局部环上一类矩阵广义逆的偏序

设R是局部环,A=P^-1（I^（r）＋D）P∈Mn（R）,其中D=diag{d1,…,dn-r}或D=0,d1,…,dn-r∈M,.研究R上集合意义下广义逆的矩阵偏序A≤^[3]和A≤^[2,3],确定了具有偏序A≤^[3]和A≤^[2,3]的矩阵集Mn（B┇A≤^[3]B）和Mn（B┇A≤^[2,3]B）都不是单点集。     

Defective models induced by gamma frailty term for survival data with cured fraction

In this paper, we propose a defective model induced by a frailty term for modeling the proportion of cured. Unlike most of the cure rate models, defective models have advantage of modeling the cure rate without adding any extra parameter in model. The introduction of an unobserved heterogeneity among individuals has bring advantages for the estimated model. The influence of unobserved covariates is incorporated using a proportional hazard model. The frailty term assumed to follow a gamma distribution is introduced on the hazard rate to control the unobservable heterogeneity of the patients. We assume that the baseline distribution follows a Gompertz and inverse Gaussian defective distributions. Thus we propose and discuss two defective distributions: the defective gamma-Gompertz and gamma-inverse Gaussian regression models. Simulation studies are performed to verify the asymptotic properties of the maximum likelihood estimator. Lastly, in order to illustrate the proposed model, we present three applications in real data sets, in which one of them we are using for the first time, related to a study about breast cancer in the A.C.Camargo Cancer Center, São Paulo, Brazil.     

Adaptive Deconvolution on the Non‐negative Real Line

In this paper, we consider the problem of adaptive density or survival function estimation in an additive model defined by Z=X+Y with X independent of Y, when both random variables are non‐negative. This model is relevant, for instance, in reliability fields where we are interested in the failure time of a certain material that cannot be isolated from the system it belongs. Our goal is to recover the distribution of X (density or survival function) through n observations of Z, assuming that the distribution of Y is known. This issue can be seen as the classical statistical problem of deconvolution that has been tackled in many cases using Fourier‐type approaches. Nonetheless, in the present case, the random variables have the particularity to be supported. Knowing that, we propose a new angle of attack by building a projection estimator with an appropriate Laguerre basis. We present upper bounds on the mean squared integrated risk of our density and survival function estimators. We then describe a non‐parametric data‐driven strategy for selecting a relevant projection space. The procedures are illustrated with simulated data and compared with the performances of a more classical deconvolution setting using a Fourier approach. Our procedure achieves faster convergence rates than Fourier methods for estimating these functions.     

Dimension reduction boosting

L₂Boosting is an effective method for constructing model. In the case of high-dimensional setting, Bühlmann and Yu (2003 Bühlmann, P., Yu, B. (2003). Boosting with the L₂-loss: regression and classification. J. Amer. Stat. Assoc. 98:324–339.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) proposed the componentwise L₂Boosting, but componentwise L₂Boosting can only fit a special limited model. In this paper, by combining a boosting and sufficient dimension reduction method, e.g., sliced inverse regression (SIR), we propose a new method for regression, called dimension reduction boosting (DRBoosting). Compared with L₂Boosting, the computation of DRBoosting is less intensive and its prediction is better, especially for high-dimensional data. Simulations confirm the advantage of the new method.     

A new reproducing kernel-based nonlinear dimension reduction method for survival data

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism is constructed based on the RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements that reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate the weight function to adjust for the censoring bias. The nonlinear sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen-decomposition problem. The asymptotic property of the estimator is established based on the perturbation theory. Finally, the performance of RDSIR is illustrated on simulated and real data. The numerical results show that RDSIR is comparable with the linear SDR method. Most importantly, RDSIR can also effectively extract nonlinearity from survival data.     

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates,with application to analysis of biomarker correlates in vaccine trials

This article presents generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly robust augmented inverse probability weighted (AIPW) complete-case approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.     

Preference for Flexibility in a Savage Framework

We study preferences over Savage acts that map states to opportunity sets and satisfy the Savage axioms. Preferences over opportunity sets may exhibit a preference for flexibility due to an implicit uncertainty about future preferences reflecting anticipated unforeseen contingencies. The main result of this paper characterizes maximization of the expected indirect utility in terms of an ‘Indirect Stochastic Dominance’ axiom that expresses a preference for ‘more opportunities in expectation.’ The key technical tool of the paper, a version of Möbius inversion, has been imported from the theory of nonadditive belief functions; it allows an alternative representation using Choquet integration, and yields a simple proof of Kreps' (1979) classic result.