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插补调查数据的伪总体自助法AI 解读

The most common way to treat item nonresponse in surveys is to replace a missing value by a plausible value constructed on the basis of fully observed variables. Treating the imputed values as if they were observed may lead to invalid inferences. Bootstrap variance estimators for various finite population parameters are obtained using two pseudo-population bootstrap schemes. We establish the asymptotic properties of the resulting bootstrap variance estimators for population…

一般贝叶斯更新与损失似然自助法AI 解读

In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined through minimizing an expected negative loglikelihood under an unknown sampling distribution. This interpretation enables us to extend the weighted likelihood bootstrap to posterior…

干扰下因果效应的随机化检验AI 解读

Many causal questions involve interactions between units, also known as interference, for example between individuals in households, students in schools, or firms in markets. In this paper we formalize the concept of a conditioning mechanism, which provides a framework for constructing valid and powerful randomization tests under general forms of interference. We describe our framework in the context of two-stage randomized designs and apply our approach to a randomized…

广义错误控制下序贯多重检验的渐近最优性理论AI 解读

The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_{1}$ false positives and at least $k_{2}$ false negatives are simultaneously controlled. For each formulation, the optimal expected sample size is characterized, to a first-order asymptotic approximation as the error probabilities go to 0, and a…

通过广义信赖推断进行高维线性模型的非惩罚变量选择AI 解读

Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design matrix is collinear. To overcome this challenge, an entirely new perspective on variable selection is presented within a generalized fiducial inference framework. This new procedure is able to effectively account for linear dependencies…

Wiener 泛函最大值的高斯近似及高频数据应用AI 解读

This paper establishes an upper bound for the Kolmogorov distance between the maximum of a high-dimensional vector of smooth Wiener functionals and the maximum of a Gaussian random vector. As a special case, we show that the maximum of multiple Wiener–Itô integrals with common orders is well approximated by its Gaussian analog in terms of the Kolmogorov distance if their covariance matrices are close to each other and the maximum of the fourth cumulants of the multiple…

多来源合并数据的大样本理论AI 解读

We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not identified and (3) a sample from the same data source is dependent due to sampling without replacement. We propose and study a new weighted empirical process and extend empirical process theory to a dependent and biased sample with…

基于稀疏充分降维的稳健高效因果推断AI 解读

A fundamental assumption used in causal inference with observational data is that treatment assignment is ignorable given measured confounding variables. This assumption of no missing confounders is plausible if a large number of baseline covariates are included in the analysis, as we often have no prior knowledge of which variables can be important confounders. Thus, estimation of treatment effects with a large number of covariates has received considerable attention in…

模型选择后预测器的有效置信区间AI 解读

We consider inference post-model-selection in linear regression. In this setting, Berk et al. [Ann. Statist. 41 (2013a) 802–837] recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain nonstandard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this paper, we generalize the PoSI intervals to confidence intervals for post-model-selection…

高维均值的两样本与 ANOVA 检验AI 解读

This paper considers testing the equality of two high dimensional means. Two approaches are utilized to formulate $L_{2}$-type tests for better power performance when the two high dimensional mean vectors differ only in sparsely populated coordinates and the differences are faint. One is to conduct thresholding to remove the nonsignal bearing dimensions for variance reduction of the test statistics. The other is to transform the data via the precision matrix for signal…

高斯有序模型选择中的自助法调参AI 解读

The paper focuses on the problem of model selection in linear Gaussian regression with unknown possibly inhomogeneous noise. For a given family of linear estimators $\{\widetilde{\boldsymbol{{\theta}}}_{m},m\in\mathscr{M}\}$, ordered by their variance, we offer a new “smallest accepted” approach motivated by Lepski’s device and the multiple testing idea. The procedure selects the smallest model which satisfies the acceptance rule based on comparison with all larger models.…

Zig-Zag 过程与大数据贝叶斯分析的超高效抽样AI 解读

Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We introduce a new family of Monte Carlo methods based upon a multidimensional version of the Zig-Zag process of [Ann. Appl. Probab. 27 (2017)…

因果 Dantzig：加性干预下含隐藏变量线性结构方程模型的快速推断AI 解读

Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number of causal predictors. It was recently shown in Peters, Bühlmann and Meinshausen (2016) (J. R. Stat. Soc. Ser. B. Stat. Methodol. 78 947–1012) that causal inference for the full model is possible when data from distinct observational…

分位数回归过程的分布式推断AI 解读

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parallel computing environment; (ii) construct a conditional quantile regression process through projection based on these estimated…

路径图的极大似然阈值AI 解读

Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and bidirected edges that indicate possible correlations among noise terms. Using this graphical representation, we determine the maximum likelihood threshold, that is, the minimum sample size at which the likelihood function of a Gaussian…

分位数回归折点设计的因果推断AI 解读

The quantile regression kink design (QRKD) is proposed by empirical researchers, but its causal interpretation remains unknown. We show that the QRKD estimand measures a weighted average of heterogeneous marginal effects at respective conditional quantiles of outcome given a designed kink point. We also derive limit processes for the QRKD estimator to conduct statistical inference on heterogeneous treatment effects using the QRKD. Applying our methods to the Continuous Wage…

倾向得分的设定检验AI 解读

This paper proposes new nonparametric diagnostic tools to assess the asymptotic validity of different treatment effects estimators that rely on the correct specification of the propensity score. We derive a particular restriction relating the propensity score distribution of treated and control groups, and develop specification tests based upon it. The resulting tests do not suffer from the “curse of dimensionality” when the vector of covariates is high-dimensional, are…

一阶退化下的泛函推断AI 解读

This paper presents a unified framework for inference on parameters of the form ϕ(θ0), where θ0 is unknown but can be estimated by θˆn, and ϕ is known with null first order derivative at θ0. We show the “standard” bootstrap is consistent if and only if the second order derivative ϕθ0′′=0 under regularity conditions, thereby identifying a source of bootstrap failures distinct from that in Fang and Santos (2018). Two consistent bootstrap schemes are proposed: one based on Babu…

双重差分回归中简便可靠的渐近 t 检验AI 解读

We propose an asymptotically valid t test that uses Student’s t distribution as the reference distribution in a difference-in-differences regression. For the asymptotic variance estimation, we adopt the clustering-by-time approach to accommodate cross-sectional dependence. This approach often assumes the clusters to be independent across time, but we allow them to be temporally dependent. The proposed t test is based on a special heteroscedasticity and autocorrelation robust…

离散选择模型条件矩不等式的降维推断AI 解读

This paper studies inference of preference parameters in semiparametric discrete choice models when these parameters are not point-identified and the identified set is characterized by a class of conditional moment inequalities. Exploring the semiparametric modeling restrictions, we show that the identified set can be equivalently formulated by moment inequalities conditional on only two continuous indexing variables. Such formulation holds regardless of the covariate…

聚类样本的渐近理论AI 解读

We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix estimation. Our theory allows for clustered observations with heterogeneous and unbounded cluster sizes. Our conditions cleanly nest the classical results for i.n.i.d. observations, in the sense that our conditions specialize to the classical…

阈值回归模型的稳健推断AI 解读

This paper considers robust inference in threshold regression models when the practitioners do not know whether at the threshold point the true specification has a kink or a jump, nesting previous works that assume either continuity or discontinuity at the threshold. We find that the parameter values under the kink restriction are irregular points of the Hessian matrix, destroying the asymptotic normality and inducing the cube-root convergence rate for the threshold…

存在内生性时分位数处理效应的闭式估计AI 解读

This paper studies the estimation of quantile treatment effects based on the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2005). I develop a class of flexible plug-in estimators based on closed-form solutions derived from the IVQR moment conditions. The proposed estimators remain tractable and root-n-consistent, while allowing for rich patterns of effect heterogeneity. Functional central limit theorems and bootstrap validity results for…

利用离散样本估计连续时间随机过程的长期方差AI 解读

This paper develops the methodology and asymptotic theory for the estimation of longrun variance of continuous time process. We analyze the asymptotic bias and variance of the longrun variance estimator in continuous time, and provide the optimal bandwidth balancing them off and minimizing the asymptotic mean squared error. In the paper, we present not only how to consistently estimate the longrun variance of continuous time process, but also how to choose bandwidth…