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半参数因果推断中的 Cp 模型选择准则AI 解读

Summary For marginal structural models, which play an important role in causal inference, we consider a model selection problem within a semiparametric framework using inverse-probability-weighted estimation or doubly robust estimation. In this framework, the modelling target is a potential outcome that may be missing, so there is no classical information criterion. We define a mean squared error for treating the potential outcome and derive an asymptotic unbiased estimator…

高维情形下的分布无关独立性检验AI 解读

We consider the testing of mutual independence among all entries in a $d$-dimensional random vector based on $n$ independent observations. We study two families of distribution-free test statistics, which include Kendall’s tau and Spearman’s rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and we propose tests that control the Type I error in the high-dimensional setting where…

病例对照研究中复杂多基因与环境交互作用的半参数分析AI 解读

Many methods have recently been proposed for efficient analysis of case-control studies of gene-environment interactions using a retrospective likelihood framework that exploits the natural assumption of gene-environment independence in the underlying population. However, for polygenic modelling of gene-environment interactions, which is a topic of increasing scientific interest, applications of retrospective methods have been limited due to a requirement in the literature…

贝叶斯局部极值样条AI 解读

Summary We consider shape-restricted nonparametric regression on a closed set $\mathcal{X} \subset \mathbb{R},$ where it is reasonable to assume that the function has no more than $H$ local extrema interior to $\mathcal{X}$. Following a Bayesian approach we develop a nonparametric prior over a novel class of local extremum splines. This approach is shown to be consistent when modelling any continuously differentiable function within the class considered, and we use itto…

两个随机向量之间的投影相关AI 解读

We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We…

具有依赖结构的广义函数型线性模型AI 解读

This paper considers testing for no effect of functional covariates on response variables in multivariate regression. We use generalized estimating equations to determine the underlying parameters and establish their joint asymptotic normality. This is then used to test the significance of the effect of predictors on the vector of response variables. Simulations demonstrate the importance of considering existing correlation structures in the data. To explore the effect of…

多数据流中的最优序贯检测AI 解读

Consider a large number of detectors each generating a data stream. The task is to detect online, distribution changes in a small fraction of the data streams. Previous approaches to this problem include the use of mixture likelihood ratios and sum of CUSUMs. We provide here extensions and modifications of these approaches that are optimal in detecting normal mean shifts. We show how the (optimal) detection delay depends on the fraction of data streams undergoing…

多个稀疏高斯图模型的结构相似性与差异检验AI 解读

We present a new framework on inferring structural similarities and differences among multiple high-dimensional Gaussian graphical models (GGMs) corresponding to the same set of variables under distinct experimental conditions. The new framework adopts the partial correlation coefficients to characterize the potential changes of dependency strengths between two variables. A hierarchical method has been further developed to recover edges with different or similar dependency…

高维广义线性模型的权重放松模型平均AI 解读

Model averaging has long been proposed as a powerful alternative to model selection in regression analysis. However, how well it performs in high-dimensional regression is still poorly understood. Recently, Ando and Li [J. Amer. Statist. Assoc. 109 (2014) 254–265] introduced a new method of model averaging that allows the number of predictors to increase as the sample size increases. One notable feature of Ando and Li’s method is the relaxation on the total model weights so…

扩展条件独立及其在因果推断中的应用AI 解读

The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions the calculus that applies for the two cases separately (axioms of a separoid) still applies for the extended case. These results provide a rigorous basis for a wide range of statistical concepts, including ancillarity and sufficiency, and,…

一致随机序的非参数拟合优度检验AI 解读

We propose $L^{p}$ distance-based goodness-of-fit (GOF) tests for uniform stochastic ordering with two continuous distributions $F$ and $G$, both of which are unknown. Our tests are motivated by the fact that when $F$ and $G$ are uniformly stochastically ordered, the ordinal dominance curve $R=FG^{-1}$ is star-shaped. We derive asymptotic distributions and prove that our testing procedure has a unique least favorable configuration of $F$ and $G$ for $p\in [1,\infty]$. We use…

最优治疗规则及其平均回报推断的靶向序贯设计AI 解读

, assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adaptive statistical parameter is worthy of interest on its own. Our main result is a central limit theorem which enables the…

高斯白噪声模型中的自适应Bernstein–von Mises定理AI 解读

We investigate Bernstein–von Mises theorems for adaptive nonparametric Bayesian procedures in the canonical Gaussian white noise model. We consider both a Hilbert space and multiscale setting with applications in $L^{2}$ and $L^{\infty}$, respectively. This provides a theoretical justification for plug-in procedures, for example the use of certain credible sets for sufficiently smooth linear functionals. We use this general approach to construct optimal frequentist…

利用循环近正交阵列进行 fMRI 实验最优设计AI 解读

Functional magnetic resonance imaging (fMRI) is a pioneering technology for studying brain activity in response to mental stimuli. Although efficient designs on these fMRI experiments are important for rendering precise statistical inference on brain functions, they are not systematically constructed. Design with circulant property is crucial for estimating a hemodynamic response function (HRF) and discussing fMRI experimental optimality. In this paper, we develop a theory…

LASSO 与近似消息传递的参数一致估计AI 解读

This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as $n$, the…

长记忆下重抽样方法的有效性AI 解读

For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However, due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to…

高维半参数回归的似然比推断框架AI 解读

We propose a new inferential framework for high-dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high-dimensional data analysis, including incomplete data, selection bias and heterogeneity. Our work has three main contributions: (i) We develop a regularized statistical chromatography approach to infer the parameter of interest under the proposed semiparametric generalized linear model without the need of…

主成分数量选择：含噪矩阵真实秩的估计AI 解读

Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of principal components. In order to address this challenge, we propose distribution-based methods with exact type 1 error controls for hypothesis testing and construction of confidence intervals for signals in a noisy matrix with finite samples. Assuming Gaussian noise, we derive exact type 1 error controls based on the…

CoCoLasso：协变量含测量误差的高维回归AI 解读

Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright [Ann. Statist. 40 (2012) 1637–1664] proposed a nonconvex modification of the Lasso for doing high-dimensional regression with noisy and missing data. It is generally agreed that the virtues of convexity contribute fundamentally the success…

自助法迭代的离散模型AI 解读

The bootstrap can be validated by considering the sequence of P values obtained by bootstrap iteration, rather than asymptotically. If this sequence converges to a random variable with the uniform U(0,1) distribution, the bootstrap is valid. Here, the model is made discrete and finite, characterised by a three-dimensional array of probabilities. This renders bootstrap iteration to any desired order feasible. A unit-root test for a process driven by a stationary MA(1) process…

含温和爆炸性回归量的连续系统推断AI 解读

New limit theory is developed for co-moving systems with explosive processes, connecting continuous and discrete time formulations. The theory uses double asymptotics with infill (as the sampling interval tends to zero) and large time span asymptotics. The limit theory explicitly involves initial conditions, allows for drift in the system, is provided for single and multiple explosive regressors, and is feasible to implement in practice. Simulations show that double…

利用因子模型进行充分预测AI 解读

We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive…

私人类型相关的二元博弈：模型相容性与识别AI 解读

This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for type correlation is crucial in global games and in models with social interactions as it represents correlated private information and homophily, respectively. Our approach is fully nonparametric in the joint distribution of types and the strategic effects in the payoffs. First, under monotone pure Bayesian Nash Equilibrium strategy, we…

通过目标化实现高效两步估计AI 解读

The standard description of two-step extremum estimation amounts to plugging-in a first-step estimator of nuisance parameters to simplify the optimization problem and then deducing a user friendly, but potentially inefficient, estimator for the parameters of interest. In this paper, we consider a more general setting of two-step estimation where we do not necessarily have ‘nuisance parameters’ but rather awkward occurrences of the parameters of interest. The efficiency…