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Cox模型中随协变量变化的中位生存时间置信带AI 解读

Let ξp (x) be the pth quantile of the distribution of the life length of an individual with covariate vector x in the Cox model. We introduce an estimator ξp (x) of ξp (x) and develop several families of confidence bands for ξ(x) as a function of x. To construct one type of band, we proceed as follows. We show that as n → ∞, where n is the number of individuals in the study, ) converges weakly to a Gaussian process W(x) with a complicated covariance structure. We then…

分位数过程弱收敛的初等方法及其在删失生存数据中的应用AI 解读

Let ξ be a continuously differentiable function with positive derivative, and let ξ n be a sequence of right-continuous increasing processes. We show that if n 1/2(ξ n − ξ) W, where W is continuous, then n 1/2(ξ−1 n − ξ−1) − W(ξ−1)/ξ′(ξ−1). This result is applied to classical processes such as the empirical distribution function, the Kaplan-Meier estimator, and some other situations. We also prove an analogous result for the bootstrapped version of n 1/2(ξ n − ξ) and show…

中位数的贝叶斯非参数估计：第二部分，估计量的渐近性质AI 解读

For data $\theta + \varepsilon_i, i = 1, \ldots, n$ where $\varepsilon_i$ are i.i.d. $\sim F$ with the median of $F$ equal to $0$ but $F$ otherwise unknown, it is desired to estimate $\theta$. In Doss (1985) priors are put on the pair $(F, \theta)$, the marginal posterior distribution of $\theta$ is computed, and the mean of the posterior is taken as the estimate of $\theta$. In the present paper a frequentist point of view is adopted. The consistency properties of the Bayes…