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过参数化单指标模型中的隐式正则化AI 解读

In this paper, we leverage over-parameterization to design regularization-free algorithms for the high-dimensional single index model and provide theoretical guarantees for the induced implicit regularization phenomenon. Specifically, we study both vector and matrix single index models where the link function is nonlinear and unknown, the signal parameter is either a sparse vector or a low-rank symmetric matrix, and the response variable can be heavy-tailed. To gain a better…

企业违约概率：单指标风险率模型方法AI 解读

Corporate probability of default (PD) prediction is vitally important for risk management and asset pricing. In search of accurate PD prediction, we propose a flexible yet easy-to-interpret default-prediction single-index hazard model (DSI). By applying it to a comprehensive U.S. corporate bankruptcy database we constructed, we discover an interesting V-shaped relationship, indicating a violation of the common linear hazard specification. Most importantly, the single-index…

Google 数据何时有助于 GDP 即时预测？预筛选与收缩方法AI 解读

Alternative datasets are widely used for macroeconomic nowcasting together with machine learning–based tools. The latter are often applied without a complete picture of their theoretical nowcasting properties. Against this background, this article proposes a theoretically grounded nowcasting methodology that allows researchers to incorporate alternative Google Search Data (GSD) among the predictors and that combines targeted preselection, Ridge regularization, and…

异质数据逐分辨率回归的非参数预测分布AI 解读

Modeling and inference for heterogeneous data have gained great interest recently due to rapid developments in personalized marketing. Most existing regression approaches are based on the conditional mean and may require additional cluster information to accommodate data heterogeneity. In this paper, we propose a novel nonparametric resolution-wise regression procedure to provide an estimated distribution of the response instead of one single value. We achieve this by…

存在大量最高效率企业时的随机前沿 LASSO 估计AI 解读

We apply the adaptive LASSO to select a set of maximally efficient firms in the panel fixed-effect stochastic frontier model. The adaptively weighted L1 penalty with sign restrictions allows simultaneous selection of a group of maximally efficient firms and estimation of firm-level inefficiency parameters with a faster rate of convergence than least squares dummy variable estimators. Our estimator possesses the oracle property. We propose a tuning parameter selection…

一般高斯设计下的 Lasso 及其假设检验应用AI 解读

The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates p is of the same order or larger than the number of observations n. Classical asymptotic normality theory does not apply to this model due to two fundamental reasons: (1) The regularized risk is nonsmooth; (2) The distance between the estimator θˆ and the true parameters vector θ∗ cannot be neglected. As a consequence, standard perturbative arguments that are the…

广义线性模型中的结构化稀疏估计量AI 解读

In this paper, we introduce structured sparsity estimators for use in Generalized Linear Models. Structured sparsity estimators in the least squares loss are introduced by Stucky and van de Geer (2018). Their proofs exclusively depend on their use of fixed design and normal errors. We extend their results to debiased structured sparsity estimators with Generalized Linear Model based loss through incorporating random design and non-sub Gaussian data. Structured sparsity…

高频事件高维计数过程的无惩罚估计AI 解读

This paper introduces a counting process for event arrivals in high-frequency trading, based on high-dimensional covariates. The novelty is that, under sparsity conditions on the true model, we do not need to impose any model penalty or parameters shrinkage, unlike Lasso. The procedure allows us to derive a central limit theorem to test restrictions in a two-stage estimator. We achieve this by the use of a sign constraint on the intensity which necessarily needs to be…

陈云霄与徐恭军对《采用Varimax的经典因子分析可进行统计推断》的讨论AI 解读

We congratulate Rohe and Zeng for this insightful paper that elegantly connects psychometric methods and statistical and machine learning applications. We would like to mention several lines of related research. First, the problem is closely related to the latent variable selection problems (e.g., Y. Chen et al., 2015; Xu & Shang, 2018), where regularised estimation procedures are proposed to learn sparse loading structures. In fact, the vsp procedure can be viewed as the…

变系数非参数变换模型的模型选择AI 解读

Summary Based on the smoothed partial rank (SPR) loss function, we propose a group LASSO penalized SPR estimator for the varying coefficient nonparametric transformation models, and derive its estimation and model selection consistencies. It not only selects important variables, but is also able to select between varying and constant coefficients. To deal with the computational challenges in the rank loss function, we develop a group forward and backward stagewise algorithm…

仅用一阶滞后建模长记忆AI 解读

Two recent contributions have found conditions for large dimensional networks or systems to generate long memory in their individual components. We build on these and provide a multivariate methodology for modeling and forecasting series displaying long range dependence. We model long memory properties within a vector autoregressive system of order 1 and consider Bayesian estimation or ridge regression. For these, we derive a theory-driven parametric setting that informs a…

选择后推断中的分割策略AI 解读

Summary We consider the problem of providing valid inference for a selected parameter in a sparse regression setting. It is well known that classical regression tools can be unreliable in this context because of the bias generated in the selection step. Many approaches have been proposed in recent years to ensure inferential validity. In this article we consider a simple alternative to data splitting based on randomizing the response vector, which allows for higher selection…

利用阈值化 graphical lasso 处理潜变量AI 解读

Summary Structural learning of Gaussian graphical models in the presence of latent variables has long been a challenging problem. Chandrasekaran et al. (2012) proposed a convex program for estimating a sparse graph plus a low-rank term that adjusts for latent variables; however, this approach poses challenges from both computational and statistical perspectives. We propose an alternative, simple solution: apply a hard-thresholding operator to existing graph selection…

因子增强逆回归及其微生物组数据分析应用AI 解读

We investigate the relationship between count data that inform the relative abundance of features of a composition, and factors that influence the composition. Our work is motivated from microbiome studies aiming to extract microbial signatures that are predictive of host phenotypes based on data collected from a group of individuals harboring radically different microbial communities. We introduce multinomial Factor Augmented Inverse Regression (FAIR) of the count vector…

高维正则化回归估计量的普适性AI 解读

The Convex Gaussian Min–Max Theorem (CGMT) has emerged as a prominent theoretical tool for analyzing the precise stochastic behavior of various statistical estimators in the so-called high-dimensional proportional regime, where the sample size and the signal dimension are of the same order. However, a well-recognized limitation of the existing CGMT machinery rests in its stringent requirement on the exact Gaussianity of the design matrix, therefore rendering the obtained…

凸约束下含噪线性逆问题的高维精确风险渐近AI 解读

In the standard Gaussian linear measurement model Y=Xμ0+ξ∈Rm with a fixed noise level σ>0, we consider the problem of estimating the unknown signal μ0 under a convex constraint μ0∈K, where K is a closed convex set in Rn. We show that the risk of the natural convex constrained least squares estimator (LSE) μˆ(σ) can be characterized exactly in high-dimensional limits, by that of the convex constrained LSE μˆKseq in the corresponding Gaussian sequence model at a different…

信号去噪的交叉验证框架：趋势滤波、二分 CART 等应用AI 解读

This paper formulates a general cross-validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as trend filtering and dyadic CART. The resulting cross-validated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross-validated versions of trend filtering or dyadic CART. To illustrate the…

放宽独立同分布假设：通过平方根熵正则化实现自适应极小极大遗憾AI 解读

We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semi-adversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm—long known to be minimax (rate) optimal in the adversarial…

连接因子模型与稀疏模型AI 解读

Factor and sparse models are widely used to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a supervised learning methodology that allows for efficiently exploring all the information in high-dimensional datasets. The method is based on a flexible model for high-dimensional panel data with observable and/or latent common factors and idiosyncratic…

稀疏分位数回归AI 解读

We consider both ℓ0-penalized and ℓ0-constrained quantile regression estimators. For the ℓ0-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and apply it to obtain non-asymptotic upper bounds on the mean-square parameter and regression function estimation errors. We also derive analogous results for the ℓ0-constrained estimator. The resulting rates of convergence are nearly minimax-optimal and the same as…

第一价格拍卖模型的函数估计方法AI 解读

This paper introduces new methods of identification and estimation of the first-price sealed bid auction model and compares them with the previous existing ones. The first method of estimation allows us to estimate directly (through an iterative algorithm) the cumulative distribution function of the private values without estimating the private values beforehand. In the second method, we use a quantile approach. Although the first-price auction is a complex nonlinear inverse…

纵向数据惩罚分位数回归的野生 bootstrap 推断AI 解读

The existing theory of penalized quantile regression for longitudinal data has focused primarily on point estimation. In this work, we investigate statistical inference. We propose a wild residual bootstrap procedure and show that it is asymptotically valid for approximating the distribution of the penalized estimator. The model puts no restrictions on individual effects, and the estimator achieves consistency by letting the shrinkage decay in importance asymptotically. The…

集合识别线性模型的去偏机器学习AI 解读

This paper provides estimation and inference methods for an identified set’s boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample splitting ideas, I construct a root-N consistent, uniformly asymptotically Gaussian estimator of the boundary and propose a multiplier bootstrap procedure to…

面板数据潜在群组结构的估计与识别AI 解读

This paper provides a framework for joint estimation and identification of latent group structures in panel data models using a pairwise fusion penalized approach. The latent structure of the model allows individuals to be classified into different groups where the number of groups and the group membership are unknown. The individuals within a group have common slope parameters, while parameter heterogeneity is allowed across the groups. A penalized least squares (PLS)…