Lin Liu, Rajarshi Mukherjee, James M. Robins
This is the rejoinder to the discussion by Kennedy, Balakrishnan and Wasserman on the paper "On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning" published in Statistical Science.
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Rejoinder to Reader Reaction "On exact randomization-based covariate-adjusted confidence intervals" by Jacob Fiksel
针对Fiksel的评论，提出解析反转Fisher随机化检验的新方法，处理非单调p值函数（如学生化t统计量），构造保证覆盖率的基于随机化的置信区间，解决现有矛盾并提高计算效率。
We congratulate the authors on their exciting paper, which introduces a novel idea for assessing the estimation bias in causal estimates. Doubly robust estimators are now part of the standard set of tools in causal inference, but a typical analysis stops with an estimate and a confidence interval. The authors give an approach for a unique type of model-checking that allows the user to check whether the bias is sufficiently small with respect to the standard error, which is generally required for confidence intervals to be reliable.
When does conformal calibration need censoring weights? Cause-of-failure prediction sets under competing risks
本文研究竞争风险下共形预测集的校准问题，发现完全案例校准可能偏离名义覆盖率，而正确指定删失模型的权重可恢复覆盖率，并给出有限样本下界。
For many causal effect parameters of interest, doubly robust machine learning (DRML) estimators $\hatψ_{1}$ are the state-of-the-art, incorporating the good prediction performance of machine learning; the decreased bias of doubly robust estimators; and the analytic tractability and bias reduction of sample splitting with cross fitting. Nonetheless, even in the absence of confounding by unmeasured factors, the nominal $(1 - α)$ Wald confidence interval $\hatψ_{1} \pm z_{α/ 2} \widehat{\mathsf{se}} [\hatψ_{1}]$ may still undercover even in large samples, because the bias of $\hatψ_{1}$ may be of…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller than the nominal confidence level. In this paper a new confidence interval is proposed. The construction needs only information on sample sizes and sample odds ratio. The coverage probability of the proposed confidence interval is at least the nominal confidence level.
We introduce a new framework for creating point-wise confidence intervals for the distribution of event times for current status data. Existing methods are based on asymptotics. Our framework is based on binomial properties and motivates confidence intervals that are very simple to apply and are valid, i.e., guarantee nominal coverage. Although these confidence intervals are necessarily conservative for small sample sizes, asymptotically their coverage rate approaches the nominal one. This binomial framework also motivates approximately valid confidence intervals, and simulations show that the…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly smaller than the nominal confidence level. In this paper a new confidence interval is proposed. The construction needs only information on sample sizes and sample difference between proportions. The coverage probability of the proposed confidence interval is at least the nominal confidence level. The new confidence interval is illustrated by a medical example.
Conformal Multi-Target Hyperrectangles
本文提出用于多目标回归的共形超矩形预测区域及分割共形预测算法，无需协方差估计即可实现渐近名义覆盖与边际平衡，并在模拟和真实数据上优于现有方法。
Confidence intervals for the means of multiple normal populations are often based on a hierarchical normal model. While commonly used interval procedures based on such a model have the nominal coverage rate on average across a population of groups, their actual coverage rate for a given group will be above or below the nominal rate, depending on the value of the group mean. Alternatively, a coverage rate that is constant as a function of a group's mean can be simply achieved by using a standard $t$-interval, based on data only from that group. The standard $t$-interval, however, fails to share…
The asymptotic behaviour of the commonly used bootstrap percentile confidence interval is investigated when the parameters are subject to linear inequality constraints. We concentrate on the important one- and two-sample problems with data generated from general parametric distributions in the natural exponential family. The focus of this paper is on quantifying the coverage probabilities of the parametric bootstrap percentile confidence intervals, in particular their limiting behaviour near boundaries. We propose a local asymptotic framework to study this subtle coverage behaviour. Under this…
Constructing confidence intervals for constrained parameters via valid prior-free inferential models
本文提出先验无关推断模型方法，用于构建正态和泊松分布中受限参数的置信区间，解决传统方法在处理未知干扰参数时覆盖概率不准确的问题，通过随机加权技术提升性能，验证了其在高能物理实验数据中的有效性。
Local conformal prediction for individual causal effects
针对强处理效应异质性下标准CATE估计器失效问题，提出ICP框架，结合因果森林等技术构造有效共形区间，在高异质性合成数据和IHDP基准上验证了局部策略的精度与覆盖率优势。
Significance-First Splitting: Aligning Treatment Heterogeneity Detection with Honest Estimation
针对现有树方法在CATE估计中的权衡痛点，提出融合显著性分裂与诚实样本拆分的混合算法，兼顾交互识别灵敏度与合法置信区间覆盖性能。
Beyond Data Splitting: Full-Data Conformal Prediction by Differential Privacy
本文提出一种基于差分隐私的全数据符合预测框架，通过稳定性控制和保守分位数程序实现隐私保护下的高覆盖水平。
Comparing Two Survival Functions at a Fixed Timepoint
本文针对右删失下固定时间点的两条生存函数比较问题，将单样本Greenwood方差调整纳入delta法两样本应用，扩展BPCP融合区间为中p版本，经模拟发现BPCP融合可保证全场景覆盖率，中p版本覆盖率最接近名义，还提供了bpcp R包函数。
In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a high coverage probability close to the nominal level and a shorter interval length. However, these two concepts are in opposition to each other: high and low coverages are associated with longer and shorter interval lengths respectively. Some methods, such as bootstrap calibration, modify the nominal level to improve the coverage and thereby allow the selectio…
Model-Agnostic Bounds for Augmented Inverse Probability Weighted Estimators' Wald-Confidence Interval Coverage in Randomized Controlled Trials
本文推导了AIPW估计量Wald置信区间覆盖率的非渐近Berry-Esseen型界，并分析了方差估计量的偏差，解释了交叉拟合为何能改善覆盖率。
We evaluate the model averaged profile likelihood confidence intervals proposed by Fletcher and Turek (2011) in a simple situation in which there are two linear regression models over which we average. We obtain exact expressions for the coverage and the scaled expected length of the intervals and use these to compute these quantities in particular situations. We show that the Fletcher-Turek confidence intervals can have coverage well below the nominal coverage and expected length greater than that of the standard confidence interval with coverage equal to the same minimum coverage. In these s…
A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any distributional assumptions. It can be applied to both frequentist and Bayesian inference where interval estimates are desired. We provide theoretical results for the consistency of the proposed estimator, and give two complex examples, on confidence interval correction for composite likelihood estimators and in approximate Bayesian computation (ABC), to demonstrat…
In the analysis of clustered and longitudinal data, which includes a covariate that varies both between and within clusters (e.g. time-varying covariate in longitudinal data), a Hausman pretest is commonly used to decide whether subsequent inference is made using the linear random intercept model or the fixed effects model. We assess the effect of this pretest on the coverage probability and expected length of a confidence interval for the slope parameter. Our results show that for the small levels of significance of the Hausman pretest commonly used in applications, the minimum coverage proba…
Multi-Scale Conformal Prediction: A Theoretical Framework with Coverage Guarantees
本文提出多尺度共形预测框架，通过在各尺度定义符合性函数并相交预测集，在保持有限样本覆盖保证的同时生成更小更精确的预测集。
Score-based confidence intervals for variance-covariance parameters in linear mixed models
针对线性混合模型中方差-协方差参数，提出基于修正剖面得分统计量的置信区间，在参数接近边界时仍保持接近名义覆盖率，且比通用推断区间窄 1.7 至 3.1 倍。
Training-Conditional Coverage Bounds under Covariate Shift
本文研究了在协变量偏移下训练条件覆盖的上界，提供PAC保证，以评估预测集的可靠性。
Universal distribution of the empirical coverage in split conformal prediction
本研究推导了可交换数据下批量拆分共形预测中经验覆盖率及其极限的精确通用分布，该分布仅由名义误覆盖率和校准样本量决定，为应用中校准样本量的选择提供了依据。
Confidence interval procedures used in low dimensional settings are often inappropriate for high dimensional applications. When a large number of parameters are estimated, marginal confidence intervals associated with the most significant estimates have very low coverage rates: They are too small and centered at biased estimates. The problem of forming confidence intervals in high dimensional settings has previously been studied through the lens of selection adjustment. In this framework, the goal is to control the proportion of non-covering intervals formed for selected parameters. In this pa…
When Is a Conformal Guarantee Fair? Auditing Silent Subgroup Under-Coverage in Alzheimer's Disease Longitudinal Prediction
该研究针对阿尔茨海默病纵向预测中总体共形预测带对高风险亚组覆盖不足的问题，提出机制驱动的共形修正框架，在两个队列中实现了几乎所有高风险亚组的目标覆盖。
Nonparametric Empirical Bayes Confidence Intervals
本文提出非参数经验贝叶斯置信区间，用于正常均值模型中不可观测的个体效应，通过非参数先验构造置信区间，具有渐近精确性，尽管存在统计成本，但模拟显示其在非高斯先验下保持名义覆盖概率。
Amortized Inference for Sampling Distributions Where the Bootstrap Fails
研究自举法失效时抽样分布估计问题，提出用神经网络基于弹球损失训练进行摊销推断，该方法在四个典型问题上表现良好，在瓦瑟斯坦距离上优于经典方法，在风险价值问题上也有较好覆盖率，还有单一通用网络匹配多个专门网络的优势。
Cluster-Robust Prediction-Powered Inference
针对聚类内依赖导致PPI置信区间覆盖率不足的问题，提出聚类稳健的PPI++，支持部分标注聚类，无需重抽样，并在电视新闻应用中实现95%覆盖率。
Silent coverage failures in rare-event searches and a degeneracy index that predicts them
该研究针对稀有事件搜寻中因模型误设导致的静默覆盖失效，提出泊松-费舍尔简并指数预测失效，通过建模变形恢复覆盖但损失灵敏度。
Drift-Aware Spectral Conformal Prediction for Non-Exchangeable Streaming Data
针对非可交换流数据的分布漂移问题，提出漂移感知谱共形预测（DASC），通过局部谱相似性加权校准残差和基于传输的漂移评分，动态调整校准池与目标误覆盖率，实现近名义覆盖并降低区间宽度。
Adjusting Regression Models for Conditional Uncertainty Calibration
针对Conformal Prediction缺乏条件覆盖保证的问题，提出一种新颖的端到端回归训练算法，通过控制条件与名义覆盖率差距的上界来改善条件覆盖，并在合成和真实数据集上验证了其有效性。
CausalGuard: Conformal Inference under Graph Uncertainty
本文提出CausalGuard，一种结构加权的契合框架，通过聚合图条件双稳健伪结果进行校准，以在图不确定性下提供无分布的有限样本边际覆盖。
Prediction Sets Adaptive to Unknown Covariate Shift
针对未知协变量偏移下预测集构建的难题，提出无分布方法PredSet-1Step，可高效构建具备渐近覆盖率保证的预测集，经理论与实验验证有效。
In the analysis of panel data that includes a time-varying covariate, a Hausman pretest is commonly used to decide whether subsequent inference is made using the random effects model or the fixed effects model. We consider the effect of this pretest on the coverage probability of a confidence interval for the slope parameter. We prove three new finite sample theorems that make it easy to assess, for a wide variety of circumstances, the effect of the Hausman pretest on the minimum coverage probability of this confidence interval. Our results show that for the small levels of significance of the…
On the Precise Asymptotics of Universal Inference
该研究针对统计推断中置信集因常数难确定导致的极端保守性问题，以模型误设下正则参数模型的通用推断为示例，明确渐近保守性来源，提出基于学生化和偏差校正的修正方法，实现名义水平的精确渐近覆盖，且特性与半参数双重稳健性相似。
This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a disease using a sample of antibody test results and measurements of the test's false positive and false negative rates. We begin by documenting erratic behavior in the coverage probabilities of standard Wald and percentile bootstrap intervals when applied to this problem. We then consider two alternative sets of intervals constructed with test inversion. The firs…
Consider panel data modelled by a linear random intercept model that includes a time-varying covariate. Suppose that we have uncertain prior information that this covariate is exogenous. We present a new confidence interval for the slope parameter that utilizes this uncertain prior information. This interval has minimum coverage probability very close to its nominal coverage. Let the scaled expected length of this new confidence interval be its expected length divided by the expected length of the confidence interval, with the same minimum coverage, constructed using the fixed effects model. T…
Cross-Fitting Under Nonregularity: Normality and Inference via Locality
针对交叉拟合在非正则性下置信区间覆盖不足的问题，提出基于局部性条件的中心极限定理及调整交叉折相关性的置信区间，并通过模拟验证其近似名义覆盖率。
Conformal Prediction under Exponential-Tilt Joint Shift
针对分布偏移下共形预测覆盖率下降问题，研究指数倾斜重加权对齐（ExTRA）与预测倾斜的组合效果，发现倾斜在特定条件下可缩短集合长度，但可能损害覆盖率，何时应用仍待解决。
We present several related methods for creating confidence intervals to assess disease prevalence in variety of survey sampling settings. These include simple random samples with imperfect tests, weighted sampling with perfect tests, and weighted sampling with imperfect tests, with the first two settings considered special cases of the third. Our methods use survey results and measurements of test sensitivity and specificity to construct melded confidence intervals. We demonstrate that our methods appear to guarantee coverage in simulated settings, while competing methods are shown to achieve …
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 that behave well uniformly over $\mathbf{P}$ in the sense that the size tends to no greater than the nominal level unifo…
It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations. Focusing on a linear model, we derive the asymptotic distribution of the difference between the conditional coverage probability of a nominal prediction interval and the conditional coverage probability of a prediction interval obtained via a residual-based bootstrap. Applying this result, we show that a prediction interval generated by the residual-based b…
Penalized spline regression is a popular method for scatterplot smoothing, but there has long been a debate on how to construct confidence intervals for penalized spline fits. Due to the penalty, the fitted smooth curve is a biased estimate of the target function. Many methods, including Bayesian intervals and the simple-shift bias-reduction, have been proposed to upgrade the coverage of the confidence intervals, but these methods usually fail to adequately improve the situation at predictor values where the function is sharply curved. In this paper, we develop a novel approach to improving th…
Confidence intervals for the Cox model test error from cross-validation
针对交叉验证估计Cox模型测试误差时置信区间覆盖率不足的问题，将嵌套CV思路推广至Cox比例风险模型，探索该场景下测试误差的多种选择，以提升置信区间覆盖率。
Imputation Uncertainty in Interpretable Machine Learning Methods
研究探讨了可解释机器学习方法中不同填补技术对置信区间覆盖概率的影响，发现单一填补会导致方差低估，而多重填补更接近预期覆盖水平。
Smooth Sailing: Lipschitz-Driven Uncertainty Quantification for Spatial Association
针对空间关联推断中模型误设和非随机位置导致现有置信区间失效的问题，本文提出一种仅依赖空间平滑性和同方差高斯误差假设的Lipschitz驱动方法，首次保证名义覆盖率并在真实与模拟实验中优于现有技术。
Conformal Calibration of Statistical Confidence Sets
本文提出TRUST和TRUST++两种方法，利用模拟数据校准统计置信集，实现无分布条件覆盖，在小样本下优于现有方法，弥合保形预测与统计推断的差距。
A Kernel Nonconformity Score for Multivariate Conformal Prediction
本文提出多变量核分数，通过保留残差分布的几何结构，提升预测区域的适应性，并证明了有限样本覆盖保证和收敛速率，适用于高维回归任务。
Consider a one-way analysis of covariance model. Suppose that the parameter of interest theta is a specified linear contrast of the expected responses, for a given value of the covariate. Also suppose that the inference of interest is a 1-alpha confidence interval for theta. The following two-stage procedure has been proposed to determine the form of the model. In Stage 1, we carry out an F test of the null hypothesis that the slopes are all zero against the alternative hypothesis that they are not all zero. If this null hypothesis is accepted then we assume that the slopes are all zero; other…
Using and extending fractional order statistic theory, we characterize the $O(n^{-1})$ coverage probability error of the previously proposed confidence intervals for population quantiles using $L$-statistics as endpoints in Hutson (1999). We derive an analytic expression for the $n^{-1}$ term, which may be used to calibrate the nominal coverage level to get $O\bigl(n^{-3/2}[\log(n)]^3\bigr)$ coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles. This new method compares favorably with as…
Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a delta method approximation to the standard deviation of the bootstrap smoothed estimator. This approximation provides an easily computed guide to the accuracy of this estimator. In addition, Efron (2014) proposed a confidence interval centered on the bootstrap smoothed estimator, with width proportional to the estimate of this approximation to the standard d…
In the analysis of survey data it is of interest to estimate and quantify uncertainty about means or totals for each of several non-overlapping subpopulations, or areas. When the sample size for a given area is small, standard confidence intervals based on data only from that area can be unacceptably wide. In order to reduce interval width, practitioners often utilize multilevel models in order to borrow information across areas, resulting in intervals centered around shrinkage estimators. However, such intervals only have the nominal coverage rate on average across areas under the assumed mod…
Adaptive Conformal Inference Under Delayed Feedback: Coverage Guarantees and a Delay-to-Memory Diagnostic
本研究分析延迟反馈下自适应共形推断的覆盖保证，提出延迟-记忆比诊断，揭示延迟影响取决于残差过程的时间尺度。
For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often violated under Cox proportion hazards models, leading to biased estimates with under-coverage confidence intervals. We propose a modified debiased lasso approach, which solves a series of quadratic programming problems to approximate the inverse information matrix without posing sparse matrix assumptions. We establish asymptotic results for the estimated regression…
Missing observations are common in cluster randomised trials. Approaches taken to handling such missing data include: complete case analysis, single-level multiple imputation that ignores the clustering, multiple imputation with a fixed effect for each cluster and multilevel multiple imputation. We conducted a simulation study to assess the performance of these approaches, in terms of confidence interval coverage and empirical bias in the estimated treatment effects. Missing-at-random clustered data scenarios were simulated following a full-factorial design. An Analysis of Variance was carried…
Exact Conditional Confidence Intervals for Cramér's V: Near-Nominal and Tight Where the Guaranteed Interval Is Wide and the Software Interval Does Not Cover
针对Cramér's V置信区间难以构造的问题，本文通过条件于观测边际计算精确分布并求逆，得到接近名义水平且宽度仅为投影区间三分之一到一半的区间，以估计目标改变为代价。
In this article, we derive and compare methods to derive \textit{p}-values and sets of confidence intervals with strong control of the family-wise error rates and coverage for estimates of treatment effects in cluster randomised trials with multiple outcomes. There are few methods for \textit{p}-value corrections and deriving confidence intervals, limiting their application in this setting. We discuss the methods of Bonferroni, Holm, and Romano \& Wolf (2005) and adapt them to cluster randomised trial inference using permutation-based methods with different test statistics. We develop a novel …
Efficient conformal prediction intervals for time series: Online PID-Expert aggregation
PID-Expert通过在线聚合多个PID校准器，在保持覆盖率的同时生成更窄的预测区间，提高了时间序列共形预测的效率。
The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson--Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Two methods of construction of such confidence bands are proposed. The weird bootstrap method is used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal--tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present …
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