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密度估计中的置信带AI 解读

Given a sample from some unknown continuous density f : ℝ→ℝ, we construct adaptive confidence bands that are honest for all densities in a “generic” subset of the union of t-Hölder balls, 0

利用扫描统计量最优且快速地检测空间聚集AI 解读

We consider the detection of multivariate spatial clusters in the Bernoulli model with N locations, where the design distribution has weakly dependent marginals. The locations are scanned with a rectangular window with sides parallel to the axes and with varying sizes and aspect ratios. Multivariate scan statistics pose a statistical problem due to the multiple testing over many scan windows, as well as a computational problem because statistics have to be evaluated on many…

广义错误率的均衡控制AI 解读

Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized family-wise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and step-down procedures that control the k-FWER in finite samples or asymptotically, depending on the situation. Moreover, the procedures are asymptotically balanced in an appropriate sense. We briefly consider control of the…

大规模多重检验中零假设密度与非零效应比例估计的最优收敛速率AI 解读

An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several important problems, including the evaluation of the minimax rate of convergence and the construction of rate-optimal estimators, remain open. In this paper, we consider optimal estimation of the null density and the proportion of nonnull…

高维重抽样的若干非渐近结果（二）：多重检验AI 解读

In the context of correlated multiple tests, we aim to nonasymptotically control the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one- and two-sided multiple testing problem for the mean values of its coordinates. We address this problem by using the confidence regions developed in the companion paper [Ann.…

分组假设的同时检验：利用外部分组信息AI 解读

In large-scale multiple testing problems, data are often collected from heterogeneous sources and hypotheses form into groups that exhibit different characteristics. Conventional approaches, including the pooled and separate analyses, fail to efficiently utilize the external grouping information. We develop a compound decision theoretic framework for testing grouped hypotheses and introduce an oracle procedure that minimizes the false nondiscovery rate subject to a…

依赖条件下多重检验的因子模型方法AI 解读

The impact of dependence between individual test statistics is currently among the most discussed topics in the multiple testing of high-dimensional data literature, especially since Benjamini and Hochberg (1995) introduced the false discovery rate (FDR). Many papers have first focused on the impact of dependence on the control of the FDR. Some more recent works have investigated approaches that account for common information shared by all the variables to stabilize the…

高维回归中的 p 值AI 解读

Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder that splits the data into two parts. The number of variables is then reduced to a manageable size using the first split, while classical variable selection techniques can be applied to the remaining…

聚类数据的半参数模型AI 解读

In the analysis of cluster data the regression coefficients are frequently assumed to be the same across all clusters. This hampers the ability to study the varying impacts of factors on each cluster. In this paper, a semiparametric model is introduced to account for varying impacts of factors over clusters by using cluster-level covariates. It achieves the parsimony of parametrization and allows the explorations of nonlinear interactions. The random effect in the…

分位数回归模型的有限样本推断AI 解读

Under minimal assumptions, finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the "conditional pivotal property" of estimating equations that quantile regression methods solve and provide valid finite sample inference for linear and nonlinear quantile models with endogenous or exogenous covariates. The confidence regions can be computed using Markov Chain Monte Carlo (MCMC) methods. We illustrate the finite…

大规模预测问题的经验贝叶斯估计AI 解读

Classical prediction methods such as Fisher's linear discriminant function were designed for small-scale problems, where the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might include n = 100 subjects measured on N = 10,000 genes, each of which is a potential predictor. This paper proposes an empirical Bayes approach to large-scale prediction, where the…

正定矩阵的内蕴回归模型及其扩散张量成像应用AI 解读

The aim of this paper is to develop an intrinsic regression model for the analysis of positive-definite matrices as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in a Euclidean space. The primary motivation and application of the proposed methodology is in medical imaging. Because the set of positive-definite matrices do not form a vector space, directly applying classical multivariate regression may be inadequate…

以错误发现率控制探索显著性AI 解读

When testing a single hypothesis, it is common knowledge that increasing the sample size after nonsignificant results and repeating the hypothesis test several times at unadjusted critical levels inflates the overall Type I error rate severely. In contrast, if a large number of hypotheses are tested controlling the False Discovery Rate, such “hunting for significance” has asymptotically no impact on the error rate. More specifically, if the sample size is increased for all…

识别警察拦截中种族偏差的双重稳健内部基准与错误发现率AI 解读

Allegations of racially biased policing are a contentious issue in many communities. Processes that flag potential problem officers have become a key component of risk management systems at major police departments. We present a statistical method to flag potential problem officers by blending three methodologies that are the focus of active research efforts: propensity score weighting, doubly robust estimation, and false discovery rates. Compared with other systems…

依赖结构下的大规模多重检验AI 解读

Summary The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two-state hidden Markov model. We propose oracle and asymptotically optimal data-driven procedures that aim to minimize the false non-discovery rate FNR subject to a constraint on the false discovery rate FDR. It is shown that the performance of a multiple-testing procedure can be…

独立性条件下具有 FDR 控制保证的自适应逐步下降程序AI 解读

In this work we study an adaptive step-down procedure for testing m hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants iq/[(m+1−i(1−q)], i=1, …, m. Motivated by its success as a model selection procedure, as well as by its asymptotic optimality, we are interested in its false discovery rate (FDR) controlling properties for a finite number of hypotheses.…

错误发现率与渐近最优拒绝曲线AI 解读

In this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate (FDR) in multiple hypotheses testing problems. We first give a heuristic motivation for this new curve and propose some procedures related to it. Then we introduce a set of possible assumptions and give a unifying short proof of FDR control for procedures based on Simes’ critical values, whereby certain types of dependency are allowed. This methodology of proof…

多重检验程序对统计量依赖的稳健性AI 解读

An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without resorting to very conservative procedures. In this paper we show that, in the context of contemporary multiple testing problems, where the number of tests is often very large, the difficulties caused by dependence are less serious than in…

离散分布下的模糊族错误率与错误发现率控制程序AI 解读

Fuzzy multiple comparisons procedures are introduced as a solution to the problem of multiple comparisons for discrete test statistics. The critical function of the randomized p-values is proposed as a measure of evidence against the null hypotheses. The classical concept of randomized tests is extended to multiple comparisons. This approach makes all theory of multiple comparisons developed for continuously distributed statistics automatically applicable to the discrete…

未知异方差与非线性依赖下线性中位数回归的有限样本无分布推断AI 解读

We construct finite-sample distribution-free tests and confidence sets for the parameters of a linear median regression, where no parametric assumption is imposed on the noise distribution. The set-up studied allows for non-normality, heteroscedasticity, non-linear serial dependence of unknown forms as well as for discrete distributions. We consider a mediangale structure--the median-based analogue of a martingale difference--and show that the signs of mediangale sequences…

高维稀疏因子建模：基因表达组学应用AI 解读

We describe studies in molecular profiling and biological pathway analysis that use sparse latent factor and regression models for microarray gene expression data. We discuss breast cancer applications and key aspects of the modeling and computational methodology. Our case studies aim to investigate and characterize heterogeneity of structure related to specific oncogenic pathways, as well as links between aggregate patterns in gene expression profiles and clinical…

早期干预效果的多重推断与性别差异：三项实验的重新评估AI 解读

The view that the returns to educational investments are highest for early childhood interventions is widely held and stems primarily from several influential randomized trials—Abecedarian, Perry, and the Early Training Project—that point to super-normal returns to early interventions. This article presents a de novo analysis of these experiments, focusing on two core issues that have received limited attention in previous analyses: treatment effect heterogeneity by gender…

非参数前沿估计量的渐近性质AI 解读

Aragon, Daouia, and Thomas-Agnan (2005, Econometric Theory 21, 358–389) introduced a new nonparametric frontier estimation. We prove the weak convergence of the empirical conditional quantile function. The distribution of the limit depends on the unknown conditional quantile density function. We provide a method to construct uniform confidence bands without estimating the conditional quantile density.

利用随机逼近算法估计错误发现率AI 解读

Testing of multiple hypotheses involves statistics that are strongly dependent in some applications, but most work on this subject is based on the assumption of independence. We propose a new method for estimating the false discovery rate of multiple hypothesis tests, in which the density of test scores is estimated parametrically by minimizing the Kullback–Leibler distance between the unknown density and its estimator using the stochastic approximation algorithm, and the…