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Localized Conformal Multi-Quantile Regression

局部化共形多分位数回归

Standard conformal prediction methods guarantee marginal coverage but often produce inefficient intervals that fail to adapt to local heteroscedasticity, while recent localized approaches often struggle to maintain validity across distinct subpopulations with varying noise profiles. To address these challenges, we introduce Localized Conformal Multi-Quantile Regression (LCMQR), a novel framework that synergizes multi-quantile information with kernel-based localization to…

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Asymptotic Theory and Phase Transitions for Variable Importance in Quantile Regression Forests

分位数回归森林变量重要性的渐近理论与相变

Quantile Regression Forests (QRF) are widely used for non-parametric conditional quantile estimation, yet statistical inference for variable importance measures remains challenging due to the non-smoothness of the loss function and the complex bias-variance trade-off. In this paper, we develop a asymptotic theory for variable importance defined as the difference in pinball loss risks. We first establish the asymptotic normality of the QRF estimator by handling the…

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A General Bayesian Nonparametric Approach for Estimating Population-Level and Conditional Causal Effects

总体与条件因果效应估计的一般贝叶斯非参数方法

We propose a Bayesian nonparametric (BNP) approach to causal inference using observational data consisting of outcome, treatment, and a set of confounders. The conditional distribution of the outcome given treatment and confounders is modeled flexibly using a dependent nonparametric mixture model, in which both the atoms and the weights vary with the confounders. The proposed BNP model is well suited for causal inference problems, as it does not rely on parametric…

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TabPFN: One Model to Rule Them All?

TabPFN:一个模型能否包办所有任务?

Hollmann et al. (Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time." Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and…

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Estimating Interpretable Heterogeneous Treatment Effect with Causal Subgroup Discovery in Survival Outcomes

通过因果子群发现估计生存结局的可解释异质性处理效应

Estimating heterogeneous treatment effect (HTE) for survival outcomes has gained increasing attention, as it captures the variation in treatment efficacy across patients or subgroups in delaying disease progression. However, most existing methods focus on post-hoc subgroup identification rather than simultaneously estimating HTE and selecting relevant subgroups. In this paper, we propose an interpretable HTE estimation framework that integrates three meta-learners that…

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Training and Testing with Multiple Splits: A Central Limit Theorem for Split-Sample Estimators

多次划分下的训练与检验:分样本估计量的中心极限定理

As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate subsamples to estimate the model and to evaluate it. However, this approach has two drawbacks, since each task uses only part of the data, and different splits can lead to widely different estimates. Averaging across multiple splits, I…

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A Large Scale Heterogeneous Treatment Effect Estimation Framework and Its Applications of Users' Journey at Snap

大规模异质性处理效应估计框架及其在 Snap 用户历程中的应用

Heterogeneous Treatment Effect (HTE) and Conditional Average Treatment Effect (CATE) models relax the assumption that treatment effects are the same for every user. We present a large scale industrial framework for estimating HTE using experimental data from hundreds of millions of Snapchat users. By combining results across many experiments, the framework uncovers latent user characteristics that were previously unmeasurable and produces stable treatment effect estimates at…

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The Asymptotic Distribution for a Single Joinpoint Changepoint Model

单连接点变点模型的渐近分布

A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact asymptotic distribution of the changepoint existence test statistic gauging whether or not a second segment is necessary. The identified asymptotic distribution, a supremum of a Gaussian process over the unit interval, is rather unwieldy. The work…

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Transfer Learning for High-dimensional Quantile Regression with Distribution Shift

分布偏移下的高维分位数回归迁移学习

Information from related source studies can often enhance the findings of a target study. However, the distribution shift between target and source studies can severely impact the efficiency of knowledge transfer. In the high-dimensional regression setting, existing transfer approaches mainly focus on the parameter shift. In this paper, we focus on the high-dimensional quantile regression with knowledge transfer under three types of distribution shift: parameter shift,…

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Spline Autoregression Method for Estimation of Quantile Spectrum

分位数谱估计的样条自回归方法

The quantile spectrum was introduced in Li (2012; 2014) as an alternative tool for spectral analysis of time series. It has the capability of providing a richer view of time series data than that offered by the ordinary spectrum especially for nonlinear dynamics such as stochastic volatility. A novel method, called spline autoregression (SAR), is proposed in this paper for estimating the quantile spectrum as a bivaraite function of frequency and quantile level, under the…

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Quantile-Crossing Spectrum and Spline Autoregression Estimation

分位数穿越谱及其样条自回归估计

The quantile-crossing spectrum is the spectrum of quantile-crossing processes created from a time series by the indicator function that shows whether or not the time series lies above or below a given quantile at a given time. This bivariate function of frequency and quantile level provides a richer view of serial dependence than that offered by the ordinary spectrum. We propose a new method for estimating the quantile-crossing spectrum as a bivariate function of frequency…

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Evaluating the Impact of Regulatory Policies on Social Welfare in Difference-in-Difference Settings

双重差分框架下监管政策对社会福利影响的评估

Quantifying the impact of regulatory policies on social welfare generally requires the identification of counterfactual distributions. Many of these policies (e.g. minimum wages or minimum working time) generate mass points and/or discontinuities in the outcome distribution. Existing approaches in the difference-in-difference literature cannot accommodate these discontinuities while accounting for selection on unobservables and non-stationary outcome distributions. We…

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Single Changepoint Procedures

单变点检验方法

Single changepoint tests have become a staple check for homogeneity of a climate time series, suggesting how climate has changed should non-homogeneity be declared. This paper summarizes the most prominent single changepoint tests used in today's climate literature, relating them to one and other and unifying their presentations. Asymptotic quantiles for the individual tests are presented. Derivations of the quantiles are given, enabling the reader to tackle cases not…

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Heterogeneous Treatment Effects and Causal Mechanisms

异质性处理效应与因果机制

The credibility revolution advances the use of research designs that permit identification and estimation of causal effects. However, understanding which mechanisms produce measured causal effects remains a challenge. The dominant current approach to the quantitative evaluation of mechanisms relies on the detection of heterogeneous treatment effects (HTEs) with respect to pre-treatment covariates. This paper develops a framework to understand when the existence of such…

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A New Causal Rule Learning Approach to Interpretable Estimation of Heterogeneous Treatment Effect

用于可解释异质性处理效应估计的因果规则学习新方法

Interpretability plays a crucial role in the application of statistical learning to estimate heterogeneous treatment effects (HTE) in complex diseases. In this study, we leverage a rule-based workflow, namely causal rule learning (CRL), to estimate and improve our understanding of HTE for atrial septal defect, addressing an overlooked question in the previous literature: what if an individual simultaneously belongs to multiple groups with different average treatment effects?…

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Individualized Prediction Bands in Causal Inference with Continuous Treatments

连续处理因果推断中的个体化预测带

Individualized treatments are crucial for optimal decision making and treatment allocation, specifically in personalized medicine based on the estimation of an individual's dose-response curve across a continuum of treatment levels, e.g., drug dosage. Current works focus on conditional mean and median estimates, which are useful but do not provide the full picture. We propose viewing causal inference with a continuous treatment as a covariate shift. This allows us to…

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A Two-step Estimating Approach for Heavy-tailed AR Models with Non-zero Median GARCH-type Noises

非零中位数 GARCH 型噪声下厚尾 AR 模型的两步估计

This paper develops a novel two-step estimating procedure for heavy-tailed AR models with non-zero median GARCH-type noises, allowing for time-varying volatility. We first establish the self-weighted quantile regression estimator (SQE) across all quantile levels $τ\in (0,1)$ for the AR parameters $θ_{0}$. We show that the SQE, less a bias, converges weakly to a Gaussian process at a rate of $n^{-1/2}$. The bias is zero if and only if $τ$ equals $τ_{0}$, the probability that…

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Synthetic Survival Control: Extending Synthetic Controls for "When-If" Decision

合成生存控制:面向事件发生时间反事实的合成控制扩展

Estimating causal effects on time-to-event outcomes from observational data is particularly challenging due to censoring, limited sample sizes, and non-random treatment assignment. The need for answering such "when-if" questions--how the timing of an event would change under a specified intervention--commonly arises in real-world settings with heterogeneous treatment adoption and confounding. To address these challenges, we propose Synthetic Survival Control (SSC) to…

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Asymptotic Distribution of Low-Dimensional Patterns Induced by Non-Differentiable Regularizers under General Loss Functions

非可微正则化下低维模式在一般损失函数中的渐近分布

This article investigates the asymptotic distribution of penalized estimators with non-differentiable penalties designed to recover low-dimensional pattern structures. Patterns play a central role in estimation, as they reveal the underlying structure of the parameter -- which coefficients are zero, which are equal, and how they are clustered. The main technical challenge stems from the discontinuous nature of these patterns (such as the sign function in the case of the…

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Variable importance measures for heterogeneous treatment effects

异质性处理效应的变量重要性度量

Motivated by applications in precision medicine and treatment effect heterogeneity, recent research has focused on estimating conditional average treatment effects (CATEs) using machine learning (ML). CATE estimates may represent complicated functions that provide little insight into the key drivers of heterogeneity. Therefore, we introduce nonparametric treatment effect variable importance measures (TE-VIMs), based on the mean-squared error (MSE) in predicting the…

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Correcting sample selection bias with categorical outcomes

分类结果的样本选择偏差校正

In this paper, I propose a method for correcting sample selection bias when the outcome of interest is categorical, such as occupational choice, health status, or field of study. Classical approaches to sample selection rely on strong parametric distributional assumptions, which may be restrictive in practice. I develop a local representation that decomposes each joint probability into marginal probabilities and a category-specific association parameter that captures how…

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Asymptotically Unbiased Synthetic Control Methods by Moment Matching

基于矩匹配的渐近无偏合成控制方法

Synthetic Control Methods (SCMs) have become a fundamental tool for comparative case studies. The core idea behind SCMs is to estimate treatment effects by predicting counterfactual outcomes for a treated unit using a weighted combination of observed outcomes from untreated units. The accuracy of these predictions is crucial for evaluating the treatment effect of a policy intervention. Subsequent research has therefore focused on estimating SC weights. In this study, we…

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Words Matter: Forecasting Economic Downside Risks with Corporate Textual Data

文字的重要性:利用企业文本数据预测经济下行风险

Accurate forecasting of downside risks to economic growth is critically important for policymakers and financial institutions, particularly in the wake of recent economic crises. This paper extends the Growth-at-Risk (GaR) approach by introducing a novel daily sentiment indicator derived from textual analysis of mandatory corporate disclosures (SEC 10-K and 10-Q reports) to forecast downside risks to economic growth. Using the Loughran--McDonald dictionary and a word-count…

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Correcting the Coverage Bias of Quantile Regression

校正分位数回归的覆盖偏差

We develop a collection of methods for adjusting the predictions of quantile regression to ensure coverage. Our methods are model agnostic and can be used to correct for high-dimensional overfitting bias with only minimal assumptions. Theoretical results show that the estimates we develop are consistent and facilitate accurate calibration in the proportional asymptotic regime where the ratio of the dimension of the data and the sample size converges to a constant. This is…

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