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空间抽样方案下的参数极大似然估计AI 解读

We study in detail asymptotic properties of maximum likelihood estimators of parameters when observations are taken from a two-dimensional Gaussian random field with a multiplicative Ornstein-Uhlenbeck covariance function. Under the complete lattice sampling plan, it is shown that the maximum likelihood estimators are strongly consistent and asymptotically normal. The asymptotic normality here is normalized by the fourth root of the sample size and is obtained through higher…

删失回归数据的序贯分析AI 解读

Motivated by Buckley and James' modification of the least squares procedure for censored regression data, we derive a score process that incorporates the time evolution and handles staggered entry data in a natural way. By censored regression data we mean that the responses are subject to a possible right censorship. Such cases often arise from clinical trials and industrial life tests. The score process can be interpreted as a weighted comparison of (transformed) survival…

删失回归数据的序贯分析AI 解读

Motivated by Buckley and James' modification of the least squares procedure for censored regression data, we derive a score process that incorporates the time evolution and handles staggered entry data in a natural way. By censored regression data we mean that the responses are subject to a possible right censorship. Such cases often arise from clinical trials and industrial life tests. The score process can be interpreted as a weighted comparison of (transformed) survival…

单变量删失下二元生存函数的简单非参数估计量AI 解读

In the presence of univariate censoring, the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at-risk probability to the survival function of the censoring time. The use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve. The estimator is strongly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process with an easily estimated…

删失回归数据秩估计的大样本研究AI 解读

Large sample approximations are developed to establish asymptotic linearity of the commonly used linear rank estimating functions, defined as stochastic integrals of counting processes over the whole line, for censored regression data. These approximations lead to asymptotic normality of the resulting rank estimators defined as solutions of the linear rank estimating equations. A second kind of approximations is also developed to show that the estimating functions can be…

单变量删失下二元生存函数的简单非参数估计AI 解读

In the presence of univariate censoring, the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at-risk probability to the survival function of the censoring time. The use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve. The estimator is strongly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process with an easily estimated…

删失数据的最小 Hellinger 型距离估计AI 解读

A Hellinger-type distance for hazard rate functions is defined. It is used to obtain a class of minimum distance estimators for data that are subject to a possible right censorship. The corresponding score process is shown to be approximated by a martingale, which is exploited to obtain the asymptotic normality under considerably weaker conditions than those normally assumed for minimum Hellinger distance estimators. It is also shown that under the parametric assumption the…

删失数据回归中修正 Buckley–James 估计量的大样本理论AI 解读

Buckley and James proposed an extension of the classical least squares estimator to the censored regression model. It has been found in some empirical and Monte Carlo studies that their approach provides satisfactory results and seems to be superior to other extensions of the least squares estimator in the literature. To develop a complete asymptotic theory for this approach, we introduce herein a slight modification of the Buckley-James estimator to get around the…

左截断与右删失数据的秩回归方法AI 解读

A class of rank estimators is introduced for regression analysis in the presence of both left-truncation and right-censoring on the response variable. By making use of martingale theory and a tightness lemma for stochastic integrals of multiparameter empirical processes, the asymptotic normality of the estimators is established under certain assumptions. Adaptive choice of the score functions to give asymptotically efficient rank estimators is also discussed.

截断与删失数据下的分布函数估计AI 解读

A minor modification of the product-limit estimator is proposed for estimating a distribution function (not necessarily continuous) when the data are subject to either truncation or censoring, or to both, by independent but not necessarily identically distributed truncation-censoring variables. Making use of martingale integral representations and empirical process theory, uniform strong consistency of the estimator is established and weak convergence results are proved for…

面向 Lp 损失函数的非线性随机逼近程序AI 解读

The classical stochastic approximation problem can be regarded as choosing design points so that the responses are close to some target level in the expected squared distance. Motivated by different loss criteria, a family of stochastic approximation algorithms is proposed. This family has the same simplicity as the classical Robbins-Monro procedure does and contains the latter as a special case. Using appropriate representations and martingale limit theorems, we establish…

截断数据的线性秩统计量AI 解读

Motivated by Prentice's (1978) generalization of linear rank statistics for censored data, we introduce a similar kernel for deriving linear rank statistics for truncated data. They take very similar forms to those of Prentice's statistics. Moreover, we also show that they can be expressed equivalently in weighted log rank-type forms, thus providing natural variance estimators. Explicit forms corresponding to Wilcoxon and log rank tests are obtained. Extensions to data…

截断数据的线性秩统计量AI 解读

Motivated by Prentice's (1978) generalization of linear rank statistics for censored data, we introduce a similar kernel for deriving linear rank statistics for truncated data. They take very similar forms to those of Prentice's statistics. Moreover, we also show that they can be expressed equivalently in weighted log rank-type forms, thus providing natural variance estimators. Explicit forms corresponding to Wilcoxon and log rank tests are obtained. Extensions to data…