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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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删失数据下风险率的直方图估计量AI 解读

A histogram type estimator of the hazard rate of lifetimes which are randomly right-censored is studied. This estimator is based on random spacings of the order statistics of uncensored observations and extends the idea of the histogram density estimation suggested by Van Ryzin (1973) to censored data. In this paper we establish pointwise large sample properties of the estimator including strong consistency, strong uniform consistency on a bounded interval, and two…

离散分布的一类平滑估计量AI 解读

This paper presents a class of smooth weight function estimators for discrete distributions. Any estimator in the class depends on choosing a parameterized set of weights. The resulting estimators are strongly consistent and asymptotically normal under mild regularity conditions. A general procedure for choosing the weight function smoothing parameter is given along with specific solutions in some cases. Mean squared error comparisons with the maximum likelihood estimator…

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随机变量线性函数的参数估计AI 解读

Summary Let W be a random variable and X be a linear function of W: X = αW + β. Given a sample of independent observations distributed as X, we wish to find maximum-likelihood estimators for the parameters α and β of the linear function. If the support of W is the whole real axis, the maximum-likelihood estimators can be found by the usual methods; in other cases restricted maximization techniques must be used. Here we restrict attention to cases in which the support is the…