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自适应设计中与闭合检验相容的同时置信区间AI 解读

We describe a general method for finding a confidence region for a parameter vector that is compatible with the decisions of a two-stage closed test procedure in an adaptive experiment. The closed test procedure is characterized by the fact that rejection or nonrejection of a null hypothesis may depend on the decisions for other hypotheses and the compatible confidence region will, in general, have a complex, nonrectangular shape. We find the smallest cross-product of…

控制错误发现率的高斯图模型估计AI 解读

This paper studies the estimation of a high-dimensional Gaussian graphical model (GGM). Typically, the existing methods depend on regularization techniques. As a result, it is necessary to choose the regularized parameter. However, the precise relationship between the regularized parameter and the number of false edges in GGM estimation is unclear. In this paper we propose an alternative method by a multiple testing procedure. Based on our new test statistics for conditional…

控制错误发现率的两阶段自适应多重检验与组合检验AI 解读

Testing multiple null hypotheses in two stages to decide which of these can be rejected or accepted at the first stage and which should be followed up for further testing having had additional observations is of importance in many scientific studies. We develop two procedures, each with two different combination functions, Fisher's and Simes’, to combine p-values from two stages, given prespecified boundaries on the first-stage p-values in terms of the false discovery rate…

病例定义与设计敏感度AI 解读

In a case-referent study, cases of disease are compared to non-cases with respect to their antecedent exposure to a treatment in an effort to determine whether exposure causes some cases of the disease. Because exposure is not randomly assigned in the population, as it would be if the population were a vast randomized trial, exposed and unexposed subjects may differ prior to exposure with respect to covariates that may or may not have been measured. After controlling for…

平滑样条模型中的局部与全局渐近推断AI 解读

This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. Statist. Math. 37 (1966) 577–580]. Equipped with this tool, we develop four interconnected procedures for inference: (i) pointwise confidence interval; (ii)…

预测回归模型中的统一推断AI 解读

The restricted likelihood has been found to provide a well-behaved likelihood ratio test in the predictive regression model even when the regressor variable exhibits almost unit root behavior. Using the weighted least squares approximation to the restricted likelihood obtained in Chen and Deo, we provide a quasi restricted likelihood ratio test (QRLRT), obtain its asymptotic distribution as the nuisance persistence parameter varies, and show that this distribution varies…

含交互项协方差分析模型中有序均值的估计与推断AI 解读

When interactions are identified in analysis of covariance models it becomes important to identify values of the covariates for which there are significant differences or, more generally, significant contrasts among the group mean responses. Inferential procedures that incorporate a priori order restrictions among the group mean responses would be expected to be superior to those that ignore this information. In this paper we focus on analysis of covariance models with…

构造函数非参数置信带的简单 Bootstrap 方法AI 解读

Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches, and others based on…

最优功效之谜：审视多重检验的单调似然比假设AI 解读

In single hypothesis testing, power is a non-decreasing function of type I error rate; hence it is desirable to test at the nominal level exactly to achieve optimal power. The puzzle lies in the fact that for multiple testing, under the false discovery rate paradigm, such a monotonic relationship may not hold. In particular, exact false discovery rate control may lead to a less powerful testing procedure if a test statistic fails to fulfil the monotone likelihood ratio…

更易判定符号的同时置信区间AI 解读

Many studies draw inferences about multiple endpoints but ignore the statistical implications of multiplicity. Effects inferred to be positive when there is no adjustment for multiplicity can lose their statistical significance when multiplicity is taken into account, perhaps explaining why such adjustments are so often omitted. We develop new simultaneous confidence intervals that mitigate this problem; these are uniformly more likely to determine signs than are standard…

大规模多重检验的扩展似然方法AI 解读

Summary To date, only frequentist, Bayesian and empirical Bayes approaches have been studied for the large-scale inference problem of testing simultaneously hundreds or thousands of hypotheses. Their derivations start with some summarizing statistics without modelling the basic responses. As a consequence testing procedures have been developed without necessarily checking model assumptions, and empirical null distributions are needed to avoid the problem of rejecting all…

函数型线性模型的极小极大自适应检验AI 解读

We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional principal component analysis. Interestingly, the procedures are completely data-driven and do not require any prior knowledge on the smoothness of the slope nor on the smoothness of the covariate functions. The levels and powers against local…

有效的模型选择后推断AI 解读

It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori. We propose to produce valid “post-selection inference” by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence…

局部识别失效下的最大似然估计与一致推断AI 解读

This paper analyzes the properties of a class of estimators, tests, and confidence sets (CSs) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter θ. This includes log likelihood, quasi-log likelihood, and least squares criterion functions.

更有利于判定符号的选择调整置信区间AI 解读

In many current large-scale problems, confidence intervals (CIs) are constructed only for the parameters that are large, as indicated by their estimators, ignoring the smaller parameters. Such selective inference poses a problem to the usual marginal CIs that no longer offer the right level of coverage, not even on the average over the selected parameters. We address this problem by developing three methods to construct short and valid CIs for the location parameter of a…

反事实分布的统计推断AI 解读

Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article, we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either…

重抽样多重检验早停规则的统计性质AI 解读

Resampling-based methods for multiple hypothesis testing often lead to long run times when the number of tests is large. This paper presents a simple rule that substantially reduces computation by allowing resampling to terminate early on a subset of tests. We prove that the method has a low probability of obtaining a set of rejected hypotheses different from those rejected without early stopping, and obtain error bounds for multiple hypothesis testing. Simulation shows that…

基因组范围基因—环境交互的独立筛选两阶段检验AI 解读

Several two-stage multiple testing procedures have been proposed to detect gene-environment interaction in genome-wide association studies. In this article, we elucidate general conditions that are required for validity and power of these procedures, and we propose extensions of two-stage procedures using the case-only estimator of gene-treatment interaction in randomized clinical trials. We develop a unified estimating equation approach to proving asymptotic independence…

右删失多状态半马尔可夫模型中停留分布的自助法置信带AI 解读

Transient semi-Markov processes have traditionally been used to describe the transitions of a patient through the various states of a multistate survival model. A survival distribution in this context is a sojourn through the states until passage to a fatal absorbing state or certain endpoint states. Using complete sojourn data, this paper shows how such survival distributions and associated hazard functions can be estimated nonparametrically and also how nonparametric…

子抽样与自助法的一致渐近有效性AI 解读

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These results are then applied (i) to construct confidence regions that behave well uniformly over $\mathbf{P}$ in the sense that the coverage probability tends to at least the nominal level uniformly over $\mathbf{P}$ and (ii) to construct tests…

可加模型的直接同时推断及营养不足建模应用AI 解读

This article proposes a simple and fast approach to build simultaneous confidence bands and perform specification tests for smooth curves in additive models. The method allows for handling of spatially heterogeneous functions and its derivatives as well as heteroscedasticity in the data. It is applied to study the determinants of chronic undernutrition of Kenyan children, with a particular focus on the highly nonlinear age pattern in undernutrition. Model estimation using…

重新审视技术交易：错误发现、持续性检验与交易成本AI 解读

We revisit the apparent historical success of technical trading rules on daily prices of the Dow Jones Industrial Average index from 1897 to 2011, and we use the false discovery rate (FDR) as a new approach to data snooping. The advantage of the FDR over existing methods is that it selects more outperforming rules, which allows diversifying against model uncertainty. Persistence tests show that, even with the more powerful FDR technique, an investor would never have been…

控制错误覆盖率的经验贝叶斯置信区间AI 解读

Summary Benjamini and Yekutieli suggested that it is important to account for multiplicity correction for confidence intervals when only some of the selected intervals are reported. They introduced the concept of the false coverage rate (FCR) for confidence intervals which is parallel to the concept of the false discovery rate in the multiple-hypothesis testing problem and they developed confidence intervals for selected parameters which control the FCR. Their approach…

函数型响应的多元变系数模型AI 解读

Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and…