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David Siegmund 对《通过下注估计有界随机变量均值》的讨论AI 解读

This contribution by Waudby-Smith and Ramdas provides a host of new insights combined with a concise, yet comprehensive, historical review of “any time valid inference”, which has blossomed in recent years after the hiatus that followed its beginnings in the mid-20th Century. Particularly, attractive is the authors’ systematic use of martingales of the form (29) to facilitate the betting interpretation and give unified derivations of a large diversity of inequalities. Given…

变点模型的分割与估计：假阳性控制和置信区域AI 解读

To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic, and give approximations for the probability of a false positive error when there are no change-points. We also study confidence regions based on the likelihood ratio statistic for the change-points and joint confidence regions for the change-points and the parameter values. Applications to…

高阶批判检验：p值与方法评析AI 解读

This paper compares the higher criticism statistic (Donoho and Jin [ Ann. Statist. 32 (2004) 962–994]), a modification of the higher criticism statistic also suggested by Donoho and Jin, and two statistics of the Berk–Jones [ Z. Wahrsch. Verw. Gebiete 47 (1979) 47–59] type. New approximations to the significance levels of the statistics are derived, and their accuracy is studied by simulations. By numerical examples it is shown that over a broad range of sample sizes the…

序贯多传感器变点检测AI 解读

We develop a mixture procedure to monitor parallel streams of data for a change-point that affects only a subset of them, without assuming a spatial structure relating the data streams to one another. Observations are assumed initially to be independent standard normal random variables. After a change-point the observations in a subset of the streams of data have nonzero mean values. The subset and the post-change means are unknown. The procedure we study uses stream…

用于连锁分析 p 值估计的重要性抽样AI 解读

Importance sampling methods are proposed for estimating the probability that the maximum of a random process exceeds a high threshold, with particular attention to assessing genome-wide significance levels in linkage analysis. The proposed algorithm is applied to computing the conditional significance level, given observed phenotypes, of scan statistics to map quantitative traits in experimental populations and in extended pedigrees of moderate size with partially…

错误发现率的强控制、保守点估计与同时保守一致性：统一方法AI 解读

Summary The false discovery rate (FDR) is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses. Benjamini and Hochberg introduced this quantity and proved that a particular step-up p-value method controls the FDR. Storey introduced a point estimate of the FDR for fixed significance regions. The former approach conservatively controls the FDR at a fixed predetermined level, and the latter…

摘要暂缺

随机场局部极大值的期望个数与管状邻域体积AI 解读

Using an expression for the expected number of local maxima of a random field, we derive an upper bound for the volume of a tube about a manifold in the unit sphere and show that under certain conditions our bound agrees with the evaluation of the tube volume in Weyl's formula. Applications to tests and confidence regions in nonlinear regression are discussed.

半线性回归中的置信区域AI 解读

For the simple semilinear regression model.y =βf(θ) +ɛ, we obtain conservative approximations to likelihood ratio confidence regions for 6 and joint regions for (θ,β) which in many cases are essentially exact. To approximate the required probability we adapt the upcrossings approach of Johnstone & Siegmund (1989). In simple examples we compare our regions with two others which have been widely discussed in the literature.

半线性回归中的置信区域AI 解读

For the simple semilinear regression model.y =βf(θ) +ɛ, we obtain conservative approximations to likelihood ratio confidence regions for 6 and joint regions for (θ,β) which in many cases are essentially exact. To approximate the required probability we adapt the upcrossings approach of Johnstone & Siegmund (1989). In simple examples we compare our regions with two others which have been widely discussed in the literature.

简单线性回归变点的似然比检验AI 解读

We consider likelihood ratio tests to detect a change-point in simple linear regression (a) when the alternative specifies that only the intercept changes and (b) when the alternative permits the intercept and the slope to change. Approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable. The approximations are compared with simulations in order to assess their accuracy. For the…

摘要暂缺

单一变点的检验AI 解读

The problem considered is that of testing a sequence of independent normal random variables with constant, known or unknown, variance for no change in mean versus alternatives with a single change-point. Various tests, such as those based on the likelihood ratio and recursive residuals, are studied. Power approximations are developed by integrating approximations for conditional boundary crossing probabilities. A comparison of several tests is made.

变点检验AI 解读

The problem considered is that of testing a sequence of independent normal random variables with constant, known or unknown, variance for no change in mean versus alternatives with a single change-point. Various tests, such as those based on the likelihood ratio and recursive residuals, are studied. Power approximations are developed by integrating approximations for conditional boundary crossing probabilities. A comparison of several tests is made.

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…

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…