删失数据平滑非参数分位估计

文中在随机右删失意义下，对于未知分布函数的分位点，基于ＰＬ估计给出了一种平滑的非参数核分位估计，推导出了该估计的逐点和一致强弱Ｂａｈａｄｕｒ类型表示定理，并由此结果获得了平滑分位计的渐近正态性及重对数律等深刻结果。     

基于指数回归模型的极值指数估计的门限选择

在本文中,我们基于指数回归模型,在渐近最小均方误差的准则下,给出了矩估计的门限值和样本点分割的选取原理和方法。利用MC方法,对Burr(1,1,1)、Burr(1,0.5,2)、Fréchet(1)、Fréchet(2)、学生-t4、学生-t6等几种常见的极值分布进行模拟,得到了理想的结果。并运用S&P500指数和Danish火灾数据进行了实证分析。     

一类新的极值指数估计

本文提出一类新的极值指数的估计,在一阶与二阶条件下,证明所提出估计具有相合性与渐近正态性.尽管新的估计与Lp估计具有相同的渐近行为,但是新的估计构造相当简单,而且在有限样本下,同一水平进行比较,新的估计表现好于Lp估计.同时,利用Monte-Carlo模拟,在最优水平下,与矩估计和混合矩估计进行比较,新的估计具有一定的...     

删失数据平滑非参数分位估计的Bahadur表示

本文讨论了在随机右删失情况下一种平滑非参数分位估计ｘｎ（ｐ）（ｘｎ（ｐ）是的解）．在一定的条件下获得了ｘｎ（ｐ）的Ｂａｈａｄｕｒ表示，作为推论获得了ｘｎ（ｐ）的渐近正态分布和重对数律．     

截断与删失数据的极大似然估计的中偏差

本文研究了截断与删失模型,运用Taylor渐近展开方法,得到模型的极大似然估计的中偏差,比渐近正态性结果更加精细.     

左截断右删失数据下分位密度估计的重对数律

在左截断右删失数据下，我们基于乘积限估计给出了分位密度估计， 获得了分位密度估计及其导数的重对数律。     

随机删失下概率密度核估计的光滑Bootstrap逼近

本文研究随机删失概率密度估计的光ｂｏｏｔｓｔｒａｐ逼近。给出了光滑ｂｏｏｔｓｔｒａｐ逼近成立的充分条件，并证明了概率密度的光滑ｂｏｏｔｓｔｒａｐ估计方差几乎处处收敛到概率密度核估计的渐近方差。     

删失数据下回归函数的最近邻估计

设（X，Y）是一随机向量且变量Y的均值存在．假定Y被另一分布G的随机变量t删失，仅能观察到不完全数据（xi，Yi^ti,δi），i＝1，2，…n，其中Yi^ti＝min（Yi，Ti）,δi=I（Yi≤ti）。为了给出回归函数m（x）＝E（Y|X）的估计。文中使用了Stute提出的最近邻型回归估计，并给出了该估计的强相合性结果．     

右删失数据下生存函数的随机加权估计

本文利用随机加权思想提出了右删失数据下生存函数的随机加权估计,证明了所给的随机加权估计的强相合性.     

左截断右删失模型下乘积限估计的强大数律(Ⅱ)

对左截断右删失模型，在不要求分布函数连续的条件下，给出乘积限估计F_n是真分布的一致强相合估计的完整结果．作为推论，还给出右删失模型下的K－M估计和左截断模型下的乘积限估计的一致强相合性的完整结果．     

Estimation of the extreme value index and extreme quantiles under random censoring

In this paper, we consider the estimation of the extreme value index and extreme quantiles in the presence of random right censoring. The generalization of the peaks over threshold method is discussed and an adaptation of the moment estimator is proposed. The corresponding extreme quantile estimators are also introduced. We make a start with the analysis of the asymptotic properties of the moment estimator and the corresponding extreme quantile estimator. The finite sample behaviour is illustrated with a small simulation study and through practical examples from survival data analysis.      

Daniels's association measures under right censoring

This paper considers extensions of the Daniels generalized measures of association (Daniels 1944) to censored data. A number of existing tests for the detection of association in the presence of right-censoring (Gehan 1965; Efron 1967; Brown, Hollander and Korwar 1974; Weier and Basu 1980) are seen to be special cases of the Daniels coefficient under particular scoring schemes. The Daniels coefficient provides a very general framework for the construction of tests and a number of other scoring schemes, simplifying to give well known tests in the non-censored case, are considered. In this paper we focus attention on tests which are, in some sense, non-parametric with respect to both variables, i.e. the explanatory variable as well as the failure time variable, such a property, though, not necessarily implying rank invariance. Parametric tests can be seen to fit in with the same formulation although no exploration of this approach is given here. Moving away from the null hypothesis of no association, it is also possible to obtain population measures of association applicable to right censored data. These will not in general converge to their non-censored equivalents although, for a large family of cases studied, they do come very close. We illustrate these findings by some simulations.     

Iterative Estimation of the Extreme Value Index

Let {X_n, n ≥ 1} be a sequence of independent random variables with common continuous distribution function F having finite and unknown upper endpoint. A new iterative estimation procedure for the extreme value index γ is proposed and one implemented iterative estimator is investigated in detail, which is asymptotically as good as the uniform minimum varianced unbiased estimator in an ideal model. Moreover, the superiority of the iterative estimator over its non iterated counterpart in the non asymptotic case is shown in a simulation study.AMS 2000 Subject Classification: 62G32Supported by Swiss National Science foundation.     

Extreme value modeling under power normalization

In this paper the mathematical modeling of extremes under power normalization is developed. An estimate of the shape parameter within the generalized extreme value distribution under power normalization is suggested. The statistical inference about the upper tail of a distribution function by using the power normalization is studied. Two models for generalized Pareto distribution under power normalization (GPDP) are given. Estimates for the shape and scale parameters within these GPDP’s are obtained. Finally, a simulation study illustrates and corroborates theoretical results.     

The strong law for the integral of P-L estimate under left truncation and right censoring

For left truncated and right censored model, letF _n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF _n pd the integral ∫ ϕdF _n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.     

On estimation of survival function under random censoring model

We study an estimator of the survival function under the random censoring model. Bahadur-type representation of the estimator is obtained and asymptotic expression for its mean squared errors is given, which leads to the consistency and asymptotic normality of the estimator. A data-driven local bandwidth selection rule for the estimator is proposed. It is worth noting that the estimator is consistent at left boundary points, which contrasts with the cases of density and hazard rate estimation. A Monte Carlo comparison of different estimators is made and it appears that the proposed data-driven estimators have certain advantages over the common Kaplan-Meier estmator.     

Wavelet estimations for mixed densities under multiplicative censoring

Using compactly supported wavelets, Chaubey et al consider L²-risk estimation for mixed density under multiplicative censoring (Chaubey YP, Chesneau C, Doosti H. Adaptive wavelet estimation of a density from mixtures under multiplicative censoring. Statistics, 2015, 49: 638-659). In this paper, we try to discuss L^p-risk (1 ≤ p<∞) estimation for that statistical model of the linear and nonlinear wavelet estimators respectively. Our results can be seen as an extension of the work of Chaubey et al.     

New estimators of the extreme value index under random right censoring,for heavy-tailed distributions

This paper presents new approaches for the estimation of the extreme value index in the framework of randomly censored samples, based on the ideas of Kaplan-Meier integration and the synthetic data approach of Leurgans (1987). These ideas are developed here in the heavy-tailed case, and lead to modifications of the Hill estimator, for which the consistency is proved under first order conditions. Simulations exhibit good performances of the two approaches, compared to the only existing adaptation of the Hill estimator in this context     

Inference for a progressive stress model from Weibull distribution under progressive type-II censoring

Based on progressively type-II censored samples, this paper considers progressive stress accelerated life tests when the lifetime of an item under use condition follows the Weibull distribution with a scale parameter satisfying the inverse power law. It is assumed that the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Point estimation of the model parameters is obtained graphically by using Weibull probability paper plot that serves as a tool for model identification and also by using the maximum likelihood method. Interval estimation is performed by finding approximate confidence intervals (CIs) for the parameters as well as the studentized-t and percentile bootstrap CIs. Monte Carlo simulation study is carried out to investigate the precision of the estimates and compare the performance of CIs obtained. Finally, two examples are presented to illustrate our results.     

Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions

In the last decades there has been a shift from the parametric statistics of extremes for IID random variables, based on the probabilistic asymptotic results in extreme value theory, towards a semi-parametric approach, where the estimation of the right tail-weight, under a quite general framework, is of major importance. After a brief presentation of classical Gumbel’s block methodology and of later improvements in the parametric framework (multivariate and multi-dimensional extreme value models for largest observations and peaks over threshold approaches), we present a coordinated overview, over the last three decades, of the developments on the estimation of the extreme value index under a semiparametric framework. Laurens de Haan has been one of the leading scientists in the field, (co-)author of many seminal ideas, that he generously shared with dozens (literally) of colleagues and students, thus achieving one of the main goals in a scientist’s life: he gathered around him a bunch of colleagues united in the endeavour of building knowledge. The last section is a personal tribute to Laurens, who fully lives his ideal that co-operation is the heart of Science. To Laurens de Haan, a token of friendship.