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CUSUM 停止时，有何统计依据认为警报并非误报？AI 解读

In the framework of the Cusum procedure, the evolution of a false alarm has a well-understood stochastic behavior. So, if observations preceding an alarm were to exhibit a behavior that is significantly different, there would be reason to reject the hypothesis that the alarm is false. We develop a test of this difference. The method is applied to detecting a change in a Covid-19 context involving a possible increase of a mean and in a context involving a possible increase in…

相关数据流并行控制图的误报等待长度渐近独立性AI 解读

Consider a process that produces a series of independent identically distributed vectors. A change in an underlying state may become manifest in a modification of one or more of the marginal distributions. Often, the dependence structure between coordinates is unknown, impeding surveillance based on the joint distribution. A popular approach is to construct control charts for each coordinate separately and raise an alarm the first time any (or some) of the control charts…

非预见估计在序贯分析与变点检测中的应用AI 解读

Suppose a process yields independent observations whose distributions belong to a family parameterized by θ∈Θ. When the process is in control, the observations are i.i.d. with a known parameter value θ0. When the process is out of control, the parameter changes. We apply an idea of Robbins and Siegmund [Proc. Sixth Berkeley Symp. Math. Statist. Probab. 4 (1972) 37–41] to construct a class of sequential tests and detection schemes whereby the unknown post-change parameters…

简单线性回归的序贯监测AI 解读

This article considers an important aspect of the general sequential analysis problem where a process is in control up to some unknown point i = ν − 1, after which the distribution from which the observations are generated changes. An extensive sequential analytic literature assumes that the change in distribution is abrupt, for example, from N(0,1) to N(μ,1). There is also an extensive literature that deals with a gradual change in the case where the decision (whether or…

回归变化检测的一阶最优性AI 解读

Observations are generated according to a regression with normal error as a function of time,when the process is in control. The process potentially changes at some unknown point oftime and then the ensuing observations are normal with the same mean function plus an arbitrary function under suitable regularity conditions. The problem is to obtain a stopping rule that is optimal in the sense that the rule minimizes the expected delay in detecting a change subject to a…

针对随机序增大备择的稳健序贯监测方案AI 解读

We sequentially observe independent observations $X_1, X_2,\ldots$ such that initially they have distribution $G_0$; at some unknown time $\nu$ they become stochastically larger, having distribution $G_1$. Neither $G_0$ nor $G_1$ is fully specified. We wish to detect that a change has taken place as soon as possible after its occurrence, subject to a constraint on the rate of false alarms. We derive a family of nonparametric sequential procedures based on ranks, with…

分布变化检测的高效序贯非参数方案AI 解读

Suppose that a system in its standard state produces i.i.d. observations whose distribution is symmetric about zero. At an unknown time the system may leave its standard state, and the observations would subsequently be stochastically larger. Subject to a bound on the rate of false alarms, one wants to detect quickly such a departure from the standard state. We present a robust method of detection which is computationally feasible and remarkably efficient. The method is…

具有误报概率界的动态抽样正态均值变化检测AI 解读

We show that when dynamic sampling is feasible, there exist surveillance schemes for which the probability of a false alarm is bounded and which have a bounded expected delay when detecting a (true) change. In the case of detecting a change of a normal mean, we probe optimality and suggest procedures. These procedures compare favorably to those having a fixed sampling rate which have been developed for an expectation constraint on the average run length until a false alarm.

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…

Suppose one is able to observe sequentially a series of independent observations $X_1, X_2, \ldots$, such that $X_1, X_2, \ldots, X_{\nu - 1}$ are i.i.d. with known density $f_0$ and $X_\nu, X_{\nu + 1}, \ldots$ are i.i.d. with density $f_\theta$ where $\nu$ is unknown. Define $R(n, \theta) = \sum^n_{k = 1} \prod^n_{i = k} \frac{f_\theta(X_i)}{f_0(X_i)}.$ It is known that rules, which call for stopping and raising an alarm the first time $n$ that $R(n, \theta)$ or a mixture…

功效为一的混合型检验之一类错误概率渐近公式AI 解读

Let $X_1,X_2,\cdots$ be iid with density $f_y$ with respect to a sigma finite measure $\mu$ where ${f_y}_(y\in\omega$, $\omega\subseteqR$ is an exponential family. Let F be a probability measure on $\omega$ and let $\theta_0\in\omega$. Define $T(B,F)=\min \big\{n \left| \int_omega \frac{f_y(X_1) \1dots f_y(X_n)} {f_{\theta_0}(X_1)\dots f_{\theta_0 (X_1) \1dots f_{\theta_0} (X_n)} dF(y)\geq B \big\}$, $T (B,F) =\infty$ if no such n exists. Previous studies have found that if F has a positive and continuous density with respect to Lebesgue measure on $…

扩散过程及其在检测布朗运动漂移变化中的应用AI 解读

The classical cusum procedure of Page (1954) and a competitor suggested independently by Shiryayev (1963) and Roberts (1966) for detecting a change in distribution are systematically compared, when the change point v = 0 and when v is large. The specific model considered is that of detecting a change in the drift of Brownian motion, for which diffusion theory yields certain explicit results that seem impossible to compute in discrete time. The Shiryayev-Roberts process turns…

分布变化的最优检测AI 解读

Suppose one is able to observe sequentially a series of independent observations $X_1, X_2, \cdots$ such that $X_1, X_2, \cdots, X_{\nu-1}$ are iid distributed according to a known distribution $F_0$ and $X_\nu, X_{\nu+1}, \cdots$ are iid distributed according to a known distribution $F_1$. Assume that $\nu$ is unknown and the problem is to raise an alarm as soon as possible after the distribution changes from $F_0$ to $F_1$. Formally, the problem is to find a stopping rule $N$…

扩散过程及其在布朗运动漂移变化检测中的应用AI 解读

The classical cusum procedure of Page (1954) and a competitor suggested independently by Shiryayev (1963) and Roberts (1966) for detecting a change in distribution are systematically compared, when the change point v = 0 and when v is large. The specific model considered is that of detecting a change in the drift of Brownian motion, for which diffusion theory yields certain explicit results that seem impossible to compute in discrete time. The Shiryayev-Roberts process turns…

正相依诱导的随机序与渐近检验水平的单调性AI 解读

An ordering of distributions related to a concept of positive dependence is studied and stochastic monotonicity with respect to this ordering is established for a wide class of two-sample test statistics. Asymptotic conservativeness of test sizes under certain departures from independence between samples is discussed. For example, if the observations are paired and the joint density is positive semidefinite then tests such as Kolmogorov-Smirnov, $\chi^2$ and Cramer-von…