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通过约束似然重建高斯有向无环图AI 解读

Directed acyclic graphs are widely used to describe directional pairwise relations. Such relations are estimated by reconstructing a directed acyclic graph's structure, which is challenging when the ordering of nodes of the graph is unknown. In such a situation, existing methods such as the neighbourhood and search-and-score methods have high estimation errors or computational complexities, especially when a local or sequential approach is used to enumerate edge directions…

利用隐马尔可夫模型 knockoff 变量寻找关联基因AI 解读

Modern scientific studies often require the identification of a subset of explanatory variables. Several statistical methods have been developed to automate this task, and the framework of knockoffs has been proposed as a general solution for variable selection under rigorous Type I error control, without relying on strong modelling assumptions. In this paper, we extend the methodology of knockoffs to problems where the distribution of the covariates can be described by a…

中介分析中的主层可忽略性：贯通并超越序贯可忽略性AI 解读

In causal mediation analysis, the definitions of the natural direct and indirect effects involve potential outcomes that can never be observed, so-called a priori counterfactuals. This conceptual challenge translates into issues in identification, which requires strong and often unverifiable assumptions, including sequential ignorability. Alternatively, we can deal with post-treatment variables using the principal stratification framework, where causal effects are defined as…

统计稀疏性AI 解读

The main contribution of this paper is a mathematical definition of statistical sparsity, which is expressed as a limiting property of a sequence of probability distributions. The limit is characterized by an exceedance measure |$H$| and a rate parameter |$\rho > 0$|⁠, both of which are unrelated to sample size. The definition encompasses all sparsity models that have been suggested in the signal-detection literature. Sparsity implies that |$\rho$| is small, and a sparse…

变平面Cox模型AI 解读

We propose a projection pursuit technique in survival analysis for finding lower-dimensional projections that exhibit differentiated survival outcome. This idea is formally introduced as the change-plane Cox model, a non-regular Cox model with a change-plane in the covariate space dividing the population into two subgroups whose hazards are proportional. The proposed technique offers a potential framework for principled subgroup discovery. Estimation of the change-plane is…

不定时间跨度下动态治疗方案的构建AI 解读

Existing methods for estimating optimal dynamic treatment regimes are limited to cases where a utility function is optimized over a fixed time period. We develop an estimation procedure for the optimal dynamic treatment regime over an indefinite time period and derive associated large-sample results. The proposed method can be used to estimate the optimal dynamic treatment regime in chronic disease settings. We illustrate this by simulating a dataset corresponding to a…

累积风险估计的尺度变换AI 解读

Time-to-event outcomes are often evaluated on the hazard scale, but interpreting hazards may be difficult. Recently in the causal inference literature concerns have been raised that hazards actually have a built-in selection bias that prevents simple causal interpretations. This is a problem even in randomized controlled trials, where hazard ratios have become a standard measure of treatment effects. Modelling on the hazard scale is nevertheless convenient, for example to…

异方差误差下惩罚分位数回归的野生残差自助推断AI 解读

We consider a heteroscedastic regression model in which some of the regression coefficients are zero but it is not known which ones. Penalized quantile regression is a useful approach for analysing such data. By allowing different covariates to be relevant for modelling conditional quantile functions at different quantile levels, it provides a more complete picture of the conditional distribution of a response variable than mean regression. Existing work on penalized…

利用未观测混杂因素的代理变量识别因果效应AI 解读

We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the confounder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl…

网络相关结果下的模型辅助实验设计AI 解读

In this paper we consider how to assign treatment in a randomized experiment in which the correlation among the outcomes is informed by a network available pre-intervention. Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes. We use these models to develop restricted randomization strategies for allocating treatment optimally, by minimizing the mean squared error of the estimated…

配对实验中平均处理效应的回归辅助推断AI 解读

In paired randomized experiments individuals in a given matched pair may differ on prognostically important covariates despite the best efforts of practitioners. We examine the use of regression adjustment as a way to correct for persistent covariate imbalances after randomization, and present two regression assisted estimators for the sample average treatment effect in paired experiments. Using the potential outcomes framework, we prove that these estimators are consistent…

高维稀疏切片逆回归的凸优化表述AI 解读

Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the covariates. The estimated linear combinations include all covariates, making results difficult to interpret and perhaps unnecessarily variable, particularly when the number of covariates is large. In this paper, we propose a convex…

多维函数型数据弱可分性的检验及其脑连接研究应用AI 解读

This paper concerns the modelling of multi-way functional data where double or multiple indices are involved. We introduce a concept of weak separability. The weakly separable structure supports the use of factorization methods that decompose the signal into its spatial and temporal components. The analysis reveals interesting connections to the usual strongly separable covariance structure, and provides insights into tensor methods for multi-way functional data. We propose…

通过函数型线性回归模型平均进行函数预测AI 解读

Prediction is often the primary goal of data analysis. In this work, we propose a novel model averaging approach to the prediction of a functional response variable. We develop a crossvalidation model averaging estimator based on functional linear regression models in which the response and the covariate are both treated as random functions. We show that the weights chosen by the method are asymptotically optimal in the sense that the squared error loss of the predicted…

线性回归模型选择后推断的自助法方案AI 解读

We propose a general bootstrap recipe for estimating the distributions of post-model-selection least squares estimators under a linear regression model. The recipe constrains residual bootstrapping within the most parsimonious, approximately correct, models to yield a distribution estimator which is consistent provided any wrong candidate model is sufficiently separated from the approximately correct ones. Our theory applies to a broad class of model selection methods based…

局部平稳小波时间序列中无混叠或局部白噪声的检验AI 解读

Aliasing is often overlooked in time series analysis but can seriously distort the spectrum, the autocovariance and their estimates.We show that dyadic subsampling of a locally stationary wavelet process, which can cause aliasing, results in a process that is the sum of asymptotic white noise and another locally stationary wavelet process with a modified spectrum.We develop a test for the absence of aliasing in a locally stationary wavelet series at a fixed location, and…

利用平方根套索进行未知方差下的选择后推断AI 解读

There has been much recent work on inference after model selection in situations where the noise level is known. However, the error variance is rarely known in practice and its estimation is difficult in high-dimensional settings. In this work we propose using the square-root lasso, also known as the scaled lasso, to perform inference for selected coefficients and the noise level simultaneously. The square-root lasso has the property that the choice of a reasonable tuning…

泊松过程强度的连续检验：扫描统计量的新视角AI 解读

We propose a continuous testing framework to test the intensities of Poisson processes that allows a rigorous definition of the complete testing procedure, from an infinite number of hypotheses to joint error rates. Our work extends procedures based on scanning windows by controlling the familywise error rate and the false discovery rate in a non-asymptotic manner and in a continuous way. We introduce the p-value process on which the decision rule is based. Our method is…

高维自协方差矩阵的Durbin–Levinson正则化估计AI 解读

The autocovariance matrix of a stationary random process plays a central role in prediction theory and time series analysis. When the dimension of the matrix is of the same order of magnitude as the number of observations, the sample autocovariance matrix gives an inconsistent estimator. In the nonparametric framework, recent proposals have concentrated on banding and tapering the sample autocovariance matrix. We introduce an alternative approach via a modified…

序贯回归程序何时选入第一个无关变量？AI 解读

Applied statisticians use sequential regression procedures to rank explanatory variables and, in settings of low correlations between variables and strong true effect sizes, expect that variables at the top of this ranking are truly relevant to the response. In a regime of certain sparsity levels, however, we show that the lasso, forward stepwise regression, and least angle regression include the first spurious variable unexpectedly early. We derive a sharp prediction of the…

β-混合随机向量极端依赖的结构突变检验AI 解读

We derive a structural break test for extremal dependence in |$\beta$|-mixing, possibly high-dimensional random vectors with either asymptotically dependent or asymptotically independent components. Existing tests require serially independent observations with asymptotically dependent components. To avoid estimating a long-run variance, we use self-normalization, which obviates the need to estimate the coefficient of tail dependence when components are asymptotically…

粒子滤波中的方差估计AI 解读

SummaryThis paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances of a number of Monte Carlo approximations that particle filters deliver. All our estimators can be computed from a single run of a particle filter. We establish that, as the number of particles grows, our estimators are weakly…

高维超阈值极值推断AI 解读

Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. |${r}$|-Pareto processes are mathematically simpler and have the potential advantage of incorporating all relevant extreme events, by generalizing the notion of a univariate exceedance. In this paper we investigate the use of proper scoring rules for high-dimensional…

对称秩协方差：非参数依赖度量的广义框架AI 解读

The need to test whether two random vectors are independent has spawned many competing measures of dependence. We focus on nonparametric measures that are invariant under strictly increasing transformations, such as Kendall’s tau, Hoeffding’s |$D$|⁠, and the Bergsma–Dassios sign covariance. Each exhibits symmetries that are not readily apparent from their definitions. Making these symmetries explicit, we define a new class of multivariate nonparametric measures of dependence…