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回归样条的局部渐近性质与置信区域AI 解读

In this paper, we study the local behavior of regression splines. In particular, explicit expressions for the asymptotic pointwise bias and variance of regression splines are obtained. In addition, asymptotic normality for regression splines is established, leading to the construction of approximate confidence intervals and confidence bands for the regression function.

In this paper, we analyze the statistic which is the difference in the values of an estimating function evaluated at its local maxima on two different subsets of the parameter space, assuming that the true parameter is in each subset, but possibly on the boundary. Our results extend known methods by covering a large class of estimation problems which allow sampling from nonidentically distributed random variables. Specifically, the existence and consistency of the local…

生存数据中的充分随访与异常值检验AI 解读

A situation in which a sample of failure times with many of the largest times censored may be taken as evidence of a proportion of “immune” or “cured” individuals, who are not subject to failure, in the population. A plot of the Kaplan-Meier empirical distribution function for such data will tend to level off near its right extreme, provided that follow-up of individuals has been continued for long enough. This article develops a diagnostic test for sufficient follow-up in…

An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune…

删失样本中免疫个体比例的估计AI 解读

An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune…