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线性模型中无限多个对比的 Benjamini–Hochberg 方法AI 解读

Benjamini and Hochberg's method for controlling the false discovery rate is applied to the problem of testing infinitely many contrasts in linear models. Exact, easily calculated critical values are derived, defining a new multiple comparisons method for testing contrasts in linear models. The method is adaptive, depending on the data through the F-statistic, like the Waller–Duncan Bayesian multiple comparisons method. Comparisons with Scheffé's method are given, and the…

大模型空间下用于模型选择的扩展贝叶斯信息准则AI 解读

The ordinary Bayesian information criterion is too liberal for model selection when the model space is large. In this paper, we re-examine the Bayesian paradigm for model selection and propose an extended family of Bayesian information criteria, which take into account both the number of unknown parameters and the complexity of the model space. Their consistency is established, in particular allowing the number of covariates to increase to infinity with the sample size.…

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear auto-regressive processes. The results are applied to the S&P 500 Index data.

密度的多尺度推断AI 解读

We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The procedure provides guaranteed finite-sample significance levels, is easy to implement and possesses certain asymptotic optimality and adaptivity properties.

非零正态均值的比例：通用预言等价与一致一致估计AI 解读

Summary Since James and Stein's seminal work, the problem of estimating n normal means has received plenty of enthusiasm in the statistics community. Recently, driven by the fast expansion of the field of large-scale multiple testing, there has been a resurgence of research interest in the n normal means problem. The new interest, however, is more or less concentrated on testing n normal means: to determine simultaneously which means are 0 and which are not. In this setting,…

纵向与聚类数据中ROC曲线非参数比较的统一方法AI 解读

We present a unified approach to nonparametric comparisons of receiver operating characteristic (ROC) curves for a paired design with clustered data. Treating empirical ROC curves as stochastic processes, their asymptotic joint distribution is derived in the presence of both between-marker and within-subject correlations. A Monte Carlo method is developed to approximate their joint distribution without involving nonparametric density estimation. The developed theory is…

偏微分方程估计及其金融应用AI 解读

Linear parabolic partial differential equations (PDE's) and diffusion models are closely linked through the celebrated Feynman-Kac representation of solutions to PDE's. In asset pricing theory, this leads to the representation of derivative prices as solutions to PDE's. Very often implied derivative prices are calculated given preliminary estimates of the diffusion model for the underlying variable. We demonstrate that the implied derivative prices are consistent and derive…

自适应置信带AI 解读

We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f⋆ which is close to, but simpler than, f. The surrogate captures the significant features in f. We establish lower bounds on the width for any confidence band for f⋆ and construct a procedure that comes within a small constant factor of attaining the lower bound for…

与最优总体的边际比较及效率测度问题AI 解读

Consider a set of N populations ranked by an unknown scalar parameter, where a larger parameter value is better. An existing procedure, multiple comparisons with the best, constructs a set of upper and lower bounds for the N – 1 differences between the parameter value of the best population and the other populations, where these bounds hold jointly with a given probability. This article constructs the corresponding upper and lower bounds that hold marginally (for a single…

利用空间经验似然进行变差函数模型的点估计与区间估计AI 解读

We present a spatial blockwise empirical likelihood method for estimating variogram model parameters in the analysis of spatial data on a grid. The method produces point estimators that require no spatial variance estimates to compute, unlike least squares methods for variogram fitting, but are as efficient as the best least squares estimator in large samples. Our approach also produces confidence regions for the variogram, without requiring knowledge of the full joint…

控制错误发现率的层级检验方法AI 解读

We discuss methodology for controlling the false discovery rate (FDR) in complex large-scale studies that involve testing multiple families of hypotheses; the tested hypotheses are arranged in a tree of disjoint subfamilies, and the subfamilies of hypotheses are hierarchically tested by the Benjamini and Hochberg FDR-controlling (BH) procedure. We derive an approximation for the multiple family FDR for independently distributed test statistics: q, the level at which the BH…

一族贝叶斯多重检验程序AI 解读

Under the model of independent test statistics, we propose a two-parameter family of Bayes multiple testing procedures. The two parameters can be viewed as tuning parameters. Using the Benjamini–Hochberg step-up procedure for controlling false discovery rate as a baseline for conservativeness, we choose the tuning parameters to compromise between the operating characteristics of that procedure and a less conservative procedure that focuses on alternatives that a priori might…

谱密度估计的同时置信带AI 解读

We propose a method for the construction of simultaneous confidence bands for a smoothed version of the spectral density of a Gaussian process based on nonparametric kernel estimators obtained by smoothing the periodogram. A studentized statistic is used to determine the width of the band at each frequency and a frequency-domain bootstrap approach is employed to estimate the distribution of the supremum of this statistic over all frequencies. We prove by means of strong…

依赖情形下的错误发现控制AI 解读

A popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent. This paper generalizes the random effects model to a conditional dependence model which allows dependence between null hypotheses. The dependence can be useful to characterize the spatial structure of the null hypotheses. Asymptotic properties of false discovery proportions and numbers of rejected hypotheses are explored and a large-sample…

推广 Simes 检验与 Hochberg 逐步上升程序AI 解读

In a multiple testing problem where one is willing to tolerate a few false rejections, procedure controlling the familywise error rate (FWER) can potentially be improved in terms of its ability to detect false null hypotheses by generalizing it to control the k-FWER, the probability of falsely rejecting at least k null hypotheses, for some fixed k>1. Simes’ test for testing the intersection null hypothesis is generalized to control the k-FWER weakly, that is, under the…

粗化预测变量下非参数回归的加速收敛AI 解读

We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while one has available a sample (W1, Y1), …, (Wn, Yn) of independent and identically distributed data, representing observations with precisely measured predictors, where E(Yi|Wi)=g(Wi), instead of the smooth regression function g, the target…

控制广义 FWER 与广义 FDR 的逐步上升程序AI 解读

In many applications of multiple hypothesis testing where more than one false rejection can be tolerated, procedures controlling error rates measuring at least k false rejections, instead of at least one, for some fixed k≥1 can potentially increase the ability of a procedure to detect false null hypotheses. The k-FWER, a generalized version of the usual familywise error rate (FWER), is such an error rate that has recently been introduced in the literature and procedures…

空间信号的错误发现率控制AI 解读

The problem of multiple testing for the presence of signal in spatial data can involve numerous locations. Traditionally, each location is tested separately for signal presence, but then the findings are reported in terms of clusters of nearby locations. This is an indication that the units of interest for testing are clusters rather than individual locations. The investigator may know a priori these more natural units or an approximation to them. We suggest testing these…

控制错误发现率的理想与自适应复合决策规则AI 解读

We develop a compound decision theory framework for multiple-testing problems and derive an oracle rule based on the z values that minimizes the false nondiscovery rate (FNR) subject to a constraint on the false discovery rate (FDR). We show that many commonly used multiple-testing procedures, which are p value–based, are inefficient, and propose an adaptive procedure based on the z values. The z value–based adaptive procedure asymptotically attains the performance of the z…

自回归模型中的一致有效推断AI 解读

The purpose of this paper is to provide theoretical justification for some existing methods for constructing confidence intervals for the sum of coefficients in autoregressive models. We show that the methods of Stock (1991), Andrews (1993), and Hansen (1999) provide asymptotically valid confidence intervals, whereas the subsampling method of Romano and Wolf (2001) does not. In addition, we generalize the three valid methods to a larger class of statistics. We also clarify…

依赖性与错误发现率：渐近分析AI 解读

Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing $n$ hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when $n$ tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of…

FDR 控制的性能约束与一种局部解决方案AI 解读

The False Discovery Rate (FDR) paradigm aims to attain certain control on Type I errors with relatively high power for multiple hypothesis testing. The Benjamini–Hochberg (BH) procedure is a well-known FDR controlling procedure. Under a random effects model, we show that, in general, unlike the FDR, the positive FDR (pFDR) of the BH procedure cannot be controlled at an arbitrarily low level due to the limited evidence provided by the observations to separate false and true…

多重检验中广义错误率的控制AI 解读

Consider the problem of testing $s$ hypotheses simultaneously. The usual approach restricts attention to procedures that control the probability of even one false rejection, the familywise error rate (FWER). If $s$ is large, one might be willing to tolerate more than one false rejection, thereby increasing the ability of the procedure to correctly reject false null hypotheses. One possibility is to replace control of the FWER by control of the probability of $k$ or more…

“大维度、小样本”范式的边际渐近理论及微阵列应用AI 解读

The “large $p$, small $n$” paradigm arises in microarray studies, image analysis, high throughput molecular screening, astronomy, and in many other high dimensional applications. False discovery rate (FDR) methods are useful for resolving the accompanying multiple testing problems. In cDNA microarray studies, for example, $p$-values may be computed for each of $p$ genes using data from $n$ arrays, where typically $p$ is in the thousands and $n$ is less than 30. For FDR…