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单调平均剩余寿命的估计AI 解读

In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age $x, M(x)$, defined by $$M(x) = E[X - x|X > x],$$ where $X$ is a lifetime. $M$ is called the mean residual life function.In many applications it is reasonable to assume that $M$ is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of $M$ and…

一致随机序约束下某类分布一致估计量的渐近分布理论AI 解读

We identify the asymptotic behavior of the estimators proposed by Rojo and Samaniego and Mukerjee of a distribution $F$ assumed to be uniformly stochastically smaller than a known baseline distribution $G$.We show that these estimators are $\sqrt{n}$-convergent to a limit distribution with mean squared error smaller than or equal to the mean squared error of the empirical survival function. By examining the mean squared error of the limit distribution, we are able to…

如何成为更好的贝叶斯统计学家AI 解读

Consider an experiment yielding an observable random quantity X whose distribution is indexed by a real parameter ø. Suppose that a statistician is prepared to execute a Bayes procedure in estimating ø and has quantified available prior information about ø in his chosen prior distribution G. Suppose that before this estimation process is completed, the statistician becomes aware of the outcome Y of a “similar” experiment. In this article we investigate the questions of…

走向贝叶斯与频率学派点估计的协调AI 解读

The Bayesian and frequentist approaches to point estimation are reviewed. The status of the debate regarding the use of one approach over the other is discussed, and its inconclusive character is noted. A criterion for comparing Bayesian and frequentist estimators within a given experimental framework is proposed. The competition between a Bayesian and a frequentist is viewed as a contest with the following components: a random observable, a true prior distribution unknown…

基于排序集样本的非参数最大似然估计AI 解读

A ranked set sample consists entirely of independently distributed order statistics and can occur naturally in many experimental settings, including problems in reliability. When each ranked set from which an order statistic is drawn is of the same size, and when the statistic of each fixed order is sampled the same number of times, the ranked set sample is said to be balanced. Stokes and Sager have shown that the edf F n of a balanced ranked set sample from the cdf F is an…

利用提名样本估计分布函数AI 解读

A nomination sample consists of independently distributed maxima from subsamples of a population with the same underlying distribution. Nomination sampling occurs when only the item with largest value is chosen from each of n independent subsamples. If the subsamples differ in size, then these observed order statistics are not identically distributed, so estimation schemes built on assumptions of independently and identically distributed (iid) data are most likely…

利用提名样本估计分布函数AI 解读

A nomination sample consists of independently distributed maxima from subsamples of a population with the same underlying distribution. Nomination sampling occurs when only the item with largest value is chosen from each of n independent subsamples. If the subsamples differ in size, then these observed order statistics are not identically distributed, so estimation schemes built on assumptions of independently and identically distributed (iid) data are most likely…

一致随机序约束下的生存曲线估计AI 解读

If F and G are cumulative distribution functions on [0, ∞) governing the lifetimes of specific systems under study, and if F and G are their corresponding survival functions, then F is said to be uniformly stochastically smaller than G, denoted by F <(+) G, if and only if the ratio l(x) = G (x)/ F (x) is nondecreasing for x ∈ [0, sup{t: [0, sup {(t: F (t) > 0}). When F and G are absolutely continuous, F (+) G is equivalent to the assumption that the corresponding failure…

不完全修复系统的可靠性估计AI 解读

This study of statistical inference for repairable systems focuses on the development of estimation procedures for the life distribution F of a new system based on data on system lifetimes between consecutive repairs. The Brown—Proschan imperfect-repair model postulates that at failure the system is repaired to a condition as good as new with probability p, and is otherwise repaired to the condition just prior to failure. In treating issues of statistical inference for this…

基于提名抽样的分布函数估计AI 解读

Nomination sampling is a sampling process in which every observation is the maximum of a random sample from some population. Assuming that all samples are taken from a single underlying distribution F, data may be viewed as consisting of pairs (Xi , Ki ), where Ki is the size of the ith sample and, given Ki = ki, Xi is distributed according to F ki. Willemain (1980), who discussed nomination sampling in the context of health care delivery, proposed an estimator for the…

具有正依赖的多元二元数据建模与推断AI 解读

A model is proposed for multivariate binary data that incorporates positive dependence among components in a natural way. The model is derived from reliability-theoretic concepts, but is regarded as appropriate for analysis of multivariate binary data in any field when positive dependence is an appropriate assumption. Maximum likelihood estimation by iterative solution of likelihood equations is discussed for the general model, and asymptotically efficient estimates are…

具有正相依性的多元二元数据建模与推断AI 解读

A model is proposed for multivariate binary data that incorporates positive dependence among components in a natural way. The model is derived from reliability-theoretic concepts, but is regarded as appropriate for analysis of multivariate binary data in any field when positive dependence is an appropriate assumption. Maximum likelihood estimation by iterative solution of likelihood equations is discussed for the general model, and asymptotically efficient estimates are…

离散多元冲击模型的最大似然估计AI 解读

A k-variate Bernoulli distribution with k + 1 parameters is obtained as a shock model in which shocks are fatal to single components only or to all components simultaneously in a k-component system. The maximum likelihood estimator (MLE) for model parameters is fully characterized. In the most complex case, the MLE is displayed as a simple function of the smallest positive root of a kth degree polynomial. An iterative scheme that converges monotonically to the desired root…

伪最大似然估计：理论与应用AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. random variables with probability distribution $F_{\theta, p}$ indexed by two real parameters. Let $\hat{p} = \hat{p}(X_1, \cdots, X_n)$ be an estimate of $p$ other than the maximum likelihood estimate, and let $\hat{\theta}$ be the solution of the likelihood equation $\partial/\partial \theta \ln L(\mathbf{x}, \theta, \hat{p}) = 0$ which maximizes the likelihood. We call $\hat{\theta}$ a pseudo maximum likelihood estimate of $\theta$, and…

离散噪声中二项信号的最大似然估计AI 解读

Let X be the sum of independent variables Y and Z, where Y is binomially distributed and Z is a nonnegative integer-valued variable whose distribution does not depend on the binomial parameter p. Convoluted binomial distributions describing variables like X are characterized by regularity conditions and equations of the form ∂/∂p P(X = x)=c[P(X = x − 1) − P(X = x)]. The characterization, together with a monotonicity property for probability ratios, is shown to facilitate…

离散噪声中二项分布信号的最大似然估计AI 解读

Let X be the sum of independent variables Y and Z, where Y is binomially distributed and Z is a nonnegative integer-valued variable whose distribution does not depend on the binomial parameter p. Convoluted binomial distributions describing variables like X are characterized by regularity conditions and equations of the form ∂/∂p P(X = x)=c[P(X = x − 1) − P(X = x)]. The characterization, together with a monotonicity property for probability ratios, is shown to facilitate…