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分位数与分布:分位数回归、分布回归、分布效应与随机占优。
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Realised quantile-based estimation of the integrated variance

基于已实现分位数的积分方差估计

In this paper, we propose a new jump robust quantile-based realised variance measure of ex-post return variation that can be computed using potentially noisy data. The estimator is consistent for the integrated variance and we present feasible central limit theorems which show that it converges at the best attainable rate and has excellent efficiency. Asymptotically, the quantile-based realised variance is immune to finite activity jumps and outliers in the price series,…

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Rerandomization for quantile treatment effects

分位数处理效应的再随机化设计与推断

Although complete randomization is widely regarded as the gold standard for causal inference, covariate imbalance can still arise by chance in finite samples. Rerandomization has emerged as an effective tool to improve covariate balance across treatment groups and enhance the precision of causal effect estimation. While existing work focuses on average treatment effects, quantile treatment effects (QTEs) provide a richer characterization of treatment heterogeneity by…

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High-Dimensional Tail Index Regression

高维尾指数回归

Motivated by the empirical observation of power-law distributions in the credits (e.g., ``likes'') of viral posts in social media, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference of its parameters. First, we propose a regularized estimator, establish its consistency, and derive its convergence rate. Second, we debias the regularized estimator to facilitate inference and prove its asymptotic normality. Simulation…

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Extremal Quantiles under Two-Way Clustering

双向聚类依赖下的极端分位数

This paper studies extremal quantiles under two-way clustered dependence. We show that the limiting distribution of unconditional intermediate-order tail quantiles is Gaussian. This result is notable because two-way clustering typically leads to non-Gaussian limiting behavior. Remarkably, extremal quantiles remain asymptotically Gaussian even in degenerate cases. Building on this insight, we extend our analysis to extremal quantile regression at intermediate orders.…

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Causal Inference under Threshold Manipulation: Bayesian Mixture Modeling and Heterogeneous Treatment Effects

阈值操纵下的因果推断:贝叶斯混合模型与异质处理效应

Many marketing applications, including credit card incentive programs, offer rewards to customers who exceed specific spending thresholds to encourage increased consumption. Quantifying the causal effect of these thresholds on customers is crucial for effective marketing strategy design. Although regression discontinuity design is a standard method for such causal inference tasks, its assumptions can be violated when customers, aware of the thresholds, strategically…

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causalfe: Causal Forests with Fixed Effects in Python

causalfe:带固定效应的因果森林 Python 实现

The causalfe package provides a Python implementation of Causal Forests with Fixed Effects (CFFE) for estimating heterogeneous treatment effects in panel data settings. Standard causal forest methods struggle with panel data because unit and time fixed effects induce spurious heterogeneity in treatment effect estimates. The CFFE approach addresses this by performing node-level residualization during tree construction, removing fixed effects within each candidate split rather…

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Semiparametric inference for inequality measures under nonignorable nonresponse using callback data

利用回访数据处理非可忽略无应答下不平等指标的半参数推断

This paper develops semiparametric methods for estimation and inference of widely used inequality measures when survey data are subject to nonignorable nonresponse, a challenging setting in which response probabilities depend on the unobserved outcomes. Such nonresponse mechanisms are common in household surveys and invalidate standard inference procedures due to selection bias and lack of population representativeness. We address this problem by exploiting callback data…

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Model selection by cross-validation in an expectile linear regression

期望分位线性回归中基于交叉验证的模型选择

For linear models that may have asymmetric errors, we study variable selection by cross-validation. The data are split into training and validation sets, with the number of observations in the validation set much larger than in the training set. For the model coefficients, the expectile or adaptive LASSO expectile estimators are calculated on the training set. These estimators will be used to calculate the cross-validation mean score (CVS) on the validation set. We show that…

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Lee Bounds for Random Objects

随机对象的 Lee 界

In applied research, Lee (2009) bounds are widely applied to bound the average treatment effect in the presence of selection bias. This paper extends the methodology of Lee bounds to accommodate outcomes in a general metric space, such as compositional and distributional data. By exploiting a representation of the Fréchet mean of the potential outcome via embedding in an Euclidean or Hilbert space, we present a feasible characterization of the identified set of the causal…

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Bayesian Smoothed Quantile Regression

贝叶斯平滑分位数回归

The standard asymmetric Laplace framework for Bayesian quantile regression (BQR) suffers from a fundamental decision-theoretic misalignment, yielding biased finite-sample estimates, and precludes gradient-based computation due to non-smoothness. We propose Bayesian smoothed quantile regression (BSQR), a principled framework built on a kernel-smoothed, fully differentiable likelihood. Methodologically, the symmetrizing property of our objective reduces inferential bias and…

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Quantile Selection in the Gender Pay Gap

性别工资差距中的分位数选择校正

We propose a new approach to estimate selection-corrected quantiles of the gender wage gap. Our method employs instrumental variables that explain variation in the latent variable but, conditional on the latent process, do not directly affect selection. We provide semiparametric identification of the quantile parameters without imposing parametric restrictions on the selection probability, derive the asymptotic distribution of the proposed estimator based on constrained…

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Dimension-reduced outcome-weighted learning for estimating individualized treatment regimes in observational studies

观察研究中估计个体化治疗规则的降维结局加权学习

Individualized treatment regimes (ITRs) aim to improve clinical outcomes by assigning treatment based on patient-specific characteristics. However, existing methods often struggle with high-dimensional covariates, limiting accuracy, interpretability, and real-world applicability. We propose a novel sufficient dimension reduction approach that directly targets the contrast between potential outcomes and identifies a low-dimensional subspace of the covariates capturing…

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Event Studies with Feedback

存在反馈的事件研究

Event studies often conflate direct treatment effects with indirect effects operating through endogenous covariate adjustment. We develop a dynamic panel event study framework that separates these effects. The framework allows for persistent outcomes and treatment effects and for covariates that respond to past outcomes and treatment exposure. Under sequential exogeneity and homogeneous feedback, we establish point identification of common parameters governing outcome and…

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Minimax regret treatment rules with finite samples when a quantile is the object of interest

以分位数为目标的有限样本极小极大遗憾处理规则

Consider a setup in which a decision maker is informed about the population by a finite sample and based on that sample has to decide whether or not to apply a certain treatment. We work out finite sample minimax regret treatment rules under various sampling schemes when outcomes are restricted onto the unit interval. In contrast to Stoye (2009) where the focus is on maximization of expected utility the focus here is instead on a particular quantile of the outcome…

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Sensitivity Analysis in Unconditional Quantile Effects

无条件分位数效应的敏感性分析

This paper proposes a framework to analyze the effects of counterfactual policies on the unconditional quantiles of an outcome variable. For a given counterfactual policy, we obtain identified sets for the effect of both marginal and global changes in the proportion of treated individuals. To conduct a sensitivity analysis, we introduce the quantile breakdown frontier, a curve that (i) indicates whether a sensitivity analysis is possible or not, and (ii) when a sensitivity…

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Scalable Ultra-High-Dimensional Quantile Regression with Genomic Applications

Modern datasets arising from social media, genomics, and biomedical informatics are often heterogeneous and (ultra) high-dimensional, creating substantial challenges for conventional modeling techniques. Quantile regression (QR) not only offers a flexible way to capture heterogeneous effects across the conditional distribution of an outcome, but also naturally produces prediction intervals that help quantify uncertainty in future predictions. However, classical QR methods…

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Multivariate quantile regression

多元分位数回归

This paper introduces a new framework for multivariate quantile regression based on the multivariate distribution function, termed multivariate quantile regression (MQR). In contrast to existing approaches--such as directional quantiles, vector quantile regression, or copula-based methods--MQR defines quantiles through the conditional probability structure of the joint conditional distribution function. The method constructs multivariate quantile curves using sequential…

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Nonparametric methods for comparing distribution functionals for dependent samples with application to inequality measures

依赖样本下分布泛函比较的非参数方法及不平等应用

This paper proposes asymptotically distribution-free inference methods for comparing a broad range of welfare indices across dependent samples, including those employed in inequality, poverty, and risk analysis. Two distinct situations are considered. \emph{First}, we propose asymptotic and bootstrap intersection methods which are completely robust to arbitrary dependence between two samples. \emph{Second}, we focus on the common case of overlapping samples -- a special form…

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Adaptive Test for High Dimensional Quantile Regression

高维分位数回归的自适应检验

Testing high-dimensional quantile regression coefficients is crucial, as tail quantiles often reveal more than the mean in many practical applications. Nevertheless, the sparsity pattern of the alternative hypothesis is typically unknown in practice, posing a major challenge. To address this, we propose an adaptive test that remains powerful across both sparse and dense alternatives.We first establish the asymptotic independence between the max-type test statistic proposed…

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Multidimensional Stochastic Dominance Test Based on Center-outward Quantiles

基于中心向外分位数的多维随机占优检验

Stochastic dominance (SD) provides a quantile-based partial ordering of random variables and has broad applications. Its extension to multivariate settings, however, is challenging due to the lack of a canonical ordering in $\mathbb{R}^d$ ($d \ge 2$) and the set-valued character of multivariate quantiles. Based on the multivariate center-outward quantile function in Hallin et al. (2021), this paper proposes new first- and second-order multivariate stochastic dominance (MSD)…

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The $\infty$-S test via regression quantile affine LASSO

基于回归分位数仿射LASSO的∞-S检验

A novel test in the linear $\ell_1$ (LAD) and quantile regressions is proposed, based on the scores provided by the dual variables (signs) arising in the calculation of the (so-called) affine-lasso estimate--a Rao-type, Lagrange multiplier test using the thresholding, towards the null hypothesis of the test, function of the latter estimate.

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Theoretical Guarantees of Learning Ensembling Strategies with Applications to Time Series Forecasting

集成策略学习的理论保证及其时间序列预测应用

Ensembling is among the most popular tools in machine learning (ML) due to its effectiveness in minimizing variance and thus improving generalization. Most ensembling methods for black-box base learners fall under the umbrella of "stacked generalization," namely training an ML algorithm that takes the inferences from the base learners as input. While stacking has been widely applied in practice, its theoretical properties are poorly understood. In this paper, we prove a…

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Modeling the Happiness-Sustainability Nexus via Graphical Lasso and Quantile-on-Quantile Regression

用图形 Lasso 与分位数对分位数回归研究幸福感与可持续发展的联系

This paper investigates the nexus between subjective well-being and sustainability, proxied by the Sustainable Development Goals (SDG) Index, using cross-country data from 126 nations in 2022. While prior research has highlighted a positive association between happiness and sustainable development, existing approaches largely rely on linear regressions or correlation-based measures that mask distributional heterogeneity, multicollinearity, and potential nonlinear dependence.…

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A quantile-based nonadditive fixed effects model

基于分位数的非加性固定效应模型

I propose a quantile-based nonadditive fixed effects panel model to study heterogeneous causal effects. Similar to standard fixed effects (FE) model, my model allows arbitrary dependence between regressors and unobserved heterogeneity, but it generalizes the additive separability of standard FE to allow the unobserved heterogeneity to enter nonseparably. Similar to structural quantile models, my model's random coefficient vector depends on an unobserved, scalar ''rank''…

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