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检验大小、功效与错误发现率AI 解读

Modern scientific technology has provided a new class of large-scale simultaneous inference problems, with thousands of hypothesis tests to consider at the same time. Microarrays epitomize this type of technology, but similar situations arise in proteomics, spectroscopy, imaging, and social science surveys. This paper uses false discovery rate methods to carry out both size and power calculations on large-scale problems. A simple empirical Bayes approach allows the false…

反卷积密度估计中的非参数置信带AI 解读

Summary Uniform confidence bands for densities f via non-parametric kernel estimates were first constructed by Bickel and Rosenblatt. In this paper this is extended to confidence bands in the deconvolution problem g=f*ψ for an ordinary smooth error density ψ. Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distribution of the maximal deviation (L∞-distance) between a deconvolution kernel estimator f^ and f. Further…

时间序列趋势的统计推断AI 解读

Summary We consider statistical inference of trends in mean non-stationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities. The results are applied to global warming temperature data and Nile river flow data. Our confidence band of the trend of the global warming…

最优发现程序：同时显著性检验的新方法AI 解读

Summary The Neyman–Pearson lemma provides a simple procedure for optimally testing a single hypothesis when the null and alternative distributions are known. This result has played a major role in the development of significance testing strategies that are used in practice. Most of the work extending single-testing strategies to multiple tests has focused on formulating and estimating new types of significance measures, such as the false discovery rate. These methods tend to…

大规模多重比较中的零分布与非零效应比例估计AI 解读

An important issue raised by Efron in the context of large-scale multiple comparisons is that in many applications, the usual assumption that the null distribution is known is incorrect, and seemingly negligible differences in the null may result in large differences in subsequent studies. This suggests that a careful study of estimation of the null is indispensable. In this article we consider the problem of estimating a null normal distribution, and a closely related…

纵向数据变系数模型的经验似然推断AI 解读

In this article local empirical likelihood-based inference for a varying coefficient model with longitudinal data is investigated. First, we show that the naive empirical likelihood ratio is asymptotically standard chi-squared when undersmoothing is employed. The ratio is self-scale invariant and the plug-in estimate of the limiting variance is not needed. Second, to enhance the performance of the ratio, mean-corrected and residual-adjusted empirical likelihood ratios are…

相关性与大规模同时显著性检验AI 解读

Large-scale hypothesis testing problems, with hundreds or thousands of test statistics zi to consider at once, have become familiar in current practice. Applications of popular analysis methods, such as false discovery rate techniques, do not require independence of the zi's, but their accuracy can be compromised in high-correlation situations. This article presents computational and theoretical methods for assessing the size and effect of correlation in large-scale testing.…

简单线性回归置信带的最小面积置信集最优性AI 解读

The average width of a simultaneous confidence band has been used by several authors (e.g., Naiman and Piegorsch) as a criterion for the comparison of different confidence bands. In this article the area of the confidence set that corresponds to a confidence band is used as a new criterion. For simple linear regression, comparisons have been carried out under this new criterion between hyperbolic bands, two-segment bands, and three-segment bands, which include constant width…

多种生物条件下微阵列时间序列数据的隐马尔可夫模型AI 解读

Among the first microarray experiments were those measuring expression over time, and time course experiments remain common. Most methods to analyze time course data attempt to group genes sharing similar temporal profiles within a single biological condition. However, with time course data in multiple conditions, a main goal is to identify differential expression patterns over time. An intuitive approach to this problem would be to apply at each time point any of the many…

稀疏指数分布数据的错误发现率阈值估计的渐近极小极大性AI 解读

We apply FDR thresholding to a non-Gaussian vector whose coordinates Xi, i=1, …, n, are independent exponential with individual means μi. The vector μ=(μi) is thought to be sparse, with most coordinates 1 but a small fraction significantly larger than 1; roughly, most coordinates are simply ‘noise,’ but a small fraction contain ‘signal.’ We measure risk by per-coordinate mean-squared error in recovering log(μi), and study minimax estimation over parameter spaces defined by…

长预测期多变量脉冲响应函数的小样本置信区间AI 解读

Abstract Existing methods for constructing confidence bands for multivariate impulse response functions may have poor coverage at long lead times when variables are highly persistent. The goal of this paper is to propose a simple method that is not pointwise and that is robust to the presence of highly persistent processes. We use approximations based on local‐to‐unity asymptotic theory, and allow the horizon to be a fixed fraction of the sample size. We show that our method…

通过p值加权控制错误发现AI 解读

We present a method for multiple hypothesis testing that maintains control of the false discovery rate while incorporating prior information about the hypotheses. The prior information takes the form of p-value weights. If the assignment of weights is positively associated with the null hypotheses being false, the procedure improves power, except in cases where power is already near one. Even if the assignment of weights is poor, power is only reduced slightly, as long as…

控制错误发现率的自适应线性逐步上升程序AI 解读

The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and the test statistics are independent and continuous, the bound is sharp. When some of the null hypotheses are not true, the procedure is conservative by a factor which is the proportion m0/m of the true null hypotheses among the hypotheses. We provide a new two-stage procedure in…

函数型数据的自由结点样条平滑AI 解读

Summary The paper introduces free-knot regression spline estimators for the mean and the variance components of a sample of curves. The asymptotic distribution of the mean estimator is derived, and asymptotic confidence bands are constructed. A comparative simulation study shows that free-knot splines estimate salient features of the functions (such as sharp peaks) more accurately than smoothing splines. This adaptive behaviour is also illustrated by an analysis of weather…

关于 Benjamini–Hochberg 方法AI 解读

We investigate the properties of the Benjamini–Hochberg method for multiple testing and of a variant of Storey’s generalization of it, extending and complementing the asymptotic and exact results available in the literature. Results are obtained under two different sets of assumptions and include asymptotic and exact expressions and bounds for the proportion of rejections, the proportion of incorrect rejections out of all rejections and two other proportions used to quantify…

k 样本模型中与最佳者的 δ 等效性AI 解读

In recent work we introduced a general, a weak, and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures. Partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures. In this article we consider the problem of establishing equivalence with the best with respect to k treatment means, where equivalence is defined in terms…

随机删失下风险率函数的置信带AI 解读

We suggest a completely empirical approach to the construction of confidence bands for hazard functions, based on smoothing the Nelsen-Aalen estimator. In particular, we introduce a local bandwidth-choice method. Our approach uses empirical information about both the survival rate and the censoring rate, and employs undersmoothing to alleviate difficulties caused by bias. We use both Edgeworth expansion and numerical simulation, the former to develop a basic formula and the…

基于层级模型的贝叶斯配准及其蛋白质生物信息学应用AI 解读

An important problem in shape analysis is to match configurations of points in space after filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are either unlabelled or have at most a partial labelling constraining the matching, and in which some points may only appear in one of the configurations. We derive procedures for simultaneous inference about the matching and the…

密度模型中的自适应拟合优度检验AI 解读

Given an i.i.d. sample drawn from a density f, we propose to test that f equals some prescribed density f0 or that f belongs to some translation/scale family. We introduce a multiple testing procedure based on an estimation of the $\mathbb{L}_{2}$-distance between f and f0 or between f and the parametric family that we consider. For each sample size n, our test has level of significance α. In the case of simple hypotheses, we prove that our test is adaptive: it achieves the…

通过控制错误发现率适应未知稀疏性AI 解读

We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways of defining sparsity of a vector: using the fraction of nonzero terms; imposing power-law decay bounds on the ordered entries; and controlling the ℓp norm for p small. We obtain a procedure which is asymptotically minimax for ℓr loss, simultaneously throughout a range of such…

函数型主成分分析的性质AI 解读

Summary Functional data analysis is intrinsically infinite dimensional; functional principal component analysis reduces dimension to a finite level, and points to the most significant components of the data. However, although this technique is often discussed, its properties are not as well understood as they might be. We show how the properties of functional principal component analysis can be elucidated through stochastic expansions and related results. Our approach…

单步多重检验中的错误发现率与错误未发现率AI 解读

Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results, providing further insights, particularly under dependence, into the notions of FDR and FNR and related measures. First, considering fixed configurations of true and false null hypotheses, inequalities are…

一般依赖结构下多重关联检验中非真零假设数量的下界AI 解读

We propose probabilistic lower bounds for the number of false null hypotheses when testing multiple hypotheses of association simultaneously. The bounds are valid under general and unknown dependence structures between the test statistics. The power of the proposed estimator to detect the full proportion of false null hypotheses is discussed and compared to other estimators. The proposed estimator is shown to deliver a tight probabilistic lower bound for the number of false…

纵向数据的函数型线性回归分析AI 解读

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth random trajectories, and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects. In longitudinal studies, the number of repeated measurements per subject is often small and may…