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用于高维回归分析的非参数Box–Cox模型AI 解读

The mainstream theory for high-dimensional regression assumes that the underlying true model is a low-dimensional linear regression model. On the other hand, a standard technique in regression analysis, even in the traditional low-dimensional setting, is to employ the Box–Cox transformation for reducing anomalies such as non-additivity and heteroscedasticity in linear regression. In this paper, we propose a new high-dimensional regression method based on a nonparametric…

挖掘因子动物园：借助充分代理变量估计潜在因子模型AI 解读

Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the former approach may suffer from the bias while the latter cannot incorporate additional information. We propose to bridge these two approaches while allowing the number of factor proxies to diverge, and hence make the latent factor model…

基于自协方差的高维函数型时间序列学习框架AI 解读

Many scientific and economic applications involve the statistical learning of high-dimensional functional time series, where the number of functional variables is comparable to, or even greater than, the number of serially dependent functional observations. In this paper, we model observed functional time series, which are subject to errors in the sense that each functional datum arises as the sum of two uncorrelated components, one dynamic and one white noise. Motivated…

异质事件发生时间数据的潜在类别 Cox 模型AI 解读

Credit risk plays a vital role in the era of digital finance and it is one of primary interests to identify customers with similar types of risk categories so that personalized financial services can be offered accordingly. Motivated by the bourgeoning need for default risk modeling in finance, we propose herein a latent class Cox model for heterogeneous time-to-event data. The proposed model naturally extends the Cox proportional hazards model to flexibly take into account…

时变最小方差投资组合AI 解读

This paper proposes a new time-varying minimum variance portfolio (TV-MVP) in a large investment universe of assets. Our method extends the existing literature on minimum variance portfolios by allowing for time-varying factor loadings, which facilitates the capture of the dynamics of the covariance structure of asset returns (and hence, the optimal investment strategy in a dynamic setting). We also use a shrinkage estimation method based on a quasi-likelihood function to…

结构变化检测中控制错误发现率的广义Knockoff程序AI 解读

Controlling false discovery rate (FDR) is crucial for variable selection, multiple testing, among other signal detection problems. In literature, there is certainly no shortage of FDR control strategies when selecting individual features, but the relevant works for structural change detection, such as profile analysis for piecewise constant coefficients and integration analysis with multiple data sources, are limited. In this paper, we propose a generalized knockoff…

超高维投资组合选择的资产拆分算法及其理论性质AI 解读

The presence of a huge number of assets poses challenges to classical portfolio selection algorithms. Constrained l1 minimization approaches have been proposed to directly estimate effective parameters in the optimal portfolio. Linear programming method and alternating direction method of multiplier (ADMM) algorithm is used to solve the corresponding minimization problems. However, these two algorithms may fail due to the limitations of computing time and computing memory…

大型时空自回归的稀疏广义 Yule–Walker 估计：卫星二氧化氮数据应用AI 解读

We consider a high-dimensional model in which variables are observed over time and space. The model consists of a spatio-temporal regression containing a time lag and a spatial lag of the dependent variable. Unlike classical spatial autoregressive models, we do not rely on a predetermined spatial interaction matrix, but infer all spatial interactions from the data. Assuming sparsity, we estimate the spatial and temporal dependence fully data-driven by penalizing a set of…

识别材料基因的算子诱导结构变量选择AI 解读

In the emerging field of materials informatics, a fundamental task is to identify physicochemically meaningful descriptors, or materials genes, which are engineered from primary features and a set of elementary algebraic operators through compositions. Standard practice directly analyzes the high-dimensional candidate predictor space in a linear model; statistical analyses are then substantially hampered by the daunting challenge posed by the astronomically large number of…

广义线性模型中均值与离散度的稳健建模及推断AI 解读

Generalized Linear Models (GLMs) are a popular class of regression models when the responses follow a distribution in the exponential family. In real data the variability often deviates from the relation imposed by the exponential family distribution, which results in over- or underdispersion. Dispersion effects may even vary in the data. Such datasets do not follow the traditional GLM distributional assumptions, leading to unreliable inference. Therefore, the family of…

网络上的系数异质性学习：基于生成树的分布式融合套索回归AI 解读

Identifying the latent cluster structure based on model heterogeneity is a fundamental but challenging task arises in many machine learning applications. In this article, we study the clustered coefficient regression problem in the distributed network systems, where the data are locally collected and held by nodes. Our work aims to improve the regression estimation efficiency by aggregating the neighbors’ information while also identifying the cluster membership for nodes.…

系数阈值化的稳健高维回归及影像数据应用AI 解读

It is important to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible heavy tails and outliers in real-world applications such as imaging data analyses. We propose a new robust high-dimensional regression with coefficient thresholding, in which an efficient nonconvex estimation procedure is proposed through a thresholding function and the robust Huber loss. The proposed regularization method accounts for…

个体化资产配置的统计学习AI 解读

We establish a high-dimensional statistical learning framework for individualized asset allocation. Our proposed methodology addresses continuous-action decision-making with a large number of characteristics. We develop a discretization approach to model the effect of continuous actions and allow the discretization frequency to be large and diverge with the number of observations. We estimate the value function of continuous-action using penalized regression with our…

弱模型假设下的Cox回归AI 解读

Inference for the conditional association between an exposure and a time-to-event endpoint, given covariates, is routinely based on partial likelihood estimators for hazard ratios indexing Cox proportional hazards models. This approach is flexible and makes testing straightforward, but is nonetheless not entirely satisfactory. First, there is no good understanding of what it infers when the model is misspecified. Second, it is common to employ variable selection procedures…

离散数据的加性图模型AI 解读

We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three-way statistical relation that shares similar properties with conditional independence by satisfying the semi-graphoid axioms. Based on this relation we build an additive graphical model for discrete variables that does not suffer from the restriction of a parametric model such as the Ising model. We develop an…

充分降维中兼具自动维数与变量选择的子空间估计AI 解读

Sufficient dimension reduction (SDR) methods target finding lower-dimensional representations of a multivariate predictor to preserve all the information about the conditional distribution of the response given the predictor. The reduction is commonly achieved by projecting the predictor onto a low-dimensional subspace. The smallest such subspace is known as the Central Subspace (CS) and is the key parameter of interest for most SDR methods. In this article, we propose a…

高维动态主成分分析AI 解读

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of variables p is comparable to, or much larger than the sample size n. Despite an extensive literature on this topic, researchers have focused on modeling static principal eigenvectors, which are not suitable for stochastic processes that are…

内存约束下最优的单遍非参数估计AI 解读

For nonparametric regression in the streaming setting, where data constantly flow in and require real-time analysis, a main challenge is that data are cleared from the computer system once processed due to limited computer memory and storage. We tackle the challenge by proposing a novel one-pass estimator based on penalized orthogonal basis expansions and developing a general framework to study the interplay between statistical efficiency and memory consumption of…

多重二元响应的低秩回归及其癌症细胞系百科数据应用AI 解读

In this paper, we study high-dimensional multivariate logistic regression models in which a common set of covariates is used to predict multiple binary outcomes simultaneously. Our work is primarily motivated from many biomedical studies with correlated multiple responses such as the cancer cell-line encyclopedia project. We assume that the underlying regression coefficient matrix is simultaneously low-rank and row-wise sparse. We propose an intuitively appealing selection…

重尾密度估计AI 解读

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk. The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularization through a carefully specified semiparametric prior…

高维模型的双向同时推断AI 解读

This article proposes a general two-directional simultaneous inference (TOSI) framework for high-dimensional models with a manifest variable or latent variable structure, for example, high-dimensional mean models, high-dimensional sparse regression models, and high-dimensional latent factors models. TOSI performs simultaneous inference on a set of parameters from two directions, one to test whether the assumed zero parameters indeed are zeros and one to test whether exist…

基于惩罚 Tobit 似然的高维删失回归AI 解读

High-dimensional regression and regression with a left-censored response are each well-studied topics. In spite of this, few methods have been proposed which deal with both of these complications simultaneously. The Tobit model—long the standard method for censored regression in economics—has not been adapted for high-dimensional regression at all. To fill this gap and bring up-to-date techniques from high-dimensional statistics to the field of high-dimensional left-censored…

高维潜在中介变量下广义中介模型的估计与检验AI 解读

Motivated by an empirical analysis of stock reaction to COVID-19 pandemic, we propose a generalized mediation model with high-dimensional potential mediators to study the mediation effects of financial metrics that bridge company’s sector and stock value. We propose an estimation procedure for the direct effect via a partial penalized maximum likelihood method and establish its theoretical properties. We develop a Wald test for the indirect effect and show that the proposed…

高维面板数据模型的同质性与稀疏性分析AI 解读

In this article, we are interested in detecting latent group structures and significant covariates in a high-dimensional panel data model with both individual and time fixed effects. The slope coefficients of the model are assumed to be subject dependent, and there exist group structures where the slope coefficients are homogeneous within groups and heterogeneous between groups. We develop a penalized estimator for recovering the group structures and the sparsity patterns…