analyze vertical discontinuities

本文提出了一种针对具有任意边界形状的边界不连续设计(BDD)的操纵测试方法，通过k-均值聚类和二项平衡测试来检测处理组与对照组的均衡性。

Conventional univariate regression discontinuity design (RDD) struggles with multidimensional threshold-based decision rules. Method: We propose boundary discontinuity design (BD design), a novel framework focusing on treatment assignment along arbitrary boundary curves in two-dimensional score space. We develop a unified identification theory characterizing local identifiability conditions, bandwidth selection challenges, and sources of estimation bias, and integrate local polynomial estimation with robust inference procedures. Contribution/Results: Synthesizing over 80 empirical studies, we trace methodological evolution and provide the first theoretical guide and practical implementation protocol for BD design. Our approach substantially improves estimation accuracy of causal effects under multidimensional cutoffs and enhances the reliability and applicability of nonexperimental causal inference in complex policy settings—such as school district zoning and credit approval—where decisions depend on multiple criteria.

This paper addresses an inherent bias in conventional univariate distance-based methods for boundary discontinuity design (BDD) when assignment boundaries are piecewise-linear or irregularly shaped—bias arising from model misspecification and thus non-eliminable. To resolve this, we propose a novel causal inference framework based on bivariate scores. Theoretically, we establish, for the first time, the fundamental bias of distance-based estimators at boundary kinks and rigorously prove the theoretical superiority and universality of the bivariate-score approach. Methodologically, we develop a robust estimator integrating local polynomial regression with bivariate kernel weighting, and derive uniform inference theory—including consistent confidence band construction—for irregular boundaries. Empirically, we provide open-source software and demonstrate substantial improvements over existing methods in both simulations and real-data applications.

This paper addresses the challenge of accurately estimating and inferring causal treatment effects under multivariate fuzzy regression discontinuity designs (RDDs) and geographic RDDs—settings where treatment assignment depends on a two-dimensional continuous boundary. We propose a novel data-driven, adaptive bandwidth selection method that supports local polynomial estimation either on the original bivariate score or on the Euclidean distance to the boundary. Within a unified bivariate nonparametric regression framework, we develop both pointwise and uniform asymptotic inference procedures. Simulations demonstrate that our approach substantially improves spatial resolution and statistical power while maintaining robustness under complex boundary curvature and heterogeneous sampling density. Our primary contribution is the first theoretically rigorous yet empirically feasible unified estimation and inference toolkit for RDDs with two-dimensional boundaries.

This paper addresses the vulnerability of conventional GeoRDD assumptions—namely, continuity of potential outcomes or local randomization—to violation in spatial point process data. To mitigate this, we propose a robust causal inference framework grounded in weaker, more plausible assumptions. Methodologically, we develop a general-purpose robust testing procedure that integrates localized estimation near the boundary with a novel adaptive spatial resampling strategy to accurately approximate the null distribution of the test statistic. Applied to evaluating the causal effect of precinct boundaries on arrest rates in New York City, our approach detects a statistically significant and robust policy effect—contrasting sharply with findings from standard GeoRDD analyses. The framework balances theoretical rigor with practical implementability, offering a generalizable tool for causal evaluation of spatial policies in urban governance and related domains.

This study addresses the challenge large language models face in detecting cross-paragraph structural inconsistencies during multi-agent collaborative long-document generation. By fixing document content, defect types, and evaluation protocols, the authors systematically evaluate ten prominent models under both single-agent and multi-agent settings. Leveraging signal detection theory decomposition, controlled experiments, private record reconstruction, and automated scoring, they find that all models exhibit a performance drop exceeding two-thirds in multi-agent coordination scenarios. Only one developer-provided model shows a significant shift in reporting criteria (p<0.001), yet its confidence scores fail to reflect cross-segment defects. This work is the first to reveal the “detection cliff” phenomenon and introduces a reproducible benchmark framework for future research.

This study addresses the identification of discontinuities in distributional treatment effects where the sign of the marginal effect abruptly changes. To this end, it proposes a unified framework that integrates horizontal discontinuity analysis (HDA) and vertical discontinuity analysis (VDA), leveraging causal forests to estimate the treatment effect curve. The approach enables inference on the non-tangentiality of local slopes through asymptotic crossing-point theory and a bias-corrected Wald statistic. Empirical validation on both synthetic data and real-world data from Mexico’s PROGRESA program demonstrates the method’s ability to reliably detect sign-switching points. By doing so, this work substantially expands the methodological toolkit for analyzing distributional treatment effects and offers a novel pathway for investigating heterogeneous causal effects.

This study addresses the lack of consistent boundary definitions for chart types—such as Gantt charts—which complicates alignment in design space construction, grammar generation, and perceptual research. To resolve this, the authors propose a functional definition approach that distinguishes essential from variable features of chart types, establishing a boundary reasoning framework. Through conceptual analysis, design space modeling, and case studies, they validate the method and uncover hidden structures like feature entanglement, thereby making scope selection explicit. The approach yields a shared vocabulary and analytical tools for boundary analysis, demonstrated across Gantt charts, radar charts, and table maps. By clarifying how chart type definitions influence generalizability, this work offers a novel theoretical perspective for visualization research.

This study addresses the longstanding disconnect between joint structure characterization and rock bolt data in rock mass support evaluation, which has hindered integrated spatial analysis. The authors propose an automated framework tailored to 3D point clouds from underground mines that, for the first time, unifies structural plane mapping and rock bolt detection within a single modeling pipeline. By integrating plane fitting, object detection, normal vector computation, and stereographic projection analysis, the method enables fully automatic processing without manual intervention. Validated on real-world data from a metal mine, the approach accurately reconstructs joint networks and rock bolt geometries in medium-scale scenes and visualizes critical quality metrics—such as bolt exposure length and installation deviation—thereby facilitating comprehensive assessment of rock bolt–rock mass spatial relationships and support effectiveness.

This study addresses the data separation phenomenon in categorical response models, which frequently renders maximum likelihood estimates nonexistent or non-unique, thereby severely compromising the reliability of statistical inference. To resolve this issue, we develop divoRce, an R package grounded in structural vector theory that integrates computational geometry, linear programming, and rational arithmetic solvers. Supporting multiple link functions and third-party extensions, this toolkit enables existence testing, type classification, and identification of the variables responsible for separation. This work contributes the most comprehensive exact diagnostic suite currently available in the literature, encompassing virtually all categorical models. We recommend incorporating divoRce into standard analytical workflows to ensure modeling robustness and safeguard the validity of downstream inferential procedures.