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大规模同时推断中稀疏模式的层次识别AI 解读

We study how to separate signals from noisy data accurately and determine the patterns of the selected signals. Controlling the inflation of false positive errors is important in large-scale simultaneous inference but has not been addressed in the pattern recognition literature. We develop a decision-theoretic framework and formulate the sparse pattern recognition problem as a simultaneous inference problem with multiple decision trees. Oracle and adaptive classifiers are…

差异网络检验及其在基因交互识别中的应用AI 解读

Model organisms and human studies have yielded increasing empirical evidence that interactions among genes contribute broadly to genetic variation of complex traits. In the presence of gene-gene interactions, the dimensionality of the feature space becomes extremely high relative to the sample size. This poses a significant methodological challenge in the identification of gene-gene interactions. In this paper, by using a Gaussian graphical model framework, we translate the…

High-throughput DNA sequencing allows for the genotyping of common and rare variants for genetic association studies. At the present time and for the foreseeable future, it is not economically feasible to sequence all individuals in a large cohort. A cost-effective strategy is to sequence those individuals with extreme values of a quantitative trait. We consider the design under which the sampling depends on multiple quantitative traits. Under such trait-dependent sampling,…

错误发现率回归及初级视觉皮层神经同步检测应用AI 解读

Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis. But this may be inappropriate for many of today's large-scale screening problems, where auxiliary information about each test is often available, and where a combined analysis can lead to poorly calibrated error rates within different subsets of the experiment. To address this issue, we introduce an approach called…

局部平稳模型中局部自相关的统计推断AI 解读

For non-stationary processes, the time-varying correlation structure provides useful insights into the underlying model dynamics. We study estimation and inferences for local autocorrelation process in locally stationary time series. Our constructed simultaneous confidence band can be used to address important hypothesis testing problems, such as whether the local autocorrelation process is indeed time-varying and whether the local autocorrelation is zero. In particular, our…

最小绝对偏差回归及其他 Z 估计问题的一致有效选择后推断AI 解读

We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation that is immunized against nonregular estimation of the nuisance part of the median regression function by using Neyman’s orthogonalization. We establish that the resulting instrumental median regression estimator of a target regression coefficient is asymptotically normally…

非参数测量误差回归的置信带AI 解读

Summary Errors-in-variables regression is important in many areas of science and social science, e.g. in economics where it is often a feature of hedonic models, in environmental science where air quality indices are measured with error, in biology where the vegetative mass of plants is frequently obscured by mismeasurement and in nutrition where reported fat intake is typically subject to substantial error. To date, in non-parametric contexts, the great majority of work has…

大规模空间多重检验中的错误发现控制AI 解读

Summary The paper develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both pointwise and clusterwise spatial analyses, and derive oracle procedures which optimally control the false discovery rate, false discovery exceedance and false cluster rate. A data-driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain. Our multiple-testing…

一类改进的 Hochberg–Hommel 混合型逐步递增多重检验程序AI 解读

In this paper we derive a new p-value based multiple testing procedure that improves upon the Hommel procedure by gaining power as well as having a simpler step-up structure similar to the Hochberg procedure. The key to this improvement is that the Hommel procedure can be improved by a consonant procedure. Exact critical constants of this new procedure can be numerically determined. The zeroth-order approximations to the exact critical constants, albeit slightly…

非参数贝叶斯程序中的 Bernstein–von Mises 现象AI 解读

We continue the investigation of Bernstein–von Mises theorems for nonparametric Bayes procedures from [Ann. Statist. 41 (2013) 1999–2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined, and prove Bernstein–von Mises theorems for a variety of priors in the setting of Gaussian nonparametric regression and in the i.i.d. sampling model. From these results we deduce several applications where posterior-based inference coincides…

反集中性与诚实、自适应置信带AI 解读

Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov–Bickel–Rosenblatt (SBR) condition; see, for example, Giné and Nickl [Probab. Theory Related Fields 143 (2009) 569–596]. This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process (equivalently, for the supremum of a Gaussian process with the same covariance…

大规模 t 检验中错误发现率控制的相变与正则化自助法AI 解读

Applying the Benjamini and Hochberg (B–H) method to multiple Student’s $t$ tests is a popular technique for gene selection in microarray data analysis. Given the nonnormality of the population, the true $p$-values of the hypothesis tests are typically unknown. Hence it is common to use the standard normal distribution $N(0,1)$, Student’s $t$ distribution $t_{n-1}$ or the bootstrap method to estimate the $p$-values. In this paper, we prove that when the population has the…

长记忆时间序列谱密度与谱分布的固定b渐近推断AI 解读

This paper studies taper-based estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework, and makes several theoretical contributions: (i) we treat multiple frequencies jointly, (ii) we allow for long-range dependence or anti-persistence at differing frequencies, (iii) we allow for tapers that are only piecewise smooth or discontinuous, including flat-top and truncation tapers, (iv) we study higher-order accuracy through the limit…

经验过程上确界的高斯近似AI 解读

This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove an abstract approximation theorem applicable to a wide variety of statistical problems, such as construction of uniform confidence bands for functions. Notably, the bound in the main approximation theorem is nonasymptotic and the theorem…

单指标调制的多重检验AI 解读

In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this paper, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate $p$-value, $(p_{1},p_{2})$, for each hypothesis, where $p_{1}$ is a preliminary $p$-value from prior information and $p_{2}$ is the primary $p$-val…

非参数回归函数的自适应置信带AI 解读

A new formulation for the construction of adaptive confidence bands in non-parametric function estimation problems is proposed. Confidence bands are constructed which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside the band and the measure of the set of points where the function lies outside the band are small. It is shown that the bands adapt over a maximum range of Lipschitz…

用稀疏线性规划优化随机试验总体与两个亚组的治疗效应检验AI 解读

We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such subpopulations could be defined by a biomarker or risk factor measured at baseline. The goal is to simultaneously learn which subpopulations benefit from an experimental treatment, while providing strong control of the familywise Type I error rate. We formalize this as a multiple testing problem and show it is…

可能弱识别的动态随机一般均衡模型推断AI 解读

This paper considers inference in log-linearized dynamic stochastic general equilibrium (DSGE) models with weakly (including un-) identified parameters. The framework allows for analysis using only part of the spectrum, say at the business cycle frequencies. First, we characterize weak identification from a frequency domain perspective and propose a score test for the structural parameter vector based on the frequency domain approximation to the Gaussian likelihood. The…

病例队列设计的自助法AI 解读

The case-cohort design facilitates economical investigation of risk factors in a large survival study, with covariate data collected only from the cases and a simple random subset of the full cohort. Methods that accommodate the design have been developed for various semiparametric models, but most inference procedures are based on asymptotic distribution theory. Such inference can be cumbersome to derive and implement, and does not permit confidence band construction. While…

多重检验与异质性处理效应：重新评估 PROGRESA 对入学率的影响AI 解读

SUMMARY The effect of a program or treatment may vary according to observed characteristics. In such a setting, it may not only be of interest to determine whether the program or treatment has an effect on some sub‐population defined by these observed characteristics, but also to determine for which sub‐populations, if any, there is an effect. This paper treats this problem as a multiple testing problem in which each null hypothesis in the family of null hypotheses specifies…

生物信息学数据中用于同时检验的二元模型AI 解读

We develop a novel approach for testing treatment effects in high-throughput data. Most previous works on this topic focused on testing for differences between the means, but recently it has been recognized that testing for differential variation is probably as important. We take it a step further, and introduce a bivariate model modeling strategy which accounts for both differential expression and differential variation. Our model-based approach, in which the differential…

稀疏函数数据均值的平滑同时置信带AI 解读

Functional data analysis (FDA) has become an important area of statistics research in the recent decade, yet a smooth simultaneous confidence corridor (SCC) does not exist in the literature for the mean function of sparse functional data. SCC is a powerful tool for making statistical inference on an entire unknown function, nonetheless classic “Hungarian embedding” techniques for establishing asymptotic correctness of SCC completely fail for sparse functional data. We…

We propose robust methods for inference about the effect of a treatment variable on a scalar outcome in the presence of very many regressors in a model with possibly non-Gaussian and heteroscedastic disturbances. We allow for the number of regressors to be larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small…

自回归误差分布的预言效率估计与同时置信带AI 解读

We propose kernel estimator for the distribution function of unobserved errors in autoregressive time series, based on residuals computed by estimating the autoregressive coefficients with the Yule–Walker method. Under mild assumptions, we establish oracle efficiency of the proposed estimator, that is, it is asymptotically as efficient as the kernel estimator of the distribution function based on the unobserved error sequence itself. Applying the result of Wang, Cheng and…