Quantile regression for right-censored and length-biased data

Length-biased data arise in many important fields, including epidemiological cohort studies, cancer screening trials and labor economics. Analysis of such data has attracted much attention in the literature. In this paper we propose a quantile regression approach for analyzing right-censored and length-biased data. We derive an inverse probability weighted estimating equation corresponding to the quantile regression to correct the bias due to length-bias sampling and informative censoring. This method can easily handle informative censoring induced by length-biased sampling. This is an appealing feature of our proposed method since it is generally difficult to obtain unbiased estimates of risk factors in the presence of length-bias and informative censoring. We establish the consistency and asymptotic distribution of the proposed estimator using empirical process techniques. A resampling method is adopted to estimate the variance of the estimator. We conduct simulation studies to evaluate its finite sample performance and use a real data set to illustrate the application of the proposed method.     

Unbiased estimation of finite population variance using auxiliary information

Unbiased estimates, using auxiliary information, are developed for finite population variance.     

PPS样本的轮换抽样

本文介绍了一些不等概连续抽样的方案。文中叙述了在两个不同时间的DesRaj和L .Kish的处理方法。同时给出了这一问题的新的处理方案     

空间半参数变系数部分线性回归中的分位数估计

本文研究了空间数据变系数部分线性回归中的分位数估计. 模型中的参数估计量通过未知系数函数的分段多项式逼近得到, 而未知系数函数的估计量通过将参数估计量代入模型中并通过局部线性逼近得到. 文中推导了未知参数向量估计量的渐近分布, 并建立了未知系数函数估计量在内点及边界点的渐近分布. 通过Monte Carlo 模拟研究了估计量的有限样本性质.     

A fast algorithm for balanced sampling

Summary  The cube method (Deville & Tillé 2004) is a large family of algorithms that allows selecting balanced samples with equal or unequal inclusion probabilities. In this paper, we propose a very fast implementation of the cube method. The execution time does not depend on the square of the population size anymore, but only on the population size. Balanced samples can thus be selected in very large populations of several hundreds of thousands of units.     

在分层抽样下有效利用辅助信息及含于层总体大小中的信息的经验似然方法

本文考虑用在分层随机抽样下的经验似然方法来获得有限总体参数的估计量\bd 我们指出, 经验似然方法非常自然地结合辅助信息和含于层总体大小中的信息\bd 我们的结果显示, 由经验似然方法可获得有效估计.     

Admissible estimators of the population total using trimming and Winsorization

In this article we provide admissibility and uniform admissibility results for estimators of the total of a finite population which employ trimming or Winsorization. These follow from application of recent Meeden-Ghosh techniques.     

Convergence in finite precision of successive iteration methods under high nonnormality

This paper is devoted to the analysis of the behaviour, in finite precision arithmetic, of the successive iteration method (SI)x ₀,x _k+1 =Ax _k +b,k ≥ 0 whereA is a real or complex matrix of ordern andx is a real or complex vector of sizen. In exact arithmetic, the behaviour of (SI) is completely understood; there is convergence for anyx ₀ if and only if ρ(A) < 1 where ρ(A) is the spectral radius ofA. When (SI) is run on a computer with finite precision arithmetic, then for certain matricesA, the convergence is not guaranteed in practice when ρ(A) < 1 is true in exact arithmetic. It is clear that the phenomenon should be attributed to the conjunction of two factors :i) the nonnormality ofA andii) the finite precision of the computer arithmetic. We perform a straightforward analysis of the convergence of (SI) in finite precision from which we try to understand the subtle interplay between factorsi) andii) which takes place inside the computer, when the iteration matrixA has a high nonnormality. Why should nonnormality be an issue in finite precision? Because only nonnormal matrices can display a significant amount of spectral instability. Therefore a small perturbation ΔA onA can result in a large perturbation of the spectrum. When the spectral instability ofA is high, it appears that a convergence condition such as ρ(A) < 1 may not be generic enough for finite precision computations.     

大规模数据的L1惩罚分位数回归方法研究--基于特征筛选和随机抽样方法

为解决大规模数据在进行回归分析时存在的计算内存不足和运行时间较长的问题,提出两个新的回归分析方法:先筛选后抽样的大规模数据L₁惩罚分位数回归方法(FSSLQR)和先抽样后筛选的大规模数据L₁惩罚分位数回归方法(SFSLQR),其数值模拟和实际应用结果表明:FSSLQR和SFSLQR方法不仅能够显著降低计算内存和运行时间,而且其估计预测和变量选择的结果与全量L₁惩罚分位数回归基本一致。此外,与Xu等(2018)提出的大规模数据的L1惩罚分位数回归方法(SLQR)相比,FSSLQR和SFSLQR方法在估计预测、变量选择和运行时间等方面都更具优势。     

Bootstrapping to choose an estimator after sampling on two occasions

Email: a.brint{at}sheffield.ac.uk Received on 22 August 2007. Accepted on 13 June 2008. When successive surveys are undertaken so as to keep a populationestimate up to date, combining the data from the most recentsurvey with data from earlier surveys is more efficient thanjust using the most recent survey. The standard approach tocombining the data forms separate estimates from the set ofitems observed on the earlier occasion and the set observedon the later occasion and then forms a combined estimate. Theapproach assumes that the population is very large and thatthe observed values of the variable of interest are continuous.In many situations, neither assumption is particularly appropriate.This paper compares an alternative approach with the standardapproach and finds that the alternative approach sometimes providesa better estimator. It then puts forward an improved estimatorbased on choosing between these approaches using a bootstrapprocedure.     

Nonparametric estimation under length-biased sampling and Type I censoring: A moment based approach

Observation of lifetimes by means of cross-sectional surveys typically results in left-truncated, right-censored data. In some applications, it may be assumed that the truncation variable is uniformly distributed on some time interval, leading to the so-called length-biased sampling. This information is relevant, since it allows for more efficient estimation of survival and related parameters. In this work we introduce and analyze new empirical methods in the referred scenario, when the sampled lifetimes are at risk of Type I censoring from the right. We illustrate the method with real economic data. Work supported by the Grants PGIDIT02PXIA30003PR and BFM2002-03213.     

A sampling theorem with error estimation for S-transform

S-transform (ST) is an extension of wavelet transform (WT) and short-time Fourier transform (STFT). The ST is depended on a scalable and moving Gaussian window. It overcomes the low-resolution factor of STFT and tackles with a lack of phase in WT. The ST is a useful tool for signal processing and analysis. In this paper, the multiresolution analysis (MRA) related with ST is introduced and after that a sampling theorem associated with ST is proposed which is based on multiresolution subspace. Additionally, truncation and aliasing error generated due to the sampling process, are also derived. The theoretical determinations are exhibited and validated using simulation results.     

强混合样本且含附加信息情形M估计和分位数估计的渐近性质（英文）

在强混合样本且含附加信息情形,本文采用经验似然方法提出了一类新的M估计和新的分位数估计.结果表明,本文提出的M估计和分位数估计具有相合性和渐近正态性,且其渐近方差比一般M估计和分位数估计的渐近方差小.     

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In this paper, we apply the empirical likelihood technique to propose a new class of M-estimators and quantile estimators in the presence of some auxiliary information under strong mixing samples. It is shown that the proposed M-estimators and quantile estimators are consistent and asymptotically normally distributed with smaller asymptotic variances than those of the usual M-estimators and quantile estimators.     

New trigonometric sums by sampling theorem

We use a sampling theorem associated with second-order discrete eigenvalue problems to derive some trigonometric identities extending the results of Byrne and Smith [G.J. Byrne, S.J. Smith, Some integer-valued trigonometric sums, Proc. Edinburg Math. Soc. 40 (1997) 393-401]. We derive both integral and non-integral valued trigonometric sums. We give illustrative examples involving representations of the trigonometric sums and in an integral-valued polynomial in (2n+1) of degree 2m, .     

Continuous sampling plans for Markov-dependent production processes under limited inspection capacity

A continuous sampling plan is a set of rules that provide a given Average Outgoing Quality (AOQ), ideally with the minimum of effort (as measured by the Average Fraction Inspected, or AFI). Most such plans are based on the assumption that the quality (either defective or not) of successive production units is uncorrelated. In this paper, we explore the impact of correlation in the production process on the design of a sampling plan when it is not possible to inspect long runs of production unit-by-unit. We shall generalize Dodge's continuous sampling plan on two counts, replacing Level 1 100% inspection by 100f_o% inspection, and considering the production process to be Markov dependent instead of consisting of independent Bernoulli trials. We derive formulae for the AOQ and AFI, and consider how best to choose the sampling plan parameters in the presence of nonzero correlation.     

左截断相依数据下条件分位数的双核局部线性估计

本文在左截断相依数据下,利用局部线性估计的方法,先提出了条件分布函数的双核估计;然后利用该估计导出了条件分位数的双核局部线性估计,并建立了这些估计的渐近正态性结果;最后,通过模拟显示该估计在偏移和边界点调节上要比一般的核估计更好.     

辅助信息下的逆抽样设计算法

通过将逆抽样设计视为一种特殊的二重抽样,建立了二重抽样和为回归估计的二重抽样的一般形式,得到了逆抽样设计算法下的回归估计.模拟分析的结果表明,以回归估计的形式引入较为合适的辅助信息,能够在估计精度上对逆抽样设计算法做出改进.     

Error estimation for non-uniform sampling in shift invariant space

To reconstruct a function from its sampling value is not always exact, error may arise due to a lot of reasons, therefore error estimation is useful in reconstruction. For non-uniform sampling in shift invariant space, three kinds of errors of the reconstruction formula are discussed in this article. For every kind of error, we give an estimation. We find the accuracy of the reconstruction formula mainly depends on the decay property of the generator and the sampling function.