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删失数据均值的 Buckley–James 型估计量AI 解读

It is shown that Buckley & James's (1979) estimator for the parameters in a linear regression model with censored data in the special case of the mean is identical to Susarla & Van Ryzin's (1980) estimator.

随机右删失数据的回归分析AI 解读

This paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown. This estimator is explicitly defined and easily computable. The paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal. A numerical example is given.

删失样本中平均生存时间估计量的大样本理论AI 解读

This paper introduces and studies the large sample properties of an estimator for the mean survival time from censored samples. Let $X_1, \cdots, X_n$ be independent identically distributed random variables with $F(x) = P\lbrack X_1 > x \rbrack.$ Let $Y_1, \cdots, Y_n$ be independent identically distributed (and independent of $X_1, \cdots, X_n$) censoring times with $G(y) = P\lbrack Y_1 > y\rbrack.$ Based on observing only $Z_i = \min(X_i, Y_i)$ and which observations are…

乘积极限估计量收敛速度的一个注记AI 解读

In this note, we give a lemma which shows that the expected squared difference between the Bayes estimator with a Dirichlet process prior and the Kaplan-Meier product limit (PL) estimator for a survival function based on censored data is $O(n^{-2})$. This lemma, together with already proven pointwise consistency properties of the Bayes estimator, is used to establish two properties of the PL estimator; namely, the mean square consistency of the PL estimator with rate $O(n^{-1})$…

基于删失样本的贝叶斯非参数生存曲线估计量的大样本理论AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. $F_0$ and let $Y_1, \cdots, Y_n$ be independent (and independent also of $X_1, \cdots, X_n$) random variables. Then assuming that $F$ is distributed according to a Dirichlet process with parameter $\alpha,$ the authors obtained the Bayes estimator $\hat{F}_\alpha$ of $F$ under the loss function $L(F, \hat{F}) = \int (F(u) - \hat{F}(u))^2 dw(u)$ when $X_1, \cdots, X_n$ are censored on the right by $Y_1, \cdots, Y_n,$ respectively, and when it…

右删失观测下分布与生存函数的经验贝叶斯估计AI 解读

This paper provides an empirical Bayes approach to the problem of nonparametric estimation of a distribution (or survival) function when the observations are censored on the right. The results use the notion of a Dirichlet process prior introduced by Ferguson. The paper presents a generalization to the case of right censored observations of the rate result of an empirical Bayes nonparametric estimator of a distribution function of Korwar and Hollander in the uncensored case.…

多重决策问题的经验贝叶斯方法AI 解读

In the empirical Bayes approach to multiple decision problems, we obtain theorems and lemmas which can be used to obtain asymptotic optimality and rate results in any multiple decision empirical Bayes problem. Applications of these results to a classification problem, a monotone multiple decision, and a selection problem are given. In addition, a special lemma unique to the monotone multiple decision problem gives improved (exact) rate results in that case.

基于不完整观测的生存曲线非参数贝叶斯估计AI 解读

This article presents a nonparametric Bayesian estimator of a survival curve based on incomplete or arbitrarily right-censored data. This estimator, a Bayes estimator under a squared-error loss function assuming a Dirichlet process prior, is shown to be a Bayesian extension of the usual product limit (Kaplan-Meier) nonparametric estimator.

卷积分布的参数估计AI 解读

Summary Parametric estimation problems are considered when one observes a random variable which is the sum of two independent non-identically distributed random variables. Some basic identifiability theorems are given which suggest the method of moments as a general method for attacking such problems, particularly when one of the summand variables is discrete. Moment estimators and their asymptotic distributions are examined for various specific examples. Some applications…