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基于包络模型的稀疏偏最小二乘AI 解读

Sparse partial least squares (SPLS) is widely used in applied sciences as a method that performs dimension reduction and variable selection simultaneously in linear regression. Several implementations of SPLS have been derived, among which the SPLS proposed in Chun and Keleş (J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25) is very popular and highly cited. However, for all of these implementations, the theoretical properties of SPLS are largely unknown. In this…

稀疏切片逆回归：最优收敛率与自适应估计AI 解读

Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the…

高维逻辑回归中最大似然估计存在性的相变AI 解读

This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp “phase transition.” We introduce an explicit boundary curve $h_{\mathrm{MLE}}$, parameterized by two scalars measuring the overall magnitude of the unknown sequence of regression coefficients, with the following property: in the limit of large sample sizes $n$ and number of features $p$ proporti…

两步半参数经验似然推断AI 解读

In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks’ theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks’ theorem breaks down. This article suggests a general approach to restore Wilks’ phenomenon in…

通过阈值化 Tyler M 估计量进行稳健稀疏协方差估计AI 解读

Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental task in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Toward bridging this gap, in this work we consider estimating a sparse shape matrix from $n$ samples following a possibly heavy-tailed elliptical distribution. We propose estimators based on thresholding either Tyler’s M-estimator or its regularized variant. We…

基于高频数据的高维最小方差组合估计AI 解读

This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators of the MVP and prove that our portfolios asymptotically achieve the minimum variance in a sharp sense. In addition, we introduce consistent estimators of the minimum variance, which…

对股票收益横截面进行收缩估计AI 解读

We construct a robust stochastic discount factor (SDF) summarizing the joint explanatory power of a large number of cross-sectional stock return predictors. Our method achieves robust out-of-sample performance in this high-dimensional setting by imposing an economically motivated prior on SDF coefficients that shrinks contributions of low-variance principal components of the candidate characteristics-based factors. We find that characteristics-sparse SDFs formed from a few…

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…

分布型数据的分位数函数对标量回归分析AI 解读

Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution…

惩罚与约束优化：高维网站广告中的应用AI 解读

Firms are increasingly transitioning advertising budgets to Internet display campaigns, but this transition poses new challenges. These campaigns use numerous potential metrics for success (e.g., reach or click rate), and because each website represents a separate advertising opportunity, this is also an inherently high-dimensional problem. Further, advertisers often have constraints they wish to place on their campaign, such as targeting specific sub-populations or…

L2RM：高维矩阵响应的低秩线性回归模型AI 解读

The aim of this paper is to develop a low-rank linear regression model (L2RM) to correlate a high-dimensional response matrix with a high dimensional vector of covariates when coefficient matrices have low-rank structures. We propose a fast and efficient screening procedure based on the spectral norm of each coefficient matrix in order to deal with the case when the number of covariates is extremely large. We develop an efficient estimation procedure based on the trace norm…

投影估计量的自由度及其在多元非参数回归中的应用AI 解读

–In this article, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as outputs of linearly constrained quadratic optimization procedures; namely, minimizers of the least-squares criterion with linear constraints and/or quadratic penalties. As special cases of our results, we derive explicit expressions for…

高维模型中处理效应的去偏推断AI 解读

This article concerns the potential bias in statistical inference on treatment effects when a large number of covariates are present in a linear or partially linear model. While the estimation bias in an under-fitted model is well understood, we address a lesser-known bias that arises from an over-fitted model. The over-fitting bias can be eliminated through data splitting at the cost of statistical efficiency, and we show that smoothing over random data splits can be…

利用电子健康记录优化个体化治疗策略的匹配学习AI 解读

Current guidelines for treatment decision making largely rely on data from randomized controlled trials (RCTs) studying average treatment effects. They may be inadequate to make individualized treatment decisions in real-world settings. Large-scale electronic health records (EHR) provide opportunities to fulfill the goals of personalized medicine and learn individualized treatment rules (ITRs) depending on patient-specific characteristics from real-world patient data. In…

基于断裂自适应岭回归的区间删失数据估计与变量选择AI 解读

The simultaneous estimation and variable selection for Cox model has been discussed by several authors (Fan and Li, 2002; Huang and Ma, 2010; Tibshirani, 1997) when one observes right-censored failure time data. However, there does not seem to exist an established procedure for interval-censored data, a more general and complex type of failure time data, except two parametric procedures given in Scolas et al. (2016) and Wu and Cook (2015). To address this, we propose a…

基于数据深度的非参数缺失值插补AI 解读

We present single imputation method for missing values which borrows the idea of data depth—a measure of centrality defined for an arbitrary point of a space with respect to a probability distribution or data cloud. This consists in iterative maximization of the depth of each observation with missing values, and can be employed with any properly defined statistical depth function. For each single iteration, imputation reverts to optimization of quadratic, linear, or…

PUlasso：仅有正例与未标记数据的高维变量选择AI 解读

In various real-world problems, we are presented with classification problems with positive and unlabeled data, referred to as presence-only responses. In this article we study variable selection in the context of presence only responses where the number of features or covariates p is large. The combination of presence-only responses and high dimensionality presents both statistical and computational challenges. In this article, we develop the PUlasso algorithm for variable…

D-CCA：面向高维数据集的分解式典型相关分析AI 解读

A typical approach to the joint analysis of two high-dimensional datasets is to decompose each data matrix into three parts: a low-rank common matrix that captures the shared information across datasets, a low-rank distinctive matrix that characterizes the individual information within a single dataset, and an additive noise matrix. Existing decomposition methods often focus on the orthogonality between the common and distinctive matrices, but inadequately consider the more…

RANK：基于图结构非线性 Knockoffs 的大规模推断AI 解读

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-X knockoffs procedure introduced recently in Candès, Fan, Janson and Lv (2018) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity…

高维约束最大似然推断AI 解读

Inference in a high-dimensional situation may involve regularization of a certain form to treat overparameterization, imposing challenges to inference. The common practice of inference uses either a regularized model, as in inference after model selection, or bias-reduction known as “debias.” While the first ignores statistical uncertainty inherent in regularization, the second reduces the bias inbred in regularization at the expense of increased variance. In this article,…

从距离相关到多尺度图相关AI 解读

Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we establish a new framework that generalizes distance correlation (Dcorr)—a correlation measure that was recently proposed and shown to be universally consistent for dependence testing against all joint distributions of finite moments—to the…

从固定设计到随机设计回归：偏差方差分解、协方差惩罚与预测误差估计AI 解读

In statistical prediction, classical approaches for model selection and model evaluation based on covariance penalties are still widely used. Most of the literature on this topic is based on what we call the “Fixed-X” assumption, where covariate values are assumed to be nonrandom. By contrast, it is often more reasonable to take a “Random-X” view, where the covariate values are independently drawn for both training and prediction. To study the applicability of covariance…

单指标模型平均偏效应的去偏推断：对Wooldridge与Zhu的评论AI 解读

There has recently been a considerable amount of interest in developing methods for statistical inference in high-dimensional regimes with more covariates than data points (Javanmard and Montanari ...

近似稀疏相关随机效应面板Probit模型的统计推断AI 解读

We propose a simple procedure based on an existing “debiased” l1-regularized method for inference of the average partial effects (APEs) in approximately sparse probit and fractional probit models with panel data, where the number of time periods is fixed and small relative to the number of cross-sectional observations. Our method is computationally simple and does not suffer from the incidental parameters problems that come from attempting to estimate as a parameter the…