Abstract Spatial varying coefficient (SVC) model offers an effective way to characterize the heterogeneous effects of covariates on the response variable. However, existing SVC models assume accurately measured covariates, ignoring real-world measurement errors that may arise from many aspects. This paper develops a novel, statistically and computationally efficient framework for the inference of SVC models based on profile model likelihood, with explicit consideration of covariate measurement error. Focusing on spatial clustered coefficient models, we formulate an SVC model that allows functional covariate measurement errors. Bias-corrected estimators are derived by leveraging techniques of high-dimensional measurement error models and unbiased estimating functions, ensuring consistent parameter estimation. A predictive SVC model is then proposed to facilitate computations for large datasets. Finally, the effectiveness of the proposed approaches is demonstrated through comprehensive simulation studies and an analysis of the Arctic sea ice dataset.

Abstract We propose CUSUM-Net, a novel nonparametric framework for detecting changes in data distributions by leveraging an integral probability metric (IPM) optimized through deep neural networks. CUSUM-Net identifies the optimal direction separating distinct distributional regimes by aggregating critic-CUSUM statistics over candidate changepoints, directly aligning changepoint detection with IPM optimization. Unlike existing parametric methods, our approach is robust to complex, high-dimensional data distributions and accommodates various data modalities including vectors, symmetric positive-definite matrices, images, and graphs. Theoretically, we establish nonparametric excess-risk bounds for the learned critic and demonstrate accelerated convergence rates under low-dimensional manifold assumptions. Furthermore, consistency of the resulting changepoint estimator is proven. Extensive numerical experiments validate the flexibility, robustness, and efficiency of CUSUM-Net.

Abstract There is growing interest in constructing conformal prediction sets that provide approximate or asymptotic conditional coverage guarantees, capturing local data heterogeneity. However, methods like localized conformal prediction (LCP) may face challenges in ensuring reliable prediction sets in regions with sparse calibration data. This paper introduces Enhanced Localized Conformal Prediction (ELCP), a novel approach that incorporates auxiliary data to refine localized prediction sets while preserving finite-sample marginal coverage guarantees. By utilizing a density-ratio-weighted kernel estimator, ELCP seamlessly integrates auxiliary and calibration data, accommodating potential distributional shifts and improving the local reliability of prediction sets. Theoretical analysis confirms that ELCP maintains marginal coverage and enhances asymptotic test-conditional coverage. Simulation results demonstrate its superior local coverage and smaller prediction sets compared to standard LCP, highlighting its effectiveness in settings with limited calibration data but available auxiliary information from related tasks.

Abstract This paper studies nonparametric local (over-)identification, in the sense of Chen and Santos (2018), and the associated semiparametric efficiency in modern causal frameworks. We develop a unified approach that begins by translating structural models with latent variables into their induced statistical models of observables and then analyzes local overidentification through conditional moment restrictions. We apply this approach to three leading models: (i) the general treatment model under unconfoundedness, (ii) the negative control model, and (iii) the long-term causal inference model under unobserved confounding. The first design yields a locally just-identified statistical model, implying that all regular asymptotically linear estimators of the treatment effect share the same asymptotic variance, equal to the (trivial) semiparametric efficiency bound. In contrast, the latter two models involve nonparametric endogeneity and are naturally locally overidentified; consequently, some doubly robust orthogonal moment estimators of the average treatment effect are inefficient. Whereas existing work typically imposes strong conditions to restore just-identification before deriving the efficiency bound, we relax such assumptions and characterize the general efficiency bound, along with efficient estimators, in the overidentified models (ii) and (iii).

Abstract This paper investigates the use of synthetic control methods for causal inference in macroeconomic settings when dealing with possibly nonstationary data. While the synthetic control approach has gained popularity for estimating counterfactual outcomes, we caution researchers against assuming a common nonstationary trend factor across units for macroeconomic outcomes, as doing so may result in misleading causal estimation—a pitfall we refer to as the spurious synthetic control problem. To address this issue, we propose a synthetic business cycle framework that explicitly separates trend and cyclical components. By leveraging the treated unit's historical data to forecast its trend and using control units only for cyclical fluctuations, our divide-and-conquer strategy eliminates spurious correlations and improves the robustness of counterfactual prediction in macroeconomic applications. As empirical illustrations, we examine the cases of German reunification and the handover of Hong Kong, demonstrating the advantages of the proposed approach.

Abstract To be determined.