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含噪矩阵补全的推断与不确定性量化AI 解读

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained estimates and how to perform statistical inference on the unknown matrix (e.g.~constructing a valid and short confidence interval for an unseen entry). This paper takes a step towards inference and uncertainty quantification for…

具有非稀疏误差的稳健主成分分析AI 解读

We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a new theoretical argument to establish consistency without assuming sparsity or the existence of any moments of the error matrix, so that fat-tailed continuous random errors such as Cauchy are allowed. The results are illustrated by…

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 (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs characterize the conditional independence of distributions by evaluating the distributional dependence structure at each quantile index. As such, CIQGMs can be used for validation of the graph structure in the causal graphical models (\cite{pearl2009causality, robins1986new, heckman2015causal}). One…

时变参数高维预测回归的提升算法AI 解读

High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for parameter instability in economic time series, but theories for parameter instability are mainly developed for models with a small number of covariates. In this paper, we present two $L_2$ boosting algorithms for estimating high…

含噪矩阵补全：通过非凸优化理解凸松弛的统计保证AI 解读

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle this problem is convex relaxation, which achieves remarkable efficacy in practice. However, the theoretical support of this approach is still far from optimal in the noisy setting, falling short of explaining its empirical success. We make…

按特征排序的投资组合：估计与推断AI 解读

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of…

非可分三角模型中结构函数的半参数估计AI 解读

Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modelling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for identification, the curse of dimensionality in estimation, and the lack of inferential tools. This paper introduces two classes of semiparametric nonseparable triangular models that address these…

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 overall number of regressors $p$ is very large, possibly larger than the sample size $n$, but only $s$ of these regressors have non-zero impact on the conditional quantile of the response variable, where $s$ grows slower than $n$. We consider quantile regression penalized by the $\ell_1$-norm of coefficients ($\ell_1$…

交叉验证、风险估计与模型选择AI 解读

Cross-validation is a popular non-parametric method for evaluating the accuracy of a predictive rule. The usefulness of cross-validation depends on the task we want to employ it for. In this note, I discuss a simple non-parametric setting, and find that cross-validation is asymptotically uninformative about the expected test error of any given predictive rule, but allows for asymptotically consistent model selection. The reason for this phenomenon is that the leading-order…

使用 Stata 进行删失分位数工具变量估计AI 解读

Many applications involve a censored dependent variable and an endogenous independent variable. Chernozhukov et al. (2015) introduced a censored quantile instrumental variable estimator (CQIV) for use in those applications, which has been applied by Kowalski (2016), among others. In this article, we introduce a Stata command, cqiv, that simplifes application of the CQIV estimator in Stata. We summarize the CQIV estimator and algorithm, we describe the use of the cqiv…

通过调整特征值阈值估计因子数量AI 解读

Determining the number of common factors is an important and practical topic in high dimensional factor models. The existing literatures are mainly based on the eigenvalues of the covariance matrix. Due to the incomparability of the eigenvalues of the covariance matrix caused by heterogeneous scales of observed variables, it is very difficult to give an accurate relationship between these eigenvalues and the number of common factors. To overcome this limitation, we appeal to…

马尔可夫依赖数据上的自适应 Huber 回归AI 解读

High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-tailed errors. However, neither of them hold in many real high-dimensional time-series data. Recently [Sun, Zhou, Fan, 2019, J. Amer. Stat. Assoc., in press] proposed Adaptive Huber Regression (AHR) to address the issue of heavy-tailed…

利用因子斜率的低秩估计推断异质效应AI 解读

We study a panel data model with general heterogeneous effects where slopes are allowed to vary across both individuals and over time. The key dimension reduction assumption we employ is that the heterogeneous slopes can be expressed as having a factor structure so that the high-dimensional slope matrix is low-rank and can thus be estimated using low-rank regularized regression. We provide a simple multi-step estimation procedure for the heterogeneous effects. The procedure…

随机注意力模型AI 解读

This paper illustrates how one can deduce preference from observed choices when attention is not only limited but also random. In contrast to earlier approaches, we introduce a Random Attention Model (RAM) where we abstain from any particular attention formation, and instead consider a large class of nonparametric random attention rules. Our model imposes one intuitive condition, termed Monotonic Attention, which captures the idea that each consideration set competes for the…

含多个内生变量的高维线性模型同时置信区间AI 解读

High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve identification. Because of the high-dimensionality in the second stage, constructing honest confidence regions with asymptotically correct coverage is non-trivial. Our main contribution is to propose estimators and confidence regions that would…

有约束与无约束的间接推断AI 解读

Indirect Inference (I-I) estimation of structural parameters $θ$ {requires matching observed and simulated statistics, which are most often generated using an auxiliary model that depends on instrumental parameters $β$.} {The estimators of the instrumental parameters will encapsulate} the statistical information used for inference about the structural parameters. As such, artificially constraining these parameters may restrict the ability of the auxiliary model to accurately…

漂移扩散模型的检验AI 解读

The drift diffusion model (DDM) is a model of sequential sampling with diffusion (Brownian) signals, where the decision maker accumulates evidence until the process hits a stopping boundary, and then stops and chooses the alternative that corresponds to that boundary. This model has been widely used in psychology, neuroeconomics, and neuroscience to explain the observed patterns of choice and response times in a range of binary choice decision problems. This paper provides a…

lspartition：基于分区的最小二乘回归AI 解读

Nonparametric partitioning-based least squares regression is an important tool in empirical work. Common examples include regressions based on splines, wavelets, and piecewise polynomials. This article discusses the main methodological and numerical features of the R software package lspartition, which implements modern estimation and inference results for partitioning-based least squares (series) regression estimation. This article discusses the main methodological and…

确定度修正随机区块模型的社区数量AI 解读

We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio statistic. To this end, we introduce a method that combines spectral clustering with binary segmentation. This approach guarantees an upper bound for the pseudo likelihood ratio statistic when the model is over-fitted. We also derive its limiting distribution when the model is under-fitted. Based on these properties, we establish the consistency of…

连续行动下的半参数有效策略学习AI 解读

We consider off-policy evaluation and optimization with continuous action spaces. We focus on observational data where the data collection policy is unknown and needs to be estimated. We take a semi-parametric approach where the value function takes a known parametric form in the treatment, but we are agnostic on how it depends on the observed contexts. We propose a doubly robust off-policy estimate for this setting and show that off-policy optimization based on this…

回归分析中的抽样不确定性与设计不确定性AI 解读

Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it…

SHOPPER：含替代与互补关系的消费者选择概率模型AI 解读

We develop SHOPPER, a sequential probabilistic model of shopping data. SHOPPER uses interpretable components to model the forces that drive how a customer chooses products; in particular, we designed SHOPPER to capture how items interact with other items. We develop an efficient posterior inference algorithm to estimate these forces from large-scale data, and we analyze a large dataset from a major chain grocery store. We are interested in answering counterfactual queries…

简便的局部多项式密度估计量AI 解读

This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other transformation of the data. We study the main asymptotic properties of the estimator, and use these results to provide principled estimation, inference, and bandwidth selection methods. As a substantive application of our results, we develop a novel…

基于分区的级数估计量的大样本性质AI 解读

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a general characterization of their leading asymptotic bias. Second, we establish integrated mean squared error approximations for the point estimator and propose feasible tuning parameter selection. Third, we develop pointwise inference methods…