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AbstractCausal discovery and causal effect estimation are two fundamental tasks in causal inference. While many methods have been developed for each task individually, statistical challenges arise when applying these methods jointly: estimating causal effects after running causal discovery algorithms on the same data leads to “double dipping,” invalidating the coverage guarantees of classical confidence intervals. To this end, we develop tools for valid post-causal-discovery inference. Across empirical studies, we show that a naive combination of causal discovery and subsequent inference algorithms leads to highly inflated miscoverage rates; on the other hand, applying our method provides reliable coverage while achieving more accurate causal discovery than data splitting. [ABSTRACT FROM AUTHOR]

Pairwise likelihood methods are commonly used for inference in parametric statistical models in cases where the full likelihood is too complex to be used, such as multivariate count data. Although pairwise likelihood methods represent a useful solution to perform inference for intractable likelihoods, several computational challenges remain. The pairwise likelihood function still requires the computation of a sum over all pairs of variables and all observations, which may be prohibitive in high dimensions. Moreover, it may be difficult to calculate confidence intervals of the resulting estimators, as they involve summing all pairs of pairs and all of the four-dimensional marginals. To alleviate these issues, we consider a randomized pairwise likelihood approach, where only summands randomly sampled across observations and pairs are used for the estimation. In addition to the usual tradeoff between statistical and computational efficiency, it is shown that, under a condition on the sampling parameter, this two-way random sampling mechanism makes the individual bivariate likelihood scores become asymptotically independent, allowing more computationally efficient confidence intervals to be constructed. The proposed approach is illustrated in tandem with copula-based models for multivariate count data in simulations, and in real data from a transcriptome study. for this article are available online. [ABSTRACT FROM AUTHOR]

The method of difference-in-differences (DID) is widely used to study the causal effect of policy interventions in observational studies. DID employs a before and after comparison of the treated and control units to remove bias due to time-invariant unmeasured confounders under the parallel trends assumption. Estimates from DID, however, will be biased if the outcomes for the treated and control units evolve differently in the absence of treatment, namely if the parallel trends assumption is violated. We propose a general identification strategy that leverages two groups of control units whose outcomes relative to the treated units exhibit a negative correlation, and achieves partial identification of the average treatment effect for the treated. The identified set is of a union bounds form that involves the minimum and maximum operators, which makes the canonical bootstrap generally inconsistent and naive methods overly conservative. By using the directional inconsistency of the bootstrap distribution, we develop a novel bootstrap method to construct confidence intervals for the identified set and parameter of interest when the identified set is of a union bounds form, and we theoretically establish the asymptotic validity of the proposed method. We develop a simple falsification test and sensitivity analysis. We apply the proposed strategy for bracketing to study whether minimum wage laws affect employment levels. for this article are available online. [ABSTRACT FROM AUTHOR]

This article studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient matrix is proposed. Our method first uses the multivariate nature of the responses by estimating and adjusting the hidden effect to construct an initial estimator of the coefficient matrix. By further deploying a low-dimensional projection procedure to reduce the bias introduced by the regularization in the previous step, a refined estimator is proposed and shown to be asymptotically normal. The asymptotic variance of the resulting estimator is derived with closed-form expression and can be consistently estimated. In addition, we propose a testing procedure for the existence of hidden effects and provide its theoretical justification. Both our procedures and their analyses are valid even when the feature dimension and the number of responses exceed the sample size. Our results are further backed up via extensive simulations and a real data analysis. for this article are available online. [ABSTRACT FROM AUTHOR]

Integrative analysis of data from multiple sources is critical to making generalizable discoveries. Associations consistently observed across multiple source populations are more likely to be generalized to target populations with possible distributional shifts. In this article, we model the heterogeneous multi-source data with multiple high-dimensional regressions and make inferences for the maximin effect (Meinshausen and Bühlmann, AoS, 43(4), 1801–1830). The maximin effect provides a measure of stable associations across multi-source data. A significant maximin effect indicates that a variable has commonly shared effects across multiple source populations, and these shared effects may be generalized to a broader set of target populations. There are challenges associated with inferring maximin effects because its point estimator can have a nonstandard limiting distribution. We devise a novel sampling method to construct valid confidence intervals for maximin effects. The proposed confidence interval attains a parametric length. This sampling procedure and the related theoretical analysis are of independent interest for solving other nonstandard inference problems. Using genetic data on yeast growth in multiple environments, we demonstrate that the genetic variants with significant maximin effects have generalizable effects under new environments. The proposed method is implemented in the R package MaximinInfer available from CRAN. for this article are available online. [ABSTRACT FROM AUTHOR]

AbstractFueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work has primarily addressed estimation. To bridge this gap, we develop a new statistical inference procedure for high-dimensional Hawkes processes. The key ingredient for the inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarize the entire history of the process. Combining recent martingale central limit theorem with the new concentration inequality, we then characterize the convergence rate of the test statistics in a continuous time domain. Finally, to account for potential non-stationarity of the process in practice, we extend our statistical inference procedure to a flexible class of Hawkes processes with time-varying background intensities and unknown transition functions. The finite sample validity of the inferential tools is illustrated via extensive simulations and further applied to a neuron spike train data set. [ABSTRACT FROM AUTHOR]

We propose Narrowest Significance Pursuit (NSP), a general and flexible methodology for automatically detecting localized regions in data sequences which each must contain a change-point (understood as an abrupt change in the parameters of an underlying linear model), at a prescribed global significance level. NSP works with a wide range of distributional assumptions on the errors, and guarantees important stochastic bounds which directly yield exact desired coverage probabilities, regardless of the form or number of the regressors. In contrast to the widely studied "post-selection inference" approach, NSP paves the way for the concept of "post-inference selection." An implementation is available in the R package nsp. for this article are available online. [ABSTRACT FROM AUTHOR]

We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulations confirm the effectiveness of our methodology, and we also illustrate its applicability on the U.S. excess deaths data from 2017 to 2020. The , which contains the proofs of our theoretical results, is available online. [ABSTRACT FROM AUTHOR]

Estimation of population size using incomplete lists has a long history across many biological and social sciences. For example, human rights groups often construct partial lists of victims of armed conflicts, to estimate the total number of victims. Earlier statistical methods for this setup often use parametric assumptions, or rely on suboptimal plug-in-type nonparametric estimators; but both approaches can lead to substantial bias, the former via model misspecification and the latter via smoothing. Under an identifying assumption that two lists are conditionally independent given measured covariates, we make several contributions. First, we derive the nonparametric efficiency bound for estimating the capture probability, which indicates the best possible performance of any estimator, and sheds light on the statistical limits of capture-recapture methods. Then we present a new estimator, that has a double robustness property new to capture-recapture, and is near-optimal in a nonasymptotic sense, under relatively mild nonparametric conditions. Next, we give a confidence interval construction method for total population size from generic capture probability estimators, and prove nonasymptotic near-validity. Finally, we apply them to estimate the number of killings and disappearances in Peru during its internal armed conflict between 1980 and 2000. for this article are available online. [ABSTRACT FROM AUTHOR]

Federal administrative data, such as tax data, are invaluable for research, but because of privacy concerns, access to these data is typically limited to select agencies and a few individuals. An alternative to sharing microlevel data is to allow individuals to query statistics without directly accessing the confidential data. This article studies the feasibility of using differentially private (DP) methods to make certain queries while preserving privacy. We also include new methodological adaptations to existing DP regression methods for using new data types and returning standard error estimates. We define feasibility as the impact of DP methods on analyses for making public policy decisions and the queries accuracy according to several utility metrics. We evaluate the methods using Internal Revenue Service data and public-use Current Population Survey data and identify how specific data features might challenge some of these methods. Our findings show that DP methods are feasible for simple, univariate statistics but struggle to produce accurate regression estimates and confidence intervals. To the best of our knowledge, this is the first comprehensive statistical study of DP regression methodology on real, complex datasets, and the findings have significant implications for the direction of a growing research field and public policy. for this article are available online. [ABSTRACT FROM AUTHOR]

This article develops a bootstrap analogue of the well-known asymptotic expansion of the tail quantile process in extreme value theory. One application of this result is to construct confidence intervals for estimators of the extreme value index such as the Probability Weighted Moment (PWM) estimator. For the peaks-over-threshold method, we show the bootstrap consistency of the confidence intervals. By contrast, the asymptotic expansion of the quantile process of the bootstrapped block maxima does not lead to a similar consistency result for the PWM estimator using the block maxima method. For both methods, We show by simulations that the sample variance of bootstrapped estimates can be a good approximation for the asymptotic variance of the original estimator. for this article are available online. [ABSTRACT FROM AUTHOR]

The weighted nearest neighbors (WNN) estimator has been popularly used as a flexible and easy-to-implement nonparametric tool for mean regression estimation. The bagging technique is an elegant way to form WNN estimators with weights automatically generated to the nearest neighbors (Steele 2009; Biau, Cérou, and Guyader 2010); we name the resulting estimator as the distributional nearest neighbors (DNN) for easy reference. Yet, there is a lack of distributional results for such estimator, limiting its application to statistical inference. Moreover, when the mean regression function has higher-order smoothness, DNN does not achieve the optimal nonparametric convergence rate, mainly because of the bias issue. In this work, we provide an in-depth technical analysis of the DNN, based on which we suggest a bias reduction approach for the DNN estimator by linearly combining two DNN estimators with different subsampling scales, resulting in the novel two-scale DNN (TDNN) estimator. The two-scale DNN estimator has an equivalent representation of WNN with weights admitting explicit forms and some being negative. We prove that, thanks to the use of negative weights, the two-scale DNN estimator enjoys the optimal nonparametric rate of convergence in estimating the regression function under the fourth-order smoothness condition. We further go beyond estimation and establish that the DNN and two-scale DNN are both asymptotically normal as the subsampling scales and sample size diverge to infinity. For the practical implementation, we also provide variance estimators and a distribution estimator using the jackknife and bootstrap techniques for the two-scale DNN. These estimators can be exploited for constructing valid confidence intervals for nonparametric inference of the regression function. The theoretical results and appealing finite-sample performance of the suggested two-scale DNN method are illustrated with several simulation examples and a real data application. [ABSTRACT FROM AUTHOR]

This article is concerned with constructing a confidence interval for a target policy's value offline based on a pre-collected observational data in infinite horizon settings. Most of the existing works assume no unmeasured variables exist that confound the observed actions. This assumption, however, is likely to be violated in real applications such as healthcare and technological industries. In this article, we show that with some auxiliary variables that mediate the effect of actions on the system dynamics, the target policy's value is identifiable in a confounded Markov decision process. Based on this result, we develop an efficient off-policy value estimator that is robust to potential model misspecification and provide rigorous uncertainty quantification. Our method is justified by theoretical results, simulated and real datasets obtained from ridesharing companies. A Python implementation of the proposed procedure is available at. [ABSTRACT FROM AUTHOR]

This article presents a Bayesian approach to multiple-output quantile regression. The prior can be elicited as ex-ante knowledge of the distance of the τ-Tukey depth contour to the Tukey median, the first prior of its kind. The parametric model is proven to be consistent and a procedure to obtain confidence intervals is proposed. A proposal for nonparametric multiple-output regression is also presented. These results add to the literature of misspecified Bayesian modeling, consistency, and prior elicitation for nonparametric multivariate modeling. The model is applied to the Tennessee Project Steps to Achieving Resilience (STAR) experiment and finds a joint increase in τ-quantile subpopulations for mathematics and reading scores given a decrease in the number of students per teacher. for this article are available online. [ABSTRACT FROM AUTHOR]

In this work, we study the transfer learning problem under high-dimensional generalized linear models (GLMs), which aim to improve the fit on target data by borrowing information from useful source data. Given which sources to transfer, we propose a transfer learning algorithm on GLM, and derive its l 1 / l 2 -estimation error bounds as well as a bound for a prediction error measure. The theoretical analysis shows that when the target and sources are sufficiently close to each other, these bounds could be improved over those of the classical penalized estimator using only target data under mild conditions. When we don't know which sources to transfer, an algorithm-free transferable source detection approach is introduced to detect informative sources. The detection consistency is proved under the high-dimensional GLM transfer learning setting. We also propose an algorithm to construct confidence intervals of each coefficient component, and the corresponding theories are provided. Extensive simulations and a real-data experiment verify the effectiveness of our algorithms. We implement the proposed GLM transfer learning algorithms in a new R package glmtrans, which is available on CRAN. for this article are available online. [ABSTRACT FROM AUTHOR]

In this article, we develop automated inference methods for "local" parameters in a collection of convexity constrained models based on the natural constrained tuning-free estimators. A canonical example is given by the univariate convex regression model, in which automated inference is drawn for the function value, the function derivative at a fixed interior point, and the anti-mode of the convex regression function, based on the widely used tuning-free, piecewise linear convex least squares estimator (LSE). The key to our inference proposal in this model is a pivotal joint limit distribution theory for the LS estimates of the local parameters, normalized appropriately by the length of certain data-driven linear piece of the convex LSE. Such a pivotal limiting distribution instantly gives rise to confidence intervals for these local parameters, whose construction requires almost no more effort than computing the convex LSE itself. This inference method in the convex regression model is a special case of a general inference machinery that covers a number of convexity constrained models in which a limit distribution theory is available for model-specific estimators. Concrete models include: (i) log-concave density estimation, (ii) s-concave density estimation, (iii) convex nonincreasing density estimation, (iv) concave bathtub-shaped hazard function estimation, and (v) concave distribution function estimation from corrupted data. The proposed confidence intervals for all these models are proved to have asymptotically exact coverage and oracle length, and require no further information than the estimator itself. We provide extensive simulation evidence that validates our theoretical results. Real data applications and comparisons with competing methods are given to illustrate the usefulness of our inference proposals. for this article are available online. [ABSTRACT FROM AUTHOR]

Sparse topic modeling under the probabilistic latent semantic indexing (pLSI) model is studied. Novel and computationally fast algorithms for estimation and inference of both the word-topic matrix and the topic-document matrix are proposed and their theoretical properties are investigated. Both minimax upper and lower bounds are established and the results show that the proposed algorithms are rate-optimal, up to a logarithmic factor. Moreover, a refitting algorithm is proposed to establish asymptotic normality and construct valid confidence intervals for the individual entries of the word-topic and topic-document matrices. Simulation studies are carried out to investigate the numerical performance of the proposed algorithms. The results show that the proposed algorithms perform well numerically and are more accurate in a range of simulation settings comparing to the existing literature. In addition, the methods are illustrated through an analysis of the COVID-19 Open Research Dataset (CORD-19). [ABSTRACT FROM AUTHOR]

We consider three problems in high-dimensional linear mixed models. Without any assumptions on the design for the fixed effects, we construct asymptotic statistics for testing whether a collection of random effects is zero, derive an asymptotic confidence interval for a single random effect at the parametric rate n , and propose an empirical Bayes estimator for a part of the mean vector in ANOVA type models that performs asymptotically as well as the oracle Bayes estimator. We support our theoretical results with numerical simulations and provide comparisons with oracle estimators. The procedures developed are applied to the Trends in International Mathematics and Sciences Study (TIMSS) data. for this article are available online. [ABSTRACT FROM AUTHOR]

In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response—in other words, to gauge the variable importance of features. Most recent work on variable importance assessment has focused on describing the importance of features within the confines of a given prediction algorithm. However, such assessment does not necessarily characterize the prediction potential of features, and may provide a misleading reflection of the intrinsic value of these features. To address this limitation, we propose a general framework for nonparametric inference on interpretable algorithm-agnostic variable importance. We define variable importance as a population-level contrast between the oracle predictiveness of all available features versus all features except those under consideration. We propose a nonparametric efficient estimation procedure that allows the construction of valid confidence intervals, even when machine learning techniques are used. We also outline a valid strategy for testing the null importance hypothesis. Through simulations, we show that our proposal has good operating characteristics, and we illustrate its use with data from a study of an antibody against HIV-1 infection. for this article are available online. [ABSTRACT FROM AUTHOR]

Stratification and rerandomization are two well-known methods used in randomized experiments for balancing the baseline covariates. Renowned scholars in experimental design have recommended combining these two methods; however, limited studies have addressed the statistical properties of this combination. This article proposes two rerandomization methods to be used in stratified randomized experiments, based on the overall and stratum-specific Mahalanobis distances. The first method is applicable for nearly arbitrary numbers of strata, strata sizes, and stratum-specific proportions of the treated units. The second method, which is generally more efficient than the first method, is suitable for situations in which the number of strata is fixed with their sizes tending to infinity. Under the randomization inference framework, we obtain the asymptotic distributions of estimators used in these methods and the formulas of variance reduction when compared to stratified randomization. Our analysis does not require any modeling assumption regarding the potential outcomes. Moreover, we provide asymptotically conservative variance estimators and confidence intervals for the average treatment effect. The advantages of the proposed methods are exhibited through an extensive simulation study and a real-data example. [ABSTRACT FROM AUTHOR]

This article develops a unified statistical inference framework for high-dimensional binary generalized linear models (GLMs) with general link functions. Both unknown and known design distribution settings are considered. A two-step weighted bias-correction method is proposed for constructing confidence intervals (CIs) and simultaneous hypothesis tests for individual components of the regression vector. Minimax lower bound for the expected length is established and the proposed CIs are shown to be rate-optimal up to a logarithmic factor. The numerical performance of the proposed procedure is demonstrated through simulation studies and an analysis of a single cell RNA-seq dataset, which yields interesting biological insights that integrate well into the current literature on the cellular immune response mechanisms as characterized by single-cell transcriptomics. The theoretical analysis provides important insights on the adaptivity of optimal CIs with respect to the sparsity of the regression vector. New lower bound techniques are introduced and they can be of independent interest to solve other inference problems in high-dimensional binary GLMs. [ABSTRACT FROM AUTHOR]

In surveys, the interest lies in estimating finite population parameters such as population totals and means. In most surveys, some auxiliary information is available at the estimation stage. This information may be incorporated in the estimation procedures to increase their precision. In this article, we use random forests (RFs) to estimate the functional relationship between the survey variable and the auxiliary variables. In recent years, RFs have become attractive as National Statistical Offices have now access to a variety of data sources, potentially exhibiting a large number of observations on a large number of variables. We establish the theoretical properties of model-assisted procedures based on RFs and derive corresponding variance estimators. A model-calibration procedure for handling multiple survey variables is also discussed. The results of a simulation study suggest that the proposed point and estimation procedures perform well in terms of bias, efficiency and coverage of normal-based confidence intervals, in a wide variety of settings. Finally, we apply the proposed methods using data on radio audiences collected by Médiamétrie, a French audience company. for this article are available online. [ABSTRACT FROM AUTHOR]

Classical randomized experiments, equipped with randomization-based inference, provide assumption-free inference for treatment effects. They have been the gold standard for drawing causal inference and provide excellent internal validity. However, they have also been criticized for questionable external validity, in the sense that the conclusion may not generalize well to a larger population. The randomized survey experiment is a design tool that can help mitigate this concern, by randomly selecting the experimental units from the target population of interest. However, as pointed out by Morgan and Rubin, chance imbalances often exist in covariate distributions between different treatment groups even under completely randomized experiments. Not surprisingly, such covariate imbalances also occur in randomized survey experiments. Furthermore, the covariate imbalances happen not only between different treatment groups, but also between the sampled experimental units and the overall population of interest. In this article, we propose a two-stage rerandomization design that can actively avoid undesirable covariate imbalances at both the sampling and treatment assignment stages. We further develop asymptotic theory for rerandomized survey experiments, demonstrating that rerandomization provides better covariate balance, more precise treatment effect estimators, and shorter large-sample confidence intervals. We also propose covariate adjustment to deal with remaining covariate imbalances after rerandomization, showing that it can further improve both the sampling and estimated precision. Our work allows general relationship among covariates at the sampling, treatment assignment and analysis stages, and generalizes both rerandomization in classical randomized experiments and rejective sampling in survey sampling. [ABSTRACT FROM AUTHOR]

Adaptive collection of data is commonplace in applications throughout science and engineering. From the point of view of statistical inference, however, adaptive data collection induces memory and correlation in the samples, and poses significant challenge. We consider the high-dimensional linear regression, where the samples are collected adaptively, and the sample size n can be smaller than p, the number of covariates. In this setting, there are two distinct sources of bias: the first due to regularization imposed for consistent estimation, for example, using the LASSO, and the second due to adaptivity in collecting the samples. We propose "online debiasing," a general procedure for estimators such as the LASSO, which addresses both sources of bias. In two concrete contexts (i) time series analysis and (ii) batched data collection, we demonstrate that online debiasing optimally debiases the LASSO estimate when the underlying parameter θ0 has sparsity of order o (n / log p) . In this regime, the debiased estimator can be used to compute p-values and confidence intervals of optimal size. [ABSTRACT FROM AUTHOR]

Estimating treatment effects for survival outcomes in the high-dimensional setting is critical for many biomedical applications and any application with censored observations. This article establishes an "orthogonal" score for learning treatment effects, using observational data with a potentially large number of confounders. The estimator allows for root-n, asymptotically valid confidence intervals, despite the bias induced by the regularization. Moreover, we develop a novel hazard difference (HDi), estimator. We establish rate double robustness through the cross-fitting formulation. Numerical experiments illustrate the finite sample performance, where we observe that the cross-fitted HDi estimator has the best performance. We study the radical prostatectomy's effect on conservative prostate cancer management through the SEER-Medicare linked data. Last, we provide an extension to machine learning both approaches and heterogeneous treatment effects. for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous confidence regions for the differences of population mean vectors. It is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a natural feature in relevant applications, we are able to provide dimension-free and nearly parametric convergence rates for Gaussian approximation, bootstrap approximation, and the size of the test. We demonstrate the proposed approach with ANOVA problems for functional data and sparse count data. The proposed methodology is shown to work well in simulations and several real data applications. [ABSTRACT FROM AUTHOR]

Fusion learning refers to synthesizing inferences from multiple sources or studies to make a more effective inference and prediction than from any individual source or study alone. Most existing methods for synthesizing inferences rely on parametric model assumptions, such as normality, which often do not hold in practice. We propose a general nonparametric fusion learning framework for synthesizing inferences for multiparameters from different studies. The main tool underlying the proposed framework is the new notion of depth confidence distribution (depth-CD), which is developed by combining data depth and confidence distribution. Broadly speaking, a depth-CD is a data-driven nonparametric summary distribution of the available inferential information for a target parameter. We show that a depth-CD is a powerful inferential tool and, moreover, is an omnibus form of confidence regions, whose contours of level sets shrink toward the true parameter value. The proposed fusion learning approach combines depth-CDs from the individual studies, with each depth-CD constructed by nonparametric bootstrap and data depth. The approach is shown to be efficient, general and robust. Specifically, it achieves high-order accuracy and Bahadur efficiency under suitably chosen combining elements. It allows the model or inference structure to be different among individual studies. And, it readily adapts to heterogeneous studies with a broad range of complex and irregular settings. This last property enables the approach to use indirect evidence from incomplete studies to gain efficiency for the overall inference. We develop the theoretical support for the proposed approach, and we also illustrate the approach in making combined inference for the common mean vector and correlation coefficient from several studies. The numerical results from simulated studies show the approach to be less biased and more efficient than the traditional approaches in nonnormal settings. The advantages of the approach are also demonstrated in a Federal Aviation Administration study of aircraft landing performance. for this article are available online. [ABSTRACT FROM AUTHOR]

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for the estimated signal trajectories. We establish the estimation optimality and selection consistency of kernel ODE under both the low-dimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. Our proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA as well. We demonstrate the efficacy of our method through numerous ODE examples. [ABSTRACT FROM AUTHOR]

With undersmoothing, the bias can be made asymptotically disappear, providing a confidence region for I g i in terms of the supremum distance, which can readily induce an asymptotically valid confidence interval for Graph HT ht . Then Graph HT ht stands for the posterior expectation of a function Graph HT ht of I i . A more general, but admittedly somewhat abstract, process of enlarging a credible region is given by Graph HT ht of a credible region I D SB n sb i for I f SB G sb i , where I SB n sb i is the posterior contraction rate for I f SB G sb i with respect to a distance I d i , and I M i > 0 is a sufficiently large constant. [Extracted from the article]

6.2 Heteroscedasticity, Dependence, and Computation Xie and Stephens raise the issue of heteroscedasticity: Do the proposed methods extend for example, to the setting with Graph HT ht , where the noise variance Graph HT ht varies from unit to unit? In Section 5 we demonstrate a choice of Graph HT ht in the Poisson problem with smoothness, as suggested by Efron. Construct an I F i -localization Graph HT ht . [Extracted from the article]

Further suppose that the distribution of I Z SB i sb i has a density Graph HT ht for some Graph HT ht . However, a confidence interval for Graph HT ht is not a confidence interval for I SB i sb i . We say this interval procedure has I constant coverage i , in the sense that Graph HT ht is constant as a function of Graph HT ht . [Extracted from the article]

That is, replacing the Graph HT ht matrix in (2) with a known diagonal matrix. We wonder whether this issue is related to the theoretical results showing that Graph HT ht estimates converge extremely slowly? In particular Graph HT ht is discontinuous as prior mass moves from near 0 to exactly 0. Thus one should not expect Graph HT ht values to be estimated precisely. [Extracted from the article]

In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of when and why empirical Bayes point estimates accurately recover oracle Bayes behavior. In this paper, we develop flexible and practical confidence intervals that provide asymptotic frequentist coverage of empirical Bayes estimands, such as the posterior mean or the local false sign rate. The coverage statements hold even when the estimands are only partially identified or when empirical Bayes point estimates converge very slowly. for this article are available online. [ABSTRACT FROM AUTHOR]

This article proposes an innovative method for constructing confidence intervals and assessing p-values in statistical inference for high-dimensional linear models. The proposed method has successfully broken the high-dimensional inference problem into a series of low-dimensional inference problems: For each regression coefficient βi, the confidence interval and p-value are computed by regressing on a subset of variables selected according to the conditional independence relations between the corresponding variable Xi and other variables. Since the subset of variables forms a Markov neighborhood of Xi in the Markov network formed by all the variables X 1 , X 2 , ... , X p , the proposed method is coined as Markov neighborhood regression (MNR). The proposed method is tested on high-dimensional linear, logistic, and Cox regression. The numerical results indicate that the proposed method significantly outperforms the existing ones. Based on the MNR, a method of learning causal structures for high-dimensional linear models is proposed and applied to identification of drug sensitive genes and cancer driver genes. The idea of using conditional independence relations for dimension reduction is general and potentially can be extended to other high-dimensional or big data problems as well. for this article are available online. [ABSTRACT FROM AUTHOR]

Nearest-neighbor matching is a popular nonparametric tool to create balance between treatment and control groups in observational studies. As a preprocessing step before regression, matching reduces the dependence on parametric modeling assumptions. In current empirical practice, however, the matching step is often ignored in the calculation of standard errors and confidence intervals. In this article, we show that ignoring the matching step results in asymptotically valid standard errors if matching is done without replacement and the regression model is correctly specified relative to the population regression function of the outcome variable on the treatment variable and all the covariates used for matching. However, standard errors that ignore the matching step are not valid if matching is conducted with replacement or, more crucially, if the second step regression model is misspecified in the sense indicated above. Moreover, correct specification of the regression model is not required for consistent estimation of treatment effects with matched data. We show that two easily implementable alternatives produce approximations to the distribution of the post-matching estimator that are robust to misspecification. A simulation study and an empirical example demonstrate the empirical relevance of our results. for this article are available online. [ABSTRACT FROM AUTHOR]

There is a growing expectation that data collected by government-funded studies should be openly available to ensure research reproducibility, which also increases concerns about data privacy. A strategy to protect individuals' identity is to release multiply imputed (MI) synthetic datasets with masked sensitivity values. However, information loss or incorrectly specified imputation models can weaken or invalidate the inferences obtained from the MI-datasets. We propose a new masking framework with a data-augmentation (DA) component and a tuning mechanism that balances protecting identity disclosure against preserving data utility. Applying it to a restricted-use Canadian Scleroderma Research Group (CSRG) dataset, we found that this DA-MI strategy achieved a 0% identity disclosure risk and preserved all inferential conclusions. It yielded 95% confidence intervals (CIs) that had overlaps of 98.5% (95.5%) on average with the CIs constructed using the full, unmasked CSRG dataset in a work-disability (interstitial lung disease) study. The CI-overlaps were lower for several other methods considered, ranging from 73.9% to 91.9% on average with the lowest value being 28.1%; such low CI-overlaps further led to some incorrect inferential conclusions. These findings indicate that the DA-MI masking framework facilitates sharing of useful research data while protecting participants' identities. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

We develop a unified theory and methodology for the inference of evolutionary Fourier power spectra for a general class of locally stationary and possibly nonlinear processes. In particular, simultaneous confidence regions (SCR) with asymptotically correct coverage rates are constructed for the evolutionary spectral densities on a nearly optimally dense grid of the joint time-frequency domain. A simulation based bootstrap method is proposed to implement the SCR. The SCR enables researchers and practitioners to visually evaluate the magnitude and pattern of the evolutionary power spectra with asymptotically accurate statistical guarantee. The SCR also serves as a unified tool for a wide range of statistical inference problems in time-frequency analysis ranging from tests for white noise, stationarity and time-frequency separability to the validation for non-stationary linear models. [ABSTRACT FROM AUTHOR]

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Here we study the problem of estimating the density of an arbitrary subgraph, given a noisy version of some underlying network as data. Under a simple model of network error, we show that consistent estimation of such densities is impossible when the rates of error are unknown and only a single network is observed. Accordingly, we develop method-of-moment estimators of network subgraph densities and error rates for the case where a minimal number of network replicates are available. These estimators are shown to be asymptotically normal as the number of vertices increases to infinity. We also provide confidence intervals for quantifying the uncertainty in these estimates based on the asymptotic normality. To construct the confidence intervals, a new and nonstandard bootstrap method is proposed to compute asymptotic variances, which is infeasible otherwise. We illustrate the proposed methods in the context of gene coexpression networks. for this article are available online. [ABSTRACT FROM AUTHOR]

One of the properties of such nonparametric classes is that they are broad enough, so misspecification of Graph HT ht stops being an issue. The present paper studies much more narrow choices of Graph HT ht . The latter also highlights what choices of Graph HT ht is most appropriate. [Extracted from the article]

In this article, we develop a new estimation and valid inference method for single or low-dimensional regression coefficients in high-dimensional generalized linear models. The number of the predictors is allowed to grow exponentially fast with respect to the sample size. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the selected variables. The proposed confidence interval (CI) achieves valid coverage without assuming consistency of the model selection procedure. When the selection consistency is achieved, we show the length of the proposed CI is asymptotically the same as the CI of the "oracle" method which works as well as if the support of the control variables were known. In addition, we prove the proposed CI is asymptotically narrower than the CIs constructed based on the desparsified Lasso estimator and the decorrelated score statistic. Simulation studies and real data applications are presented to back up our theoretical findings. for this article are available online. [ABSTRACT FROM AUTHOR]

Valid inference after model selection is currently a very active area of research. The polyhedral method, introduced in an article by Lee et al., allows for valid inference after model selection if the model selection event can be described by polyhedral constraints. In that reference, the method is exemplified by constructing two valid confidence intervals when the Lasso estimator is used to select a model. We here study the length of these intervals. For one of these confidence intervals, which is easier to compute, we find that its expected length is always infinite. For the other of these confidence intervals, whose computation is more demanding, we give a necessary and sufficient condition for its expected length to be infinite. In simulations, we find that this sufficient condition is typically satisfied, unless the selected model includes almost all or almost none of the available regressors. For the distribution of confidence interval length, we find that the κ-quantiles behave like 1 / (1 − κ) for κ close to 1. Our results can also be used to analyze other confidence intervals that are based on the polyhedral method. [ABSTRACT FROM AUTHOR]

We derive new variance formulas for inference on a general class of estimands of causal average treatment effects in a randomized control trial. We generalize the seminal work of Robins and show that when the researcher's objective is inference on sample average treatment effect of the treated (SATT), a consistent variance estimator exists. Although this estimand is equal to the sample average treatment effect (SATE) in expectation, potentially large differences in both accuracy and coverage can occur by the change of estimand, even asymptotically. Inference on SATE, even using a conservative confidence interval, provides incorrect coverage of SATT. We demonstrate the applicability of the new theoretical results using an empirical application with hundreds of online experiments with an average sample size of approximately 100 million observations per experiment. An R package, estCI, that implements all the proposed estimation procedures is available. for this article are available online. [ABSTRACT FROM AUTHOR]

Abstract–Detection and attribution of climate change plays a central role in establishing the causal relationship between the observed changes in the climate and their possible causes. Optimal fingerprinting has been widely used as a standard method for detection and attribution analysis for mean climate conditions, but there has been no satisfactory analog for climate extremes. Here, we turn an intuitive concept, which incorporates the expected climate responses to external forcings into the location parameters of the marginal generalized extreme value (GEV) distributions of the observed extremes, to a practical and better-understood method. Marginal approaches based on a weighted sum of marginal GEV score equations are promising for no need to specify the dependence structure. The computational efficiency makes them feasible in handling multiple forcings simultaneously. The method under working independence is recommended because it produces robust results where there are errors-in-variables. Our analyses show human influences on temperature extremes at the subcontinental scale. Compared with previous studies, we detected human influences in a slightly smaller number of regions. This is possibly due to the under-coverage of the confidence intervals in existing works, suggesting the need for careful examinations of the properties of the statistical methods in practice. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

The book "Confidence Intervals for Discrete Data in Clinical Research" by Vivek Pradhan, Ashis K. Gangopadhyay, Sandeep M. Menon, Cynthia Basu, and Tathagata Banerjee argues that significance testing is overemphasized and that data analysts should focus more on analyses using confidence intervals. The book provides a comprehensive overview of various methods for calculating confidence intervals for discrete data, including those based on asymptotic versions of tests, exact versions using small-sample discrete distributions, and small-sample methods with conditional and unconditional approaches. The authors also discuss frequentist and Bayesian approaches and provide examples and instructions for obtaining results using software such as SAS and StatXact. However, the book has some limitations, such as the lack of detail in certain methods and the omission of the odds ratio. Overall, it is a valuable resource for researchers interested in analyzing contingency tables and comparing the performance of different methods. [Extracted from the article]

Scientists use high-dimensional measurement assays to detect and prioritize regions of strong signal in spatially organized domain. Examples include finding methylation-enriched genomic regions using microarrays, and active cortical areas using brain-imaging. The most common procedure for detecting potential regions is to group neighboring sites where the signal passed a threshold. However, one needs to account for the selection bias induced by this procedure to avoid diminishing effects when generalizing to a population. This article introduces pin-down inference, a model and an inference framework that permit population inference for these detected regions. Pin-down inference provides nonasymptotic point and confidence interval estimators for the mean effect in the region that account for local selection bias. Our estimators accommodate nonstationary covariances that are typical of these data, allowing researchers to better compare regions of different sizes and correlation structures. Inference is provided within a conditional one-parameter exponential family per region, with truncations that match the selection constraints. A secondary screening-and-adjustment step allows pruning the set of detected regions, while controlling the false-coverage rate over the reported regions. We apply the method to genomic regions with differing DNA-methylation rates across tissue. Our method provides superior power compared to other conditional and nonparametric approaches. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

This work proposes new inference methods for a regression coefficient of interest in a (heterogenous) quantile regression model. We consider a high-dimensional model where the number of regressors potentially exceeds the sample size but a subset of them suffices to construct a reasonable approximation to the conditional quantile function. The proposed methods are (explicitly or implicitly) based on orthogonal score functions that protect against moderate model selection mistakes, which are often inevitable in the approximately sparse model considered in the present article. We establish the uniform validity of the proposed confidence regions for the quantile regression coefficient. Importantly, these methods directly apply to more than one variable and a continuum of quantile indices. In addition, the performance of the proposed methods is illustrated through Monte Carlo experiments and an empirical example, dealing with risk factors in childhood malnutrition. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We consider inference about tail properties of a distribution from an iid sample, based on extreme value theory. All of the numerous previous suggestions rely on asymptotics where eventually, an infinite number of observations from the tail behave as predicted by extreme value theory, enabling the consistent estimation of the key tail index, and the construction of confidence intervals using the delta method or other classic approaches. In small samples, however, extreme value theory might well provide good approximations for only a relatively small number of tail observations. To accommodate this concern, we develop asymptotically valid confidence intervals for high quantile and tail conditional expectations that only require extreme value theory to hold for the largestkobservations, for a given and fixedk. Small-sample simulations show that these “fixed-k” intervals have excellent small-sample coverage properties, and we illustrate their use with mainland U.S. hurricane data. In addition, we provide an analytical result about the additional asymptotic robustness of the fixed-kapproach compared tokn→ ∞ inference. [ABSTRACT FROM PUBLISHER]

Randomized experiments on social networks pose statistical challenges, due to the possibility of interference between units. We propose new methods for finding confidence intervals on the attributable treatment effect in such settings. The methods do not require partial interference, but instead require an identifying assumption that is similar to requiring nonnegative treatment effects. Network or spatial information can be used to customize the test statistic; in principle, this can increase power without making assumptions on the data-generating process. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We introduce new point-wise confidence interval estimates for monotone functions observed with additive, dependent noise. Our methodology applies to both short- and long-range dependence regimes for the errors. The interval estimates are obtained via the method of inversion of certain discrepancy statistics. This approach avoids the estimation of nuisance parameters such as the derivative of the unknown function, which previous methods are forced to deal with. The resulting estimates are therefore more accurate, stable, and widely applicable in practice under minimal assumptions on the trend and error structure. The dependence of the errors especially long-range dependence leads to new phenomena, where new universal limits based on convex minorant functionals of drifted fractional Brownian motion emerge. Some extensions to uniform confidence bands are also developed. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

It has been more than half a century since Tukey first introduced graphical displays that relate nonoverlap of confidence intervals to statistically significant differences between parameter estimates. In this article, we show how Tukey’s graphical overlap procedure can be modified to accommodate general forms of dependence within and across samples. We also develop a procedure that can be used to more effectively resolve rankings within the tails of the distributions of parameter values, thereby generalizing existing methods for “multiple comparisons with the best.” We show that these new procedures retain the simplicity of Tukey’s original procedure, while maintaining asymptotic control of the familywise error rate under very general conditions. Simple examples are used throughout to illustrate the procedures. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]