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矩阵补全、反事实与缺失数据的因子分析AI 解读

This paper proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it is shown that the common component can be consistently estimated at four different rates of convergence without requiring regularization or iteration. An asymptotic analysis of the…

增广合成控制法AI 解读

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The “synthetic control” is a weighted average of control units that balances the treated unit’s pretreatment outcomes and other covariates as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pretreatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings…

因果面板数据模型的矩阵补全方法AI 解读

In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated unit/period combinations. We propose a class of matrix completion estimators that uses the observed elements of the matrix of control outcomes corresponding to untreated unit/periods to impute the "missing" elements of the control outcome matrix,…

利用互联网搜索数据与 PRISM 预测失业保险初次申请人数AI 解读

Big data generated from the Internet offer great potential for predictive analysis. Here we focus on using online users’ Internet search data to forecast unemployment initial claims weeks into the future, which provides timely insights into the direction of the economy. To this end, we present a novel method Penalized Regression with Inferred Seasonality Module (PRISM), which uses publicly available online search data from Google. PRISM is a semiparametric method, motivated…

模型选择中多来源分块缺失数据的整合AI 解读

For multisource data, blocks of variable information from certain sources are likely missing. Existing methods for handling missing data do not take structures of block-wise missing data into consideration. In this article, we propose a multiple block-wise imputation (MBI) approach, which incorporates imputations based on both complete and incomplete observations. Specifically, for a given missing pattern group, the imputations in MBI incorporate more samples from groups…

凸约束下选择后推断的整合方法AI 解读

Inference after model selection has been an active research topic in the past few years, with numerous works offering different approaches to addressing the perils of the reuse of data. In particular, major progress has been made recently on large and useful classes of problems by harnessing general theory of hypothesis testing in exponential families, but these methods have their limitations. Perhaps most immediate is the gap between theory and practice: implementing the…

高阶全变差正则化最小二乘的预测界AI 解读

We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of (k−1)th order differences. Our approach is based on combining a general oracle inequality for the ℓ1-penalized least squares estimator with “interpolating vectors” to upper bound the “effective sparsity.” This allows one to show that the ℓ1-penalty on the kth order differences leads to an estimator that can adapt to the number of jumps in the (k−1)th order…

高斯过程回归的变量选择一致性AI 解读

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable selection, are known to also adapt to the unknown intrinsic dimension of a sparse true regression function. But it remains unclear if such extensions offer variable selection consistency, that is, if the true subset of important variables…

期权隐含状态价格密度的筛估计AI 解读

This paper proposes a nonparametric estimator for the state price density implied by a single cross-section of European options with different strikes and the same maturity. The proposed estimator has two distinctive features. First, it extracts information from both call and put options, as opposed to only call options. Second, it does not require estimating any second-order derivative; instead, it solves a constrained and penalized linear regression. The asymptotic…

高维线性回归逐协变量多重检验变量选择法的狭义复现AI 解读

Summary Chudik, Kapetanios, & Pesaran (Econometrica 2018, 86, 1479‐1512) propose a one covariate at a time, multiple testing (OCMT) approach to variable selection in high‐dimensional linear regression models as an alternative approach to penalised regression. We offer a narrow replication of their key OCMT results based on the Stata software instead of the original MATLAB routines. Using the new user‐written Stata commands baing and ocmt , we find results that match closely…

含时变协变量的非参数风险函数提升估计AI 解读

Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent…

二阶 Stein 公式：SURE 的风险估计及高维推断应用AI 解读

Stein’s formula states that a random variable of the form z⊤f(z)−divf(z) is mean-zero for all functions f with integrable gradient. Here, divf is the divergence of the function f and z is a standard normal vector. This paper aims to propose a second-order Stein formula to characterize the variance of such random variables for all functions f(z) with square integrable gradient, and to demonstrate the usefulness of this second-order Stein formula in various applications. In…

Lasso 的分布：稀疏球上的一致控制与自适应参数调节AI 解读

The Lasso is a popular regression method for high-dimensional problems in which the number of parameters θ1,…,θN, is larger than the number n of samples: N>n. A useful heuristics relates the statistical properties of the Lasso estimator to that of a simple soft-thresholding denoiser, in a denoising problem in which the parameters (θi)i≤N are observed in Gaussian noise, with a carefully tuned variance. Earlier work confirmed this picture in the limit n,N→∞, pointwise in the…

具有因子结构的多任务分位数回归AI 解读

A multivariate quantile regression model with a factor structure is proposed to study data with multivariate responses with covariates. The factor structure is allowed to vary with the quantile levels, which is more flexible than the classical factor models. Assuming the number of factors is small, and the number of responses and the input variables are growing with the sample size, the model is estimated with the nuclear norm regularization. The incurred optimization…

利用双重 Lasso 惩罚非参数估计星系团辐射率并检测点源AI 解读

Astrophysicists are interested in recovering the three-dimensional gas emissivity of a galaxy cluster from a two-dimensional telescope image. Blurring and point sources make this inverse problem harder to solve. The conventional approach requires in a first step to identify and mask the point sources. Instead we model all astrophysical components in a single Poisson generalized linear model. To enforce sparsity on the parameters, maximum likelihood estimation is regularized…

神经网络训练作为数据自适应核学习：表示与逼近收益AI 解读

Consider the problem: given the data pair (x,y) drawn from a population with f*(x)=E[y|x=x], specify a neural network model and run gradient flow on the weights over time until reaching any stationarity. How does ft , the function computed by the neural network at time t, relate to f*, in terms of approximation and representation? What are the provable benefits of the adaptive representation by neural networks compared to the pre-specified fixed basis representation in the…

利用干扰参数惩罚回归对高维数据开展目标推断AI 解读

Analysis of high dimensional data has received considerable and increasing attention in statistics. In practice, we may not be interested in every variable that is observed. Instead, often some of the variables are of particular interest, and the remaining variables are nuisance. To this end, we propose the nuisance penalized regression which does not penalize the parameters of interest. When the coherence between interest parameters and nuisance parameters is negligible, we…

基于 Metropolis–Hastings 的 Knockoff 采样AI 解读

Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which discovers true effects while rigorously controlling the expected fraction of false positives. A frequently discussed challenge to apply this method is to construct knockoff variables, which are synthetic variables obeying a crucial exchangeability property with the explanatory variables under study. This article introduces techniques for…

个体化多方向变量选择AI 解读

In this article, we propose a heterogeneous modeling framework which achieves individual-wise feature selection and heterogeneous covariates’ effects subgrouping simultaneously. In contrast to conventional model selection approaches, the new approach constructs a separation penalty with multidirectional shrinkages, which facilitates individualized modeling to distinguish strong signals from noisy ones and selects different relevant variables for different individuals.…

通过递归在线得分估计进行高维模型推断AI 解读

In this paper, we develop a new estimation and valid inference method for single or low-dimensional regression coefficients in high-dimensional generalized linear models. The number of the predictors is allowed to grow exponentially fast with respect to the sample size. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the…

函数型 Cox 模型的半参数推断AI 解读

This article studies penalized semiparametric maximum partial likelihood estimation and hypothesis testing for the functional Cox model in analyzing right-censored data with both functional and scalar predictors. Deriving the asymptotic joint distribution of finite-dimensional and infinite-dimensional estimators is a very challenging theoretical problem due to the complexity of semiparametric models. For the problem, we construct the Sobolev space equipped with a special…

回归Copula的贝叶斯推断AI 解读

We propose a new semiparametric distributional regression smoother that is based on a copula decomposition of the joint distribution of the vector of response values. The copula is high-dimensional and constructed by inversion of a pseudo regression, where the conditional mean and variance are semiparametric functions of covariates modeled using regularized basis functions. By integrating out the basis coefficients, an implicit copula process on the covariate space is…

利用 ABC 贝叶斯森林进行变量选择AI 解读

Abstract Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants thereof. In this work, we abandon the linear model framework, which can be quite detrimental when the covariates impact the outcome in a non-linear way, and turn to tree-based methods for variable selection. Such variable screening…

类别解释变量的收缩估计AI 解读

This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding weighted squared ℓ2-norm differences between group location parameters and informative first stage estimates. Under quadratic loss, the penalized estimation problem has a simple interpretable closed-form solution that nests methods…