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分位数图模型：预测、条件独立与系统性风险应用AI 解读

We propose two types of Quantile Graphical Models: (i) Conditional Independence Quantile Graphical Models (CIQGMs) characterize the conditional independence by evaluating the distributional dependence structure at each quantile index, as such, those can be used for validation of the graph structure in the causal graphical models; (ii) Prediction Quantile Graphical Models (PQGMs) characterize the statistical dependencies through the graphs of the best linear predictors under…

高维潜在面板分位数回归及其资产定价应用AI 解读

We propose a generalization of the linear panel quantile regression model to accommodate both sparse and dense parts: sparse means that while the number of covariates available is large, potentially only a much smaller number of them have a nonzero impact on each conditional quantile of the response variable; while the dense part is represent by a low-rank matrix that can be approximated by latent factors and their loadings. Such a structure poses problems for traditional…

基于级数或大量回归变量的条件分位数过程AI 解读

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR-series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a…

高维近似稀疏分位数回归模型中的有效选择后推断AI 解读

This work proposes new inference methods for a regression coefficient of interest in a (heterogeneous) quantile regression model. We consider a high-dimensional model where the number of regressors potentially exceeds the sample size but a subset of them suffice to construct a reasonable approximation to the conditional quantile function. The proposed methods are (explicitly or implicitly) based on orthogonal score functions that protect against moderate model selection…

Z 估计框架下多函数参数的正则化后一致有效置信区域AI 解读

In this paper, we develop procedures to construct simultaneous confidence bands for ${\tilde{p}}$ potentially infinite-dimensional parameters after model selection for general moment condition models where ${\tilde{p}}$ is potentially much larger than the sample size of available data, $n$. This allows us to cover settings with functional response data where each of the ${\tilde{p}}$ parameters is a function. The procedure is based on the construction of score functions that…

We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and estimation method which is computationally efficient. We develop oracle and adaptivity inequalities, as well as model selection properties, that hold under continuity of the transition probabilities and polynomial $\beta$-mixing. In particular,…

含大量控制变量的广义线性模型选择后推断AI 解读

This article considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunizes against model selection mistakes and apply it to the case of logistic binary choice model. More specifically we propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest α0, a parameter in front of the regressor…

高维面板模型中的推断：枪支管制应用AI 解读

We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high-dimensional setting. The setting allows the number of time-varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time-varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the…

偏序下的多元分位数AI 解读

This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order…

高维稀疏模型中的 ℓ1 惩罚分位数回归AI 解读

We consider median regression and, more generally, a possibly infinite collection of quantile regressions in high-dimensional sparse models. In these models, the number of regressors p is very large, possibly larger than the sample size n, but only at most s regressors have a nonzero impact on each conditional quantile of the response variable, where s grows more slowly than n. Since ordinary quantile regression is not consistent in this case, we consider ℓ1-penalized…