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非规则问题中的模型选择：数量性状基因座定位应用AI 解读

Two methods of model selection are discussed for changepoint-like problems, especially those arising in genetic linkage analysis. The first is a method that selects the model with the smallest p-value, while the second is a modification of the Bayes information criterion. The methods are compared theoretically and on examples from the literature. For these examples, they are roughly comparable although the p-value-based method is somewhat more liberal in selecting a…

用广义似然比统计量序贯检测变点AI 解读

We study sequential detection of a change-point using the generalized likelihood ratio statistic. For the special case of detecting a change in a normal mean with known variance, we give approximations to the average run lengths and compare our procedure to standard CUSUM tests and combined CUSUM-Shewhart tests. Several examples indicating extensions to problems involving multiple parameters are discussed.

初始均值未知时正态均值变化的序贯检测AI 解读

Three stopping rules are proposed to detect a change in a normal mean, when the initial value of the mean is unknown but an estimate obtained from a training sample is available. Asymptotic approximations are given for the average run length when there is no change. Under certain hypotheses about the length of time before the change occurs and the magnitude of the change, we obtain asymptotic approximations for the expected delay in detection in terms of the corresponding…

自回归参数的固定精度估计AI 解读

For a first order non-explosive autoregressive process with unknown parameter $\beta \in \lbrack -1, 1 \rbrack$, it is shown that if data are collected according to a particular stopping rule, the least squares estimator of $\beta$ is asymptotically normally distributed uniformly in $\beta$. In the case of normal residuals, the stopping rule may be interpreted as sampling until the observed Fisher information reaches a preassigned level. The situation is contrasted with the…

比例风险模型的序贯分析AI 解读

For the proportional hazards model of survival analysis, an appropriate large-sample theory is developed for cases of staggered entry and sequential analysis. The principal techniques involve an approximation of the score process by a suitable martingale and a random rescaling of time based on the observed Fisher information. As a result we show that the score process of the partial likelihood and the maximum partial likelihood estimator behave asymptotically like Brownian…

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序贯卡方与 F 检验及其相关置信区间AI 解读

Sequential χ 2 and F tests are proposed for comparing more than two treatments. Extending earlier results of the author, one obtains approximations to the significance level and power of the tests, and approximate confidence intervals for the noncentrality parameter θ. For each fixed θ a confidence region is given for the angle ω which the treatment effect vector in canonical coordinates makes with a fixed direction, and hence an overall confidence region is obtained for the…

序贯检验蒙特卡洛研究中的重要性抽样AI 解读

Let $x_1, x_2,\cdots$ be independent random variables which under $P_\theta$ have probability density function of the form $P_\theta\{x_k \in dx\} = \exp(\theta x - \Psi(\theta)) dH(x)$, where $\Psi$ is normalized so that $\Psi(0) = \Psi'(0) = 0.$ Let $a \leqq 0 < b, s_n = \sum^n_1 x_k$, and $T = \inf \{n: s_n \not\in (a, b)\}.$ For $u < 0$, an unbiased Monte Carlo estimate of $P_u(s_T \geqq b)$ is the average of independent $P_\theta$-realizations of $I_{\{s_T \geqq b\}} \exp\{(u - \theta)s_T - T(\Psi(u) - \Psi(\theta))\}$…

序贯概率比检验的错误概率与平均样本数AI 解读

Summary Let x 1, x 2, ... be independent random variables which under p θ have probability density function of the form exp (θx – Ψ(θ)} relative to some measure v, where Ψ is normalized so that Ψ(0) = Ψ‘(0) = 0. Let a ≤ 0 < b, sn = ∑1 n x k, and T=inf{n:sn∉(a,b)}. Approximations are given for p θ{sT ≥; b} and E θ(T) based on asymptotic considerations arising in renewal theory. The accuracy of these approximations is discussed for normally distributed x‘s. It is shown that…

若干功效为一的检验的期望样本量AI 解读

Asymptotic approximations to the expected sample size are given for a class of tests of power one introduced in [10]. Comparisons are made with the method of mixtures of likelihood ratios, and an application is given to Breiman's gambling theory for favorable games.