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大规模数据的结构化潜因子分析：可识别性、可估性及其含义AI 解读

–Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. When used in a confirmatory manner, design information is incorporated as zero constraints on corresponding parameters, yielding structured (confirmatory) latent factor models. In this article, we study how such design information affects the identifiability and the estimation of a structured latent factor model.…

不对可观测数据施加额外限制的灵活观察性研究敏感性分析AI 解读

A fundamental challenge in observational causal inference is that assumptions about unconfoundedness are not testable from data. Assessing sensitivity to such assumptions is therefore important in practice. Unfortunately, some existing sensitivity analysis approaches inadvertently impose restrictions that are at odds with modern causal inference methods, which emphasize flexible models for observed data. To address this issue, we propose a framework that allows (1) flexible…

非参数推断的偏差界方法AI 解读

Abstract The traditional approach to obtain valid confidence intervals for non-parametric quantities is to select a smoothing parameter such that the bias of the estimator is negligible relative to its standard deviation. While this approach is apparently simple, it has two drawbacks: first, the question of optimal bandwidth selection is no longer well-defined, as it is not clear what ratio of bias to standard deviation should be considered negligible. Second, since the…

ℓ₁惩罚稳健估计量的渐近风险与相变AI 解读

Mean square error (MSE) of the estimator can be used to evaluate the performance of a regression model. In this paper, we derive the asymptotic MSE of $l_{1}$-penalized robust estimators in the limit of both sample size $n$ and dimension $p$ going to infinity with fixed ratio $n/p\rightarrow \delta $. We focus on the $l_{1}$-penalized least absolute deviation and $l_{1}$-penalized Huber’s regressions. Our analytic study shows the appearance of a sharp phase transition in the…

耦合条件后向抽样粒子滤波器AI 解读

The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous theoretical results have not been able to demonstrate the improvement brought by backward sampling, whereas we provide rates showing that CBPF can remain effective with a fixed number of particles independent of the time horizon. Our result…

Modern data-driven approaches to modeling make extensive use of covariate/model selection. Such selection incurs a cost: it invalidates classical statistical inference. A conservative remedy to the problem was proposed by Berk et al. (Ann. Statist. 41 (2013) 802–837) and further extended by Bachoc, Preinerstorfer and Steinberger (2016). These proposals, labeled “PoSI methods,” provide valid inference after arbitrary model selection. They are computationally NP-hard and have…

受控序贯 Monte CarloAI 解读

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in statistics and related fields; for example, for inference in nonlinear non-Gaussian state space models, and in complex static models. Like many Monte Carlo sampling schemes, they rely on proposal distributions which crucially impact their…

基于几何图的两样本检验：渐近分布与检测阈值AI 解读

In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum spanning tree and the $K$-nearest neighbor (NN) graphs, among others. These tests are asymptotically distribution-free, universally consistent and computationally efficient, making them particularly useful in modern applications. However,…

哪种桥估计量最适合变量选择？AI 解读

We study the problem of variable selection for linear models under the high-dimensional asymptotic setting, where the number of observations $n$ grows at the same rate as the number of predictors $p$. We consider two-stage variable selection techniques (TVS) in which the first stage uses bridge estimators to obtain an estimate of the regression coefficients, and the second stage simply thresholds this estimate to select the “important” predictors. The asymptotic false…

基于自归一化的高维时间序列假设检验AI 解读

Self-normalization has attracted considerable attention in the recent literature of time series analysis, but its scope of applicability has been limited to low-/fixed-dimensional parameters for low-dimensional time series. In this article, we propose a new formulation of self-normalization for inference about the mean of high-dimensional stationary processes. Our original test statistic is a U-statistic with a trimming parameter to remove the bias caused by weak dependence.…

多元 Hawkes 过程的非参数贝叶斯估计AI 解读

This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First, rates are derived for $\mathbb{L}_{1}$-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the $\mathbb{L}_{1}$-norm of interactions functions of the process. Our results are exemplified by using priors based on piecewise constant functions, with regular or random…

希尔伯特空间值响应的加性回归AI 解读

This paper develops a foundation of methodology and theory for the estimation of structured nonparametric regression models with Hilbertian responses. Our method and theory are focused on the additive model, while the main ideas may be adapted to other structured models. For this, the notion of Bochner integration is introduced for Banach-space-valued maps as a generalization of Lebesgue integration. Several statistical properties of Bochner integrals, relevant for our…

马尔可夫过程的极小极大最优序贯假设检验AI 解读

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses is revisited, and it is shown that the partial derivatives of the corresponding cost function are closely related to the performance metrics of the underlying sequential test. Second, an implicit characterization of the least favorable…

社群识别中均值场变分推断的理论与计算保证AI 解读

The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative coordinate ascent variational inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method, there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been…

函数型时间序列平稳性的频域检验AI 解读

Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier…

半参数贝叶斯因果推断AI 解读

We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently, we estimate the causal effect of a treatment, correcting nonparametrically for confounding. We show that standard Gaussian process priors satisfy a semiparametric Bernstein–von Mises theorem under smoothness conditions. We further propose a novel propensity score-dependent prior that…

高集中度下球面位置参数的推断AI 解读

Motivated by the fact that circular or spherical data are often much concentrated around a location $\pmb{\theta }$, we consider inference about $\pmb{\theta }$ under high concentration asymptotic scenarios for which the probability of any fixed spherical cap centered at $\pmb{\theta }$ converges to one as the sample size $n$ diverges to infinity. Rather than restricting to Fisher–von Mises–Langevin distributions, we consider a much broader, semiparametric, class of…

因子分析与主成分分析中的置换方法AI 解读

Researchers often have datasets measuring features $x_{ij}$ of samples, such as test scores of students. In factor analysis and PCA, these features are thought to be influenced by unobserved factors, such as skills. Can we determine how many components affect the data? This is an important problem, because decisions made here have a large impact on all downstream data analysis. Consequently, many approaches have been developed. Parallel Analysis is a popular permutation…

高维纵向数据的显著性检验AI 解读

This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic…

尖峰与厚尾经验贝叶斯多重检验AI 解读

This paper explores a connection between empirical Bayes posterior distributions and false discovery rate (FDR) control. In the Gaussian sequence model this work shows that empirical Bayes-calibrated spike and slab posterior distributions allow a correct FDR control under sparsity. Doing so, it offers a frequentist theoretical validation of empirical Bayes methods in the context of multiple testing. Our theoretical results are illustrated with numerical experiments.

回应讨论AI 解读

We thank the discussants for their insightful comments. We agree with many of the points they raise, and especially welcome their thoughts on directions for future work. Here, we elaborate one point that these discussions led us to think more about. As Bonhomme notes, the audience plays a central role in our analysis, and as all discussants note, so does the nature of disagreement and uncertainty about the researcher’s assumptions. Some assumptions are what Leamer (1983)…

基于局部投影的预测误差方差分解AI 解读

We propose and study properties of an estimator of the forecast error variance decomposition in the local projections framework. We find for empirically relevant sample sizes that, after being bias-corrected with bootstrap, our estimator performs well in simulations. We also illustrate the workings of our estimator empirically for monetary policy and productivity shocks. KEYWORDS: Forecast error variance decomposition; Local projections.

基于最小对比的密度不连续性经验似然推断AI 解读

This article investigates the asymptotic properties of a simple empirical-likelihood-based inference method for discontinuity in density. The parameter of interest is a function of two one-sided limits of the probability density function at (possibly) two cut-off points. Our approach is based on the first-order conditions from a minimum contrast problem. We investigate both first-order and second-order properties of the proposed method. We characterize the leading coverage…

多条计数时间序列的贝叶斯预测AI 解读

We develop and exemplify application of new classes of dynamic models for time series of nonnegative counts. Our novel univariate models combine dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models estimate dynamic regression coefficients in both binary and nonzero count components. Sequential Bayesian analysis allows fast, parallel analysis of sets of decoupled time series. New…