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基于随机扰动的因子个数秩估计AI 解读

Summary We introduce a random-perturbation-based rank estimator of the number of factors of a large-dimensional approximate factor model. An expansion of the rank estimator demonstrates that the random perturbation reduces the biases due to the persistence of the factor series and the dependence between the factor and error series. A central limit theorem for the rank estimator with convergence rate higher than root $n$ gives a new hypothesis-testing procedure for both…

利用岭回归估计误差方差AI 解读

Summary We propose a novel estimator of error variance and establish its asymptotic properties based on ridge regression and random matrix theory. The proposed estimator is valid under both low- and high-dimensional models, and performs well not only in nonsparse cases, but also in sparse ones. The finite-sample performance of the proposed method is assessed through an intensive numerical study, which indicates that the method is promising compared with its competitors in…

函数型数据的条件均值独立性检验AI 解读

Summary We propose a new nonparametric conditional mean independence test for a response variable $Y$ and a predictor variable $X$ where either or both can be function-valued. Our test is built on a new metric, the so-called functional martingale difference divergence, which fully characterizes the conditional mean dependence of $Y$ given $X$ and extends the martingale difference divergence proposed by Shao & Zhang (2014). We define an unbiased estimator of functional…

受访者驱动抽样中树形自助法的一致性AI 解读

Summary Respondent-driven sampling is an approach for estimating features of populations that are difficult to access using standard survey tools, e.g., the fraction of injection drug users who are HIV positive. Baraff et al. (2016) introduced an approach to estimating uncertainty in population proportion estimates from respondent-driven sampling using the tree bootstrap method. In this paper we establish the consistency of this tree bootstrap approach in the case of $m$-tree…

随机对象的Fréchet方差分析AI 解读

Summary Fréchet mean and variance provide a way of obtaining a mean and variance for metric space-valued random variables, and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and operations. Examples of such data objects include covariance matrices, graph Laplacians of networks and univariate probability distribution functions. We derive a central limit theorem for the Fréchet variance under mild regularity…

利用辅助边际信息的序贯加性不可忽略缺失建模AI 解读

Summary We study a class of missingness mechanisms, referred to as sequentially additive nonignorable, for modelling multivariate data with item nonresponse. These mechanisms explicitly allow the probability of nonresponse for each variable to depend on the value of that variable, thereby representing nonignorable missingness mechanisms. These missing data models are identified by making use of auxiliary information on marginal distributions, such as marginal probabilities…

实验平台中任意干扰的检验AI 解读

Summary Experimentation platforms are essential to large modern technology companies, as they are used to carry out many randomized experiments daily. The classic assumption of no interference among users, under which the outcome for one user does not depend on the treatment assigned to other users, is rarely tenable on such platforms. Here, we introduce an experimental design strategy for testing whether this assumption holds. Our approach is in the spirit of the…

利用扩散映射与距离相关的网络依赖检验AI 解读

Summary Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high dimensionality of networks pose unique challenges to traditional dependency tests in terms of theoretical guarantees and empirical performance. We propose an approach to test network dependence via diffusion maps and distance-based correlations. We prove that the new method yields a consistent test statistic…

利用分段线性同伦快速精确构造 lasso 的共形预测集AI 解读

Summary Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set retains the good statistical properties of the original estimator under standard assumptions, and guarantees valid average coverage even when the model is mis-specified. A main challenge in applying conformal prediction in modern applications is efficient computation, as it generally requires an exhaustive search over the entire output space. In…

等方差假设下的因果发现AI 解读

Summary Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variance. We show that this fact is implied by an ordering among conditional variances. We demonstrate that ordering estimates of these variances yields a simple yet state-of-the-art method for causal structure learning that is readily extendable to high-dimensional problems.

混杂变量非随机缺失下的因果推断AI 解读

Summary It is important to draw causal inference from observational studies, but this becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. In this article we propose a novel framework for nonparametric identification of causal effects with confounders subject to an outcome-independent missingness, which means that the missing data mechanism is independent of the outcome, given…

大规模多重检验中所有假设子集的错误发现比例同时控制AI 解读

Summary Closed testing procedures are classically used for familywise error rate control, but they can also be used to obtain simultaneous confidence bounds for the false discovery proportion in all subsets of the hypotheses, allowing for inference robust to post hoc selection of subsets. In this paper we investigate the special case of closed testing with Simes local tests. We construct a novel fast and exact shortcut and use it to investigate the power of this approach…

局部平稳扩散过程的半参数分段 M 估计AI 解读

Summary We develop and implement a novel M-estimation method for locally stationary diffusions observed at discrete time-points. We give sufficient conditions for the local stationarity of general time-inhomogeneous diffusions. Then we focus on locally stationary diffusions with time-varying parameters, for which we define our M-estimators and derive their limit theory.

Tyler 形状深度AI 解读

Summary In many problems from multivariate analysis, the parameter of interest is a shape matrix: a normalized version of the corresponding scatter or dispersion matrix. In this article we propose a notion of depth for shape matrices that involves data points only through their directions from the centre of the distribution. We refer to this concept as Tyler shape depth since the resulting estimator of shape, namely the deepest shape matrix, is the median-based counterpart…

高维生物数据中不同可估程度的未观测协变量处理AI 解读

Summary An important phenomenon in high-throughput biological data is the presence of unobserved covariates that can have a significant impact on the measured response. When these covariates are also correlated with the covariate of interest, ignoring or improperly estimating them can lead to inaccurate estimates of and spurious inference on the corresponding coefficients of interest in a multivariate linear model. We first prove that existing methods to account for these…

高维谱统计量的自助法AI 解读

Summary Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of spectral statistics in low-dimensional problems, such methods are relatively unexplored in the high-dimensional setting. The aim of this article is to focus on linear spectral statistics as a class of prototypes for developing a…

通过统一偏斜正态分布实现 probit 回归的共轭贝叶斯推断AI 解读

Summary Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve as building blocks in more complex formulations, such as density regression, nonparametric classification and graphical models. Within the Bayesian framework, inference proceeds by updating the priors for the coefficients, typically taken to be Gaussians, with the likelihood induced by probit or logit regressions for the…

双重截断下非参数最大似然估计的存在性与唯一性AI 解读

Summary Doubly truncated survival data arise if failure times are observed only within certain time intervals. The nonparametric maximum likelihood estimator is widely used to estimate the underlying failure time distribution. Using a directed graph representation of the data suggested by Vardi (1985), a certain graphical condition holds if and only if the nonparametric maximum likelihood estimate exists and is unique. If this condition does not hold, then such an estimate…

信息性簇规模下多层模型的簇内重采样AI 解读

Summary A within-cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size. Our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster. We then estimate the parameters by maximizing an average, over the bootstrap samples, of a suitable composite loglikelihood. The consistency of the proposed estimator is…

贝叶斯刀切经验似然AI 解读

Summary Empirical likelihood is a very powerful nonparametric tool that does not require any distributional assumptions. Lazar (2003) showed that in Bayesian inference, if one replaces the usual likelihood with the empirical likelihood, then posterior inference is still valid when the functional of interest is a smooth function of the posterior mean. However, it is not clear whether similar conclusions can be obtained for parameters defined in terms of $U$-statistics. We…

通过扰动自助法实现 lasso 的分布一致性AI 解读

Summary The lasso is a popular estimation procedure in multiple linear regression. We develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model. We allow the underlying covariates to be either random or nonrandom, and show that the proposed bootstrap method works irrespective of the nature of the covariates. We also investigate finite-sample properties of the…

存在中介—结局混杂时路径特定效应的半参数估计AI 解读

Summary Path-specific effects constitute a broad class of mediated effects from an exposure to an outcome via one or more causal pathways along a set of intermediate variables. Most of the literature concerning estimation of mediated effects has focused on parametric models, with stringent assumptions regarding unmeasured confounding. We consider semiparametric inference of a path-specific effect when these assumptions are relaxed. In particular, we develop a suite of…

交叉随机效应模型的可扩展推断AI 解读

Summary We develop methodology and complexity theory for Markov chain Monte Carlo algorithms used in inference for crossed random effects models in modern analysis of variance. We consider a plain Gibbs sampler and propose a simple modification, referred to as a collapsed Gibbs sampler. Under some balancedness conditions on the data designs and assuming that precision hyperparameters are known, we demonstrate that the plain Gibbs sampler is not scalable, in the sense that…

连续时间过程中的结构失效时间模型半参数估计AI 解读

Summary Structural failure time models are causal models for estimating the effect of time-varying treatments on a survival outcome. G-estimation and artificial censoring have been proposed for estimating the model parameters in the presence of time-dependent confounding and administrative censoring. However, most existing methods require manually pre-processing data into regularly spaced data, which may invalidate the subsequent causal analysis. Moreover, the computation…