the limiting normal distribution of m estimators finally we compare asymptotic variances and breakdown point of both types of estimators

asymptotic normality of semiparametric and nonparametric posterior distributions in this article it is shown that the marginal semiparametric and nonparametric posterior distributions for a parameter of interest behave like an ordinary parametric posterior distribution this in practice provides support of the utility of marginal semiparametric and nonparametric posterior distributions in particular the marginal semiparametric and nonparametric posterior distributions are asymptotically normal and centered at the corresponding maximum likelihood estimates mles or posterior means with covariance matrix the inverse of the fisher information additionally the semiparametric and nonparametric mles for the parameter of interest and the marginal posterior means are asymptotically normal and centered at the true parameter with the same covariance matrix the results are a semiparametric version and a nonparametric version of the parametric bayesian central limit theorem that establish a connection between the semiparametric and the nonparametric bayesian inference and their frequentis

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

efficient estimation in additive hazards regression with current status data summary current status data arise when the exact timing of an event is unobserved and it is only known at a given point in time whether or not the event has occurred recently lin et al 1998 studied the additive semiparametric hazards model for current status data they showed that the analysis of current status data under the additive hazards model reduces to ordinary cox regression under the assumption that a proportional hazards model may be used to describe the monitoring intensity this analysis does not make efficient use of data and in some cases it may not be appropriate to assume a proportional hazards model for the monitoring times we study the semiparametric hazards model for current status data but make use of the semiparametric efficient score function the suggested approach has the advantages that it is efficient in that it reaches the semiparametric information bound and it does not involve any modelling of the monitoring times

quasi bayesian analysis of nonparametric instrumental variables models this paper aims at developing a quasi bayesian analysis of the nonparametric instrumental variables model with a focus on the asymptotic properties of quasi posterior distributions in this paper instead of assuming a distributional assumption on the data generating process we consider a quasi likelihood induced from the conditional moment restriction and put priors on the function valued parameter we call the resulting posterior quasi posterior which corresponds to gibbs posterior in the literature here we focus on priors constructed on slowly growing finite dimensional sieves we derive rates of contraction and a nonparametric bernstein von mises type result for the quasi posterior distribution and rates of convergence for the quasi bayes estimator defined by the posterior expectation we show that with priors suitably chosen the quasi posterior distribution the quasi bayes estimator attains the minimax optimal rate of contraction convergence resp these results greatly sharpen the previous related work

finite sample breakdown points of projection based multivariate location and scatter statistics finite sample breakdown points are obtained for two classes of projection based multivariate location and scatter statistics the stahel donoho statistics and the maronna yohai statistics the definition of these multivariate statistics are dependent on the value of location and scale statistics for all univariate projections of the data and consequently their properties depend on the nature of the corresponding univariate location and scale statistics used on the projected data the finite sample breakdown points of the multivariate statistics though are not directly related to those of the corresponding univariate location and scale statistics a uniform finite sample breakdown point concept is needed the median and the median absolute deviation about the median m a d are one possible choice for the univariate location and scale statistics respectively for sparse data sets in high dimensions though it is not recommended that the m a d be used as the univariate scale statistic for the projected data since its uniform finite sample breakdown point is shown to be much less than optimum a simple modification to the m a d however is shown to alleviate this problem for various reasons one may wish to consider univariate location and scale statistics other than the median and the m a d respectively a very broad and natural class of univariate location and scale statistics to consider for the projected data is the simultaneous m estimates of location and scale new results on their breakdown properties are given in this paper implicit formulas for the breakdown points of monotonic simultaneous m estimates of location and scale are known and they tend to imply rather low breakdown points for smooth choices of the defining weight functions it is shown here that this phenomenon does not occur for a large class of nonmonotonic simultaneous m estimates of location and scale furthermore explicit rather than implicit expressions for the uniform finite sample breakdown points are given for these nonmonotonic m estimates

smallest nonparametric tolerance regions we present a new natural way to construct nonparametric multivariate tolerance regions unlike the classical nonparametric tolerance intervals where the endpoints are determined by beforehand chosen order statistics we take the shortest interval that contains a certain number of observations we extend this idea to higher dimensions by replacing the class of intervals by a general class of indexing sets which specializes to the classes of ellipsoids hyperrectangles or convex sets the asymptotic behavior of our tolerance regions is derived using empirical process theory in particular the concept of generalized quantiles finite sample properties of our tolerance regions are investigated through a simulation study real data examples are also presented

harish chandra modules over the twisted heisenberg virasoro algebra in this paper we classify all indecomposable harish chandra modules of the intermediate series over the twisted heisenberg virasoro algebra meanwhile some bosonic modules are also studied

implementation of estimating function based inference procedures with markov chain monte carlo samplers under a semiparametric or nonparametric setting inferences about the unknown parameter are often made based on a nonsmooth estimating function resampling methods are quite handy for obtaining good approximations to the distribution of the consistent estimator when the estimating equation and its resampled counterparts are not difficult to solve numerically in this article we propose a simple flexible procedure that provides such approximations through the standard markov chain monte carlo sampler without solving any equations more generally the procedure may locate all possible roots of the estimating equation and provides an approximation to the distribution of each root we illustrate our proposed procedure extensively with three examples and evaluate its performance comprehensively through a simulation study

computable robust estimation of multivariate location and shape in high dimension using compound estimators abstract estimation of multivariate shape and location in a fashion that is robust with respect to outliers and is affine equivariant represents a significant challenge the use of compound estimators that use a combinatorial estimator such as rousseeuw s minimum volume ellipsoid mve or minimum covariance determinant mcd to find good starting points for high efficiency robust estimators such as s estimators has been proposed in this article we indicate why this scheme will fail in high dimension due to combinatorial explosion in the space that must be searched for the mve or mcd we propose a meta algorithm based on partitioning the data that enables compound estimators to work in high dimension we show that even when the computational effort is restricted to a linear function of the number of data points the algorithm results in an estimator with good asymptotic properties extensive computational experiments are used to confirm that significant benefits accrue in finite samples as well we also g

the behavior of the stahel donoho robust multivariate estimator abstract the stahel donoho estimators t v of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w r where w is a weight function and r is a measure of outlyingness obtained by considering all univariate projections of the data it has a high breakdown point for all dimensions and order n consistency the asymptotic bias of v for point mass contamination for suitable weight functions is compared with that of rousseeuw s minimum volume ellipsoid mve estimator a simulation shows that for a suitable w t and v exhibit high efficiency for both normal and cauchy distributions and are better than their competitors for normal data with point mass contamination the performances of the estimators for detecting outliers are compared for both a real and a synthetic data set

principal component analysis based on robust estimators of the covariance or correlation matrix influence functions and efficiencies a robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix in this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors the behaviour of several of these estimators is investigated by a simulation study it turns out that the theoretical results and simulations favour the use of s estimators since they combine a high efficiency with appealing robustness properties 2000 biometrika trust

asymptotics of reweighted estimators of multivariate location and scatter we investigate the asymptotic behavior ofa weighted sample mean and covariance where the weights are determined by the mahalanobis distances with respect to initial robust estimators we derive an explicit expansion for the weighted estimators from this expansion it can be seen that reweighting does not improve the rate ofconvergence ofthe initial estimators we also show that ifone uses smooth s estimators to determine the weights the weighted estimators are asymptotically normal finally we will compare the efficiency and local robustness of the reweighted s estimators with two other improvements of s estimators estimators and constrained m estimators

a class of single class minimax probability machines for novelty detection single class minimax probability machines mpms offer robust novelty detection with distribution free worst case bounds on the probability that a pattern will fall inside the normal region however in practice they are too cautious in labeling patterns as outlying and so have a high false negative rate fnr in this paper we propose a more aggressive version of the single class mpm that bounds the best case probability that a pattern will fall inside the normal region these two mpms can then be used together to delimit the solution space by using the hyperplane lying in the middle of this pair of mpms a better compromise between false positives fps and false negatives fns and between recall and precision can be obtained experiments on the real world data sets show encouraging results

moduli spaces of curves and representation theory we establish a canonical isomorphism between the second cohomology of the lie algebra of regular differential operators on x of degree 1 and the second singular cohomology of the moduli space hat f g 1 of quintuples c p z l wherec is a smooth genusg riemann surface p a point onc z a local parameter atp l a degreeg 1 line bundle onc and a class of local trivializations ofl atp which differ by a non zero factor the construction uses an interplay between various infinite dimensional manifolds based on the topological spaceh of germs of holomorphic functions in a neighborhood of 0 in x and related topological spaces the basic tool is a canonical map from hat f g 1 to the infinite dimensional grassmannian of subspaces ofh which is the orbit of the subspaceh of holomorphic functions on x vanishing at under the group auth as an application we give a lie algebraic proof of the mumford formula n 6n2 6n 1 1 where n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg whose fiber overc is the space of differentials of degreen onc

additive hazards regression with current status data current status data arise when the only knowledge about the failure time of interest is whether the failure occurs before or after a random monitoring time we propose to analyse such data by the semiparametric additive hazards model which specifies that the hazard function for the failure time associated with a set of possibly time dependent covariates is the sum of an arbitrary baseline hazard function and a regression function of covariates under certain conditions on the monitoring time one can make inferences about the regression parameters of the additive hazards model by using the familiar asymptotic theory and software for the proportional hazards model with right censored data an application to a carcinogenicity experiment is provided

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

noninformative priors for one parameter of many summary we consider the problem of constructing a prior that is noninformative for a single parameter in the presence of nuisance parameters our approach is to require that the resulting marginal posterior intervals have accurate frequentist coverage stein 1985 derived nonrigorously a sufficient condition for such a prior through the use of orthogonal parameters we give a general form for the class of priors satisfying stein s condition the priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters this is in contrast to jeffreys 1946 invariant prior for the overall parameter which is proportional to the square root of the determinant of the information matrix several examples are given and comparisons are made to the reference priors of bernardo 1979

a class of simple weight virasoro modules abstract for a simple module m over the positive part of the virasoro algebra actually for any simple module over some finite dimensional solvable lie algebras a r and any c a class of weight modules n m over the virasoro algebra is constructed these weight modules have infinite dimensional weight spaces if dim m 1 the necessary and sufficient conditions for n m to be simple are obtained we also determine the necessary and sufficient conditions for two such irreducible virasoro modules to be isomorphic many examples for such irreducible virasoro modules with different features are provided in particular the irreducible weight virasoro modules 1 2 1 2 are defined on the polynomial algebra c x c t t 1 for any 1 2 1 2 c with 1 or 2 nonzero by twisting the weight modules n m we also obtain nonweight simple virasoro modules n m for any nonconstant c t t 1

quantum mechanics with q deformed commutators and periodic variables a q deformed commutator for arbitrary q is derived from a variable with a periodic boundary condition such as an azimuthal angle phi 0 or phi 2 pi a hamiltonian can be written down in an hermitian form for q ealpha or q ei alpha with alpha in r and its eigenfunctions and eigenvalues are obtained algebraic structures w1 infinity and uq sl2 of this model and introductions of gauge interactions are discussed extensions to many variables and some elementary examples are presented

a semiparametric regression cure model for interval censored data motivated by medical studies in which patients could be cured of disease but the disease event time may be subject to interval censoring we present a semiparametric nonmixture cure model for the regression analysis of interval censored time to event data we develop semiparametric maximum likelihood estimation for the model using the expectation maximization method for interval censored data the maximization step for the baseline function is nonparametric and numerically challenging we develop an efficient and numerically stable algorithm via modern convex optimization techniques yielding a self consistency algorithm for the maximization step we prove the strong consistency of the maximum likelihood estimators under the hellinger distance which is an appropriate metric for the asymptotic property of the estimators for interval censored data we assess the performance of the estimators in a simulation study with small to moderate sample sizes to illustrate the method we also analyze a real dataset

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

higher order semiparametric frequentist inference with the profile sampler we consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution the first order validity of this procedure established by lee kosorok and fine 2005 is extended to second order validity in the setting where the infinite dimensional nuisance parameter achieves the parametric rate specifically we obtain higher order estimates of the maximum profile likelihood estimator and of the efficient fisher information moreover we prove that an e frequentist confidence interval for the parametric component at level alpha can be estimated by the alpha level credible set from the profile sampler with an error of order op n 1 as far as we are aware these results are the first higher order frequentist results obtained for semiparametric estimation a fully bayesian interpretation is established under a certain data dependent prior the theory is verified for three specific examples 1 introduction the focus of this paper is on higher order frequentist inference for the parametric component of a semiparametric model in addition to the d dimensional euclidean parameter semiparametric models also have an infinite dimensional parameter which is sometimes called the nuisance parameter a classic example is the cox proportional hazards model for right censored survival data 7 where interest focuses on the log hazard ratios for the regression covariate vector z the integrated baseline hazard function is the infinite dimensional nuisance parameter the involvement of an infinite dimensional nuisance parameter in semiparametric models generally complicates maximum likelihood inference for in particular estimating the limiting variance of n n 0 where 0 is the true value of usually requires estimating an infinite dimensional operator of course this is not a problem with the cox model since the profile likelihood for does not involve the nuisance parameter but for most semiparametric models this simplification of the profile likelihood does not occur and supported in part by grant ca075142

more on uq su 1 1 with q a root of unity highest weight representations of uq su 1 1 with q exp i n are investigated the structures of the irreducible highest weight modules are discussed in detail the clebsch gordan decomposition for the tensor product of two irreducible representations is discussed by using the results a representation of sl 2 r uq su 2 is also presented in terms of holomorphic sections which also have uq su 2 index furthermore zn graded supersymmetry is realized in terms of the representation an explicit realization of osp 1 2 via the highest weight representation of uq su 1 1 with q2 1 is given

a semiparametric mixture approach to case control studies with errors in covariables abstract methods are devised for estimating the parameters of a prospective logistic model in a case control study with dichotomous response d that depends on a covariate x for a portion of the sample both the gold standard x and a surrogate covariate w are available however for the greater portion of the data only the surrogate covariate w is available by using a mixture model the relationship between the true covariate and the response can be modeled appropriately for both types of data the likelihood depends on the marginal distribution of x and the measurement error density w x d the latter is modeled parametrically based on the validation sample the marginal distribution of the true covariate is modeled using a nonparametric mixture distribution in this way we can improve the efficiency and reduce the bias of the parameter estimates the results also apply when there is no validation data provided the error distribution is known or estimated from an independent data source many of the

on the accelerated failure time model for current status and interval censored data and tianxi cai this paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time model for current status and interval censored data the estimator is constructed by inverting a wald type test for testing a null proportional hazards model a numerically efficient markov chain monte carlo based resampling method is proposed for obtaining simultaneously the point estimator and a consistent estimator of its variance covariance matrix we illustrate our approach with interval censored datasets from two clinical studies extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators

new simple modules for the heisenberg virasoro algebra abstract we construct a large class of simple modules for the heisenberg virasoro algebra these modules are determined by the simple modules over the finite dimensional quotient algebras of certain natural subalgebras the known simple modules such as the highest weight modules and whittaker modules are included in particular we recover one of the main results of billig 2003 in 3 and reobtain the simplicity of the verma modules in a special case of arbarello et al 1988 in 1 we also characterize a large subclass of these modules as simple modules with locally finite actions of elements in certain positive part

statistical inference based on non smooth estimating functions summary when the estimating function for a vector of parameters is not smooth it is often rather difficult if not impossible to obtain a consistent estimator by solving the corresponding estimating equation using standard numerical techniques in this paper we propose a simple inference procedure via the importance sampling technique which provides a con sistent root of the estimating equation and also an approximation to its distribution without solving any equations or involving nonparametric function estimates the new proposal is illustrated and evaluated via two extensive examples with real and simulated datasets

smooth semiparametric regression analysis for arbitrarily censored time to event data a general framework for regression analysis of time to event data subject to arbitrary patterns of censoring is proposed the approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models such as the baseline hazard function in the proportional hazards model have densities satisfying mild smoothness conditions densities are approximated by a truncated series expansion that for fixed degree of truncation results in a parametric representation which makes likelihood based inference coupled with adaptive choice of the degree of truncation and hence flexibility of the model computationally and conceptually straightforward with data subject to any pattern of censoring the formulation allows popular models such as the proportional hazards proportional odds and accelerated failure time models to be placed in a common framework provides a principled basis for choosing among them and renders useful extensions of the models straightforward the utility and performance of the methods are demonstrated via simulations and by application to data from time to event studies

nearest neighbor clutter removal for estimating features in spatial point processes abstract we consider the problem of detecting features in spatial point processes in the presence of substantial clutter one example is the detection of minefields using reconnaissance aircraft images that identify many objects that are not mines our solution uses kth nearest neighbor distances of points in the process to classify them as clutter or otherwise the observed kth nearest neighbor distances are modeled as a mixture distribution the parameters of which are estimated by a simple em algorithm this method allows for detection of generally shaped features that need not be path connected in the minefield example this method yields high detection and low false positive rates another application to outlining seismic faults is considered with some success the method works well in high dimensions the method can also be used to produce very high breakdown point robust estimators of a covariance matrix

semiparametric bayes proportional odds models for current status data with underreporting current status data are a type of interval censored event time data in which all the individuals are either left or right censored for example our motivation is drawn from a cross sectional study which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman we propose a semiparametric bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure the proposed approach has the advantage of being straightforward to implement using a simple and efficient gibbs sampler whereas alternative semiparametric bayes event time models encounter problems for current status data the model is generalized to allow systematic underreporting in a subset of the data and the methods are applied to an epidemiologic study of uterine fibroids

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

semiparametric approach to a random effects quantile regression model we consider a random effects quantile regression analysis of clustered data and propose a semiparametric approach using empirical likelihood the random regression coefficients are assumed independent with a common mean following parametrically specified distributions the common mean corresponds to the population average effects of explanatory variables on the conditional quantile of interest whereas the random coefficients represent cluster specific deviations in the covariate effects we formulate the estimation of the random coefficients as an estimating equations problem and use empirical likelihood to incorporate the parametric likelihood of the random coefficients a likelihood like statistical criterion function is proposed that which we show is asymptotically concave in a neighborhood of the true parameter value and motivates its maximizer as a natural estimator we use markov chain monte carlo samplers in the bayesian framework and propose the resulting quasi posterior mean as an estimator

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

case control studies with errors in covariates we devise methods for estimating the parameters of a prospective logistic model with dichotomous response d and arbitrary covariates x from case control data when these covariates are measured with error we suppose that some fraction of the cases and controls provide only the error prone covariate measurements w the incomplete or reduced data whereas some of the cases and controls provide measurements on x and w the complete data we assume a measurement error density with a finite set of parameters namely fw xd w x d and nondifferential error is treated as a special case of this model fw x w x our algorithm estimates both the logistic parameters and from a pseudolikelihood because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters we also examine computationally simpler methods under t

irreducible representations of virasoro toroidal lie algebras toroidal lie algebras and their vertex operator representations were introduced in mey and a class of indecomposable modules were investigated in this work we extend the toroidal algebra by the virasoro algebra thus constructing a semi direct product algebra containing the toroidal algebra as an ideal and the virasoro algebra as a subalgebra with the use of vertex operators and certain oscillator representations of the virasoro algebra it is proved that the corresponding fock space gives rise to a class of irreducible modules for the virasoro toroidal algebra

nearest neighbor variance estimation nnve robust covariance estimation commonly proceeds by downweighting outliers in this article we measure the outlyingness of a data point by the standardized distance between the point and its kth nearest neighbor the appropriate weights for robust estimation are found by a model based mixture modeling approach that follows from considering the data cloud as a realization of a high dimensional point process to correct a potential bias when there are no outliers we introduce a boundary correction procedure that artificially adds in extra outlying points the resulting methodology is called nearest neighbor variance estimation nnve the strength of nnve is its robustness against a large proportion of noise points and against deviation from normality of the signal a consistency result for the method is established under some reasonable assumptions it is shown that the covariance estimate is bounded and that each point has only bounded influence on the final estimates nnve outperformed the popular mini

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

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

regression with interval censored data summary interval censored data result when survival times are not known exactly but are only known to have occurred between intermittent examination times here the accelerated failure time model is treated for interval censored data a class of score statistics that may be used for estimation and confidence procedures is proposed an adaptive procedure based on estimating the optimal member of the class of score statistics is explored

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial

semiparametric estimation of the accelerated failure time model with partly interval censored data summary partly interval censored pic data arise when some failure times are exactly observed while others are only known to lie within certain intervals in this article we consider efficient semiparametric estimation of the accelerated failure time aft model with pic data we first generalize the buckley james estimator for right censored data to pic data then we develop a one step estimator by deriving and estimating the efficient score for the regression parameters we show that under mild regularity conditions the generalized buckley james estimator is consistent and asymptotically normal and the one step estimator is consistent and asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound we conduct extensive simulation studies to examine the performance of the proposed estimators in finite samples and apply our methods to data derived from an aids study