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随机退出下指数平均寿命的时间序贯估计AI 解读

In the context of lifetesting, an asymptotically risk-efficient procedure for the estimation of the exponential mean lifetime is considered when the survival times of the units are subject to random censorship. The loss function is the sum of squared error due to estimation, cost of recruitment of the units, and cost of total time on test. Asymptotic properties of the sequential estimator and stopping time are described as the per unit cost of total time on test decreases to…

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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.

使用δ序列估计多元密度函数AI 解读

This paper studies some asymptotic properties of density estimates $\hat{f}$ of $f$ based on $d$-variate delta sequences. The mean-square consistency, almost sure consistency, and asymptotic normality of $\hat{f}$ have been obtained as corollaries to the $L_1$ convergence properties of these delta sequences. Estimators based on kernel functions, orthogonal series, and some histogram methods can be obtained as special cases of $\hat{f}$.

不完整数据下期望意义的新优于旧检验AI 解读

This article proposes a test for the problem of testing that a life distribution is an exponential distribution against the alternative that it is new better than used in expectation, not exponential, on the basis of randomly right censored data. The test statistic is an analog of the “total time on test” test statistic.

不完整数据下期望意义中新优于旧性质的检验AI 解读

This article proposes a test for the problem of testing that a life distribution is an exponential distribution against the alternative that it is new better than used in expectation, not exponential, on the basis of randomly right censored data. The test statistic is an analog of the “total time on test” test statistic.

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…

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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.