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动态交互半参数函数对标量回归模型AI 解读

Motivated by recent work studying massive functional data, such as the COVID-19 data, we propose a new dynamic interaction semiparametric function-on-scalar (DISeF) model. The proposed model is useful to explore the dynamic interaction among a set of covariates and their effects on the functional response. The proposed model includes many important models investigated recently as special cases. By tensor product B-spline approximating the unknown bivariate coefficient…

凸性约束单指标模型中的半参数效率AI 解读

We consider estimation and inference in a single-index regression model with an unknown convex link function. We introduce a convex and Lipschitz constrained least-square estimator (CLSE) for both the parametric and the nonparametric components given independent and identically distributed observations. We prove the consistency and find the rates of convergence of the CLSE when the errors are assumed to have only q≥2 moments and are allowed to depend on the covariates. When…

基于谱主体特征值匹配的协方差尖峰特征值数量估计AI 解读

The spiked covariance model has gained increasing popularity in high-dimensional data analysis. A fundamental problem is determination of the number of spiked eigenvalues, K. For estimation of K, most attention has focused on the use of top eigenvalues of sample covariance matrix, and there is little investigation into proper ways of using bulk eigenvalues to estimate K. We propose a principled approach to incorporating bulk eigenvalues in the estimation of K. Our method…

通过投影与收缩构造高维回归的诚实置信集AI 解读

The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level often happens after estimating the degree of smoothness. Similarly, for high-dimensional regression, oracle inequalities for sparse estimators could be utilized to construct sharp confidence sets. Yet the degree of sparsity itself is…

广义 Oaxaca–Blinder 估计量AI 解读

After performing a randomized experiment, researchers often use ordinary least-square (OLS) regression to adjust for baseline covariates when estimating the average treatment effect. It is widely known that the resulting confidence interval is valid even if the linear model is misspecified. In this article, we generalize that conclusion to covariate adjustment with nonlinear models. We introduce an intuitive way to use any “simple” nonlinear model to construct a…

随机梯度下降中的在线协方差矩阵估计AI 解读

The stochastic gradient descent (SGD) algorithm is widely used for parameter estimation, especially for huge datasets and online learning. While this recursive algorithm is popular for computation and memory efficiency, quantifying variability and randomness of the solutions has been rarely studied. This article aims at conducting statistical inference of SGD-based estimates in an online setting. In particular, we propose a fully online estimator for the covariance matrix of…

分布单指标模型AI 解读

A Distributional (Single) Index Model (DIM) is a semiparametric model for distributional regression, that is, estimation of conditional distributions given covariates. The method is a combination of classical single-index models for the estimation of the conditional mean of a response given covariates, and isotonic distributional regression. The model for the index is parametric, whereas the conditional distributions are estimated nonparametrically under a stochastic…

部分观测动态张量响应回归AI 解读

In modern data science, dynamic tensor data prevail in numerous applications. An important task is to characterize the relationship between dynamic tensor datasets and external covariates. However, the tensor data are often only partially observed, rendering many existing methods inapplicable. In this article, we develop a regression model with a partially observed dynamic tensor as the response and external covariates as the predictor. We introduce the low-rankness,…

用于嵌套数据贝叶斯非参数分析的共同原子模型AI 解读

The use of large datasets for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed for inference on nested datasets, where the observations are assumed to be organized in different units and some sharing of information is required to learn distinctive features of the units. In this manuscript, we propose a nested common atoms…

高维最优治疗规则的模型辅助一致诚实推断AI 解读

This article develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions…

用于排序聚合的分组–Mallows 模型及其推断AI 解读

Learning how to aggregate ranking lists has been an active research area for many years and its advances have played a vital role in many applications ranging from bioinformatics to internet commerce. The problem of discerning reliability of rankers based only on the rank data is of great interest to many practitioners, but has received less attention from researchers. By dividing the ranked entities into two disjoint groups, that is, relevant and irrelevant/background ones,…

利用未来曲线部分观测的函数时间序列预测AI 解读

–This article tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only completely observed trajectories. We develop a new method, called partial functional prediction (PFP), which uses both completely observed trajectories and partial information (available partial data) on the trajectory to be predicted. The PFP…

通过 Thompson 抽样进行变量选择AI 解读

–Thompson sampling is a heuristic algorithm for the multi-armed bandit problem which has a long tradition in machine learning. The algorithm has a Bayesian spirit in the sense that it selects arms based on posterior samples of reward probabilities of each arm. By forging a connection between combinatorial binary bandits and spike-and-slab variable selection, we propose a stochastic optimization approach to subset selection called Thompson variable selection (TVS). TVS is a…

条件函数型图模型AI 解读

Graphical modeling of multivariate functional data is becoming increasingly important in a wide variety of applications. The changes of graph structure can often be attributed to external variables, such as the diagnosis status or time, the latter of which gives rise to the problem of dynamic graphical modeling. Most existing methods focus on estimating the graph by aggregating samples, but largely ignore the subject-level heterogeneity due to the external variables. In this…

连续处理的断点回归设计AI 解读

The standard regression discontinuity (RD) design deals with a binary treatment. Many empirical applications of RD designs involve continuous treatments. This article establishes identification and robust bias-corrected inference for such RD designs. Causal identification is achieved by using any changes in the distribution of the continuous treatment at the RD threshold (including the usual mean change as a special case). We discuss a double-robust identification approach…

利用高斯镜像控制错误发现率AI 解读

Simultaneously, finding multiple influential variables and controlling the false discovery rate (FDR) for linear regression models is a fundamental problem. We here propose the Gaussian Mirror (GM) method, which creates for each predictor variable a pair of mirror variables by adding and subtracting a randomly generated Gaussian perturbation, and proceeds with a certain regression method, such as the ordinary least-square or the Lasso (the mirror variables can also be…

个体化治疗规则的实验评估AI 解读

The increasing availability of individual-level data has led to numerous applications of individualized (or personalized) treatment rules (ITRs). Policy makers often wish to empirically evaluate ITRs and compare their relative performance before implementing them in a target population. We propose a new evaluation metric, the population average prescriptive effect (PAPE). The PAPE compares the performance of ITR with that of non-individualized treatment rule, which randomly…

基于测度输运的多元秩无分布非参数检验AI 解读

In this article, we propose a general framework for distribution-free nonparametric testing in multi-dimensions, based on a notion of multivariate ranks defined using the theory of measure transportation. Unlike other existing proposals in the literature, these multivariate ranks share a number of useful properties with the usual one-dimensional ranks; most importantly, these ranks are distribution-free. This crucial observation allows us to design nonparametric tests that…

基于 Bootstrap 的高维多元方差分析及函数与稀疏计数数据应用AI 解读

We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous confidence regions for the differences of population mean vectors. It is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a…

在保持错误发现率控制的同时筛选拒绝集合AI 解读

Scientific hypotheses in a variety of applications have domain-specific structures, such as the tree structure of the international classification of diseases (ICD), the directed acyclic graph structure of the gene ontology (GO), or the spatial structure in genome-wide association studies. In the context of multiple testing, the resulting relationships among hypotheses can create redundancies among rejections that hinder interpretability. This leads to the practice of…

高斯随机场的线性计算成本协方差函数AI 解读

Gaussian random fields (GRF) are a fundamental stochastic model for spatiotemporal data analysis. An essential ingredient of GRF is the covariance function that characterizes the joint Gaussian distribution of the field. Commonly used covariance functions give rise to fully dense and unstructured covariance matrices, for which required calculations are notoriously expensive to carry out for large data. In this work, we propose a construction of covariance functions that…

基于分位数的众数回归自助法推断AI 解读

In this article, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop two bootstrap methods, a novel pivotal bootstrap and the nonparametric bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian…

《使用 R 的半参数回归》AI 解读

Semiparametric Regression with R by Harezlak, Ruppert, and Wand is a truly heroic book! To many of us, statistics can be roughly dichotomized into parametric and nonparametric. Semiparametric stati...

函数型混合效应聚类及其在纵向泌尿系统慢性盆腔疼痛症状数据中的应用AI 解读

By clustering patients with the urologic chronic pelvic pain syndromes (UCPPS) into homogeneous subgroups and associating these subgroups with baseline covariates and other clinical outcomes, we provide opportunities to investigate different potential elements of pathogenesis, which may also guide us in selection of appropriate therapeutic targets. Motivated by the longitudinal urologic symptom data with extensive subject heterogeneity and differential variability of…