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凸惩罚高维回归的根本障碍AI 解读

In high-dimensional regression, we attempt to estimate a parameter vector β0∈Rp from n≲p observations {(yi,xi)}i≤n, where xi∈Rp is a vector of predictors and yi is a response variable. A well-established approach uses convex regularizers to promote specific structures (e.g., sparsity) of the estimate βˆ while allowing for practical algorithms. Theoretical analysis implies that convex penalization schemes have nearly optimal estimation properties in certain settings. However,…

稀疏贝叶斯预测密度估计的极小极大最优性AI 解读

We study predictive density estimation under Kullback–Leibler loss in ℓ0-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. Fundamental for this is a new risk decomposition for sparse, or spike-and-slab priors. A surprise is the existence of a phase transition in the future-to-past variance ratio r. For r

基于重复测量的反卷积估计量的一致收敛AI 解读

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the…

数据重编码中协变量与结果的正则化最优传输AI 解读

When databases are constructed from heterogeneous sources, it is not unusual that different encodings are used for the same outcome. In such case, it is necessary to recode the outcome variable before merging two databases. The method proposed for the recoding is an application of optimal transportation where we search for a bijective mapping between the distributions of such variable in two databases. In this article, we build upon the work by Garés et al., where they…

高维非平稳 VAR 模型的结构断点检测与参数联合估计AI 解读

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to assume piecewise stationarity, where the model can change at potentially many change points. We propose a three-stage procedure for simultaneous estimation of change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and…

平滑样条半参数密度模型AI 解读

Jiahui Yua, Jian Shib, Anna Liuc & Yuedong Wangd*a Department of Mathematics and Statistics, Boston University, Boston, MAb PayPal, San Jose, CAc Department of Mathematics and Statistics, University of Massachusetts, Amherst, MAd Department Statistics and Applied Probability, University of California, Santa Barbara, CAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are…

分组回归与稀疏广义加性模型的尖峰—厚尾组 LassoAI 解读

–We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the first nonparametric variant of the spike-and-slab lasso methodology. Our model simultaneously performs group selection and estimation, while our fully Bayes treatment of the mixture proportion allows for model complexity control and…

半参数因子模型中的同质性与结构识别AI 解读

Factor modeling is an essential tool for exploring intrinsic dependence structures in financial and economic studies through the construction of common latent variables, including the famous Fama–French three factor models for the description of asset returns in finance. However, most of the existing statistical methods for analyzing latent factors have been developed through a linear approach. In this article, we consider a semiparametric factor model and present a…

局部稳健的半参数估计AI 解读

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification…

因果与结构效应的自动去偏机器学习AI 解读

Many causal and structural effects depend on regressions. Examples include policy effects, average derivatives, regression decompositions, average treatment effects, causal mediation, and parameters of economic structural models. The regressions may be high‐dimensional, making machine learning useful. Plugging machine learners into identifying equations can lead to poor inference due to bias from regularization and/or model selection. This paper gives automatic debiasing for…

高维乘法模型的信息论方法：随机贴现因子与处理效应AI 解读

This paper is concerned with estimation of functionals of a latent weight function that satisfies possibly high‐dimensional multiplicative moment conditions. Main examples are functionals of stochastic discount factors in asset pricing, missing data problems, and treatment effects. We propose to estimate the latent weight function by an information theoretic approach combined with the ℓ 1 ‐penalization technique to deal with high‐dimensional moment conditions under sparsity.…

非线性半参数模型的正则化正交机器学习AI 解读

Summary This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we estimate by modern machine learning tools. We first adjust the moment function so that the gradient of the future loss function is insensitive (formally,…

基于正则化刀切工具变量法的多工具变量异方差过度识别检验AI 解读

Summary This paper proposes a new overidentifying restrictions test in a linear model when the number of instruments (possibly weak) may be smaller or larger than the sample size n or even infinite in a heteroscedastic framework. The proposed J test combines two techniques: the jackknife method and the regularisation technique which consists in stabilising the projection matrix. We theoretically show that our new test achieves the asymptotically correct size in the presence…

带凸包约束的合成控制法：贝叶斯最大后验方法AI 解读

Summary Synthetic control methods have gained popularity among causal studies with observational data, particularly when estimating the impacts of the interventions implemented to a small number of large units. The synthetic control methods face two major challenges: (a) estimating weights for each donor to create a synthetic control and (b) providing statistical inferences. To overcome these challenges, we propose a Bayesian framework that implements the synthetic control…

度量空间值数据的总变差正则化 Fréchet 回归AI 解读

Non-Euclidean data that are indexed with a scalar predictor such as time are increasingly encountered in data applications, while statistical methodology and theory for such random objects are not well developed yet. To address the need for new methodology in this area, we develop a total variation regularization technique for nonparametric Fréchet regression, which refers to a regression setting where a response residing in a metric space is paired with a scalar predictor…

凹扩展线性模型中惩罚样条估计量的渐近性质：收敛速率AI 解读

This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that includes conditional likelihood, quasi-likelihood and pseudo-likelihood. The theory allows all feasible combinations of the spline degree, the penalty order and the smoothness of the unknown functions. According to this theory, the…

通过分组—排序—融合程序估计有限混合模型的成分数AI 解读

Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure—a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous…

一种简单的条件依赖度量AI 解读

We propose a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X1,…,Xp, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0,1], where the limit is 0 if and only if Y and Z are conditionally independent given X1,…,Xp, and is 1 if and only if Y is equal to a measurable function…

大规模数据的时变协方差矩阵估计AI 解读

Time variation is a fundamental problem in statistical and econometric analysis of macroeconomic and financial data. Recently, there has been considerable focus on developing econometric modelling that enables stochastic structural change in model parameters and on model estimation by Bayesian or nonparametric kernel methods. In the context of the estimation of covariance matrices of large dimensional panels, such data requires taking into account time variation, possible…

高维协变量观测数据中的异质性处理效应推断AI 解读

Abstract This study proposes novel estimation and inference approaches for heterogeneous local treatment effects using high-dimensional covariates and observational data without a strong ignorability assumption. To achieve this, with a binary instrumental variable, the parameters of interest are identified on an unobservable subgroup of the population (compliers). Lasso estimation under a non-convex objective function is developed for a two-stage generalized linear model,…

利用稀疏 β 模型分析网络AI 解读

Abstract Data in the form of networks are increasingly available in a variety of areas, yet statistical models allowing for parameter estimates with desirable statistical properties for sparse networks remain scarce. To address this, we propose the Sparse β-Model (SβM), a new network model that interpolates the celebrated Erdős–Rényi model and the β-model that assigns one different parameter to each node. By a novel reparameterization of the β-model to distinguish global and…

单指数 copula 模型的半参数估计与变量选择AI 解读

Summary A copula with a flexibly dependence structure can capture complexity and heterogeneity in economic and financial time series. Based on the recently proposed single‐index copula, we propose a simultaneous variable selection and estimation procedure. This method allows for choosing the most relevant state variables by using a penalized estimation with large sample properties derived. Simulation results demonstrate the good performance of the method in selecting…

结合匹配与合成控制以权衡外推和内插偏差AI 解读

The synthetic control (SC) method is widely used in comparative case studies to adjust for differences in pre-treatment characteristics. SC limits extrapolation bias at the potential expense of interpolation bias, whereas traditional matching estimators have the opposite properties. This complementarity motives us to propose a matching and synthetic control (or MASC) estimator as a model averaging estimator that combines the standard SC and matching estimators. We show how…

面向细分数据的惩罚合成控制估计量AI 解读

Synthetic control methods are commonly applied in empirical research to estimate the effects of treatments or interventions on aggregate outcomes. A synthetic control estimator compares the outcome of a treated unit to the outcome of a weighted average of untreated units that best resembles the characteristics of the treated unit before the intervention. When disaggregated data are available, constructing separate synthetic controls for each treated unit may help avoid…