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稳健 M 估计的新视角：有限样本理论与依赖调整多重检验AI 解读

Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust alternatives to the method of least squares are sorely needed. To achieve robustness against heavy-tailed sampling distributions, we revisit the Huber estimator from a new perspective by letting the tuning parameter involved diverge with…

因子模型的主成分与正则化估计AI 解读

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares with ridge regressions turns out to have the effect of shrinking the singular values of the common component and possibly reducing its rank. The method is used in the machine learning literature to recover low-rank matrices. We study the…

识别集的蒙特卡洛置信集AI 解读

In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full parameters and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. These CSs are based on level sets of optimal sample criterion functions (such as likelihood or optimally-weighted or…

半参数分位数因子模型的估计AI 解读

We propose an estimation methodology for a semiparametric quantile factor panel model. We provide tools for inference that are robust to the existence of moments and to the form of weak cross-sectional dependence in the idiosyncratic error term. We apply our method to daily stock return data.

稀疏附带参数下的部分一致性AI 解读

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this penalization principle to a linear regression model with a finite-dimensional vector of structural parameters and a high-dimensional vector of sparse incidental parameters. For the estimators of the structural parameters, we derive their…

发现是否虚假？最大虚假相关的分布及应用AI 解读

Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries from these data mining approaches be spurious due to high dimensionality and limited sample size? Can our fundamental assumptions about the exogeneity of the covariates needed for such variable selection be validated with the data? To answer these questions, we need to…

利用随机森林估计与推断异质性处理效应AI 解读

Many scientific and engineering challenges -- ranging from personalized medicine to customized marketing recommendations -- require an understanding of treatment effect heterogeneity. In this paper, we develop a non-parametric causal forest for estimating heterogeneous treatment effects that extends Breiman's widely used random forest algorithm. In the potential outcomes framework with unconfoundedness, we show that causal forests are pointwise consistent for the true…

未知样本选择概率下总体均值的形状约束部分识别AI 解读

A prevailing challenge in the biomedical and social sciences is to estimate a population mean from a sample obtained with unknown selection probabilities. Using a well-known ratio estimator, Aronow and Lee (2013) proposed a method for partial identification of the mean by allowing the unknown selection probabilities to vary arbitrarily between two fixed extreme values. In this paper, we show how to leverage auxiliary shape constraints on the population outcome distribution,…

最大范数特征向量扰动界及其在稳健协方差估计中的应用AI 解读

In statistics and machine learning, people are often interested in the eigenvectors (or singular vectors) of certain matrices (e.g. covariance matrices, data matrices, etc). However, those matrices are usually perturbed by noises or statistical errors, either from random sampling or structural patterns. One usually employs Davis-Kahan $\sin θ$ theorem to bound the difference between the eigenvectors of a matrix $A$ and those of a perturbed matrix $\widetilde{A} = A + E$, in…

随机贴现因子的非参数分解AI 解读

Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009). Our empirical framework…

重尾数据的收缩原则：高维稳健低秩矩阵恢复AI 解读

This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential or sub-Gaussian distributions to merely bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix $Θ^*$ from the trace regression model $Y=Tr (Θ^{*T}X) +ε$. It encompasses…

非参数工具变量回归非线性泛函的最优上确界范数速率与一致推断AI 解读

This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function $h_0$ and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of $h_0$ and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating $h_0$ and its derivatives, and show that the…

含测量误差的高维线性模型系数置信带AI 解读

We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to avoid non-vanishing biases in addition to handle the high dimensionality of the parameters. A recent growing literature has proposed various estimators that achieve good rates of convergence. Our main contribution complements this…

依赖限制与仅两期数据下双重差分模型的分位数处理效应AI 解读

This paper shows that the Conditional Quantile Treatment Effect on the Treated can be identified using a combination of (i) a conditional Distributional Difference in Differences assumption and (ii) an assumption on the conditional dependence between the change in untreated potential outcomes and the initial level of untreated potential outcomes for the treated group. The second assumption recovers the unknown dependence from the observed dependence for the untreated group.…

极端分位数回归综述AI 解读

Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants of low infant birth weights, and auction models. This chapter provides an overview of recent developments in the theory and empirics of extremal quantile regression. The advances in the theory have relied on the use of extreme value…

平均处理效应估计：补充分析与尚存挑战AI 解读

There is a large literature on semiparametric estimation of average treatment effects under unconfounded treatment assignment in settings with a fixed number of covariates. More recently attention has focused on settings with a large number of covariates. In this paper we extend lessons from the earlier literature to this new setting. We propose that in addition to reporting point estimates and standard errors, researchers report results from a number of supplementary…

处理效应的双重／去偏／Neyman 机器学习AI 解读

Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, and Newey (2016) provide a generic double/de-biased machine learning (DML) approach for obtaining valid inferential statements about focal parameters, using Neyman-orthogonal scores and cross-fitting, in settings where nuisance parameters are estimated using a new generation of nonparametric fitting methods for high-dimensional data, called machine learning methods. In this note, we illustrate the application of this method…

多协变量与异方差线性回归中的推断AI 解读

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates are allowed to grow as fast as the sample size. We find…

高维分位数回归中变点的预言式估计AI 解读

In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogeneous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is…

条件平均处理效应函数的双重稳健一致置信带AI 解读

In this paper, we propose a doubly robust method to present the heterogeneity of the average treatment effect with respect to observed covariates of interest. We consider a situation where a large number of covariates are needed for identifying the average treatment effect but the covariates of interest for analyzing heterogeneity are of much lower dimension. Our proposed estimator is doubly robust and avoids the curse of dimensionality. We propose a uniform confidence band…

贝叶斯因果推断的模型诊断AI 解读

The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and testing those assumptions is important to assess the validity of causal inference. We develop model criticism for Bayesian causal inference, building on the idea of posterior predictive checks to assess model fit. Our approach involves…

随机实验中的高维回归调整AI 解读

We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information, and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the average treatment effect. Our results considerably extend the range of settings where high-dimensional regression adjustments are guaranteed to provide valid inference about the population average treatment effect. We then propose…

quantreg.nonpar：非参数级数分位数回归的 R 软件包AI 解读

The R package quantreg.nonpar implements nonparametric quantile regression methods to estimate and make inference on partially linear quantile models. quantreg.nonpar obtains point estimates of the conditional quantile function and its derivatives based on series approximations to the nonparametric part of the model. It also provides pointwise and uniform confidence intervals over a region of covariate values and/or quantile indices for the same functions using analytical…

Counterfactual：反事实分析的 R 软件包AI 解读

The Counterfactual package implements the estimation and inference methods of Chernozhukov, Fernández-Val and Melly (2013) for counterfactual analysis. The counterfactual distributions considered are the result of changing either the marginal distribution of covariates related to the outcome variable of interest, or the conditional distribution of the outcome given the covariates. They can be applied to estimate quantile treatment effects and wage decompositions. This paper…