delta method

This study addresses the estimation of parameters of the form θ₀ = E[F_Y⁻¹∘F_Z(X)] in the “changes-in-changes” model, for which existing methods lack theoretical guarantees when variables are unbounded. The authors construct a plug-in estimator based on empirical quantiles and establish its √n-consistency and asymptotic normality under assumptions weaker than those in the current literature. They further propose a novel consistent estimator for the asymptotic variance. The theoretical analysis leverages empirical process theory and plug-in methods for quantile functions. Monte Carlo simulations demonstrate that the proposed variance estimator substantially outperforms existing alternatives, leading to markedly improved inference accuracy.

This study addresses volatility estimation in high-frequency financial data contaminated by market frictions or microstructure noise. The authors propose an adaptive subsampling approach that directly infers the asymptotic (conditional) covariance matrix of volatility estimators without explicitly modeling the noise structure. By employing time-rescaled statistics over local intervals to assess sampling variability, the method automatically selects tuning parameters while ensuring the resulting covariance matrix is positive semidefinite. Theoretical analysis, Monte Carlo simulations, and empirical applications demonstrate that the proposed estimator is consistent, exhibits strong finite-sample performance, and enables robust and feasible statistical inference.

Under adaptive data collection, parameter estimation in generalized linear models loses asymptotic normality due to nonparametric nuisance components, hindering valid confidence interval construction. To address this, we propose a weighted estimating equation that systematically corrects adaptive bias. We establish, for the first time, the minimal “explorability” condition required to restore asymptotic normality and guarantee reliable linear functional estimation under weaker assumptions than those in existing literature. Theoretically, our estimator is proven to be asymptotically normal, enabling principled confidence interval construction. Numerical experiments on standard linear bandits and sparse generalized bandits demonstrate both consistency and superior performance relative to state-of-the-art methods, with substantial improvements in estimation accuracy and inference validity.

This paper addresses the estimation of dynamic parameters in nonlinear time-varying time series models—including VAR, ARCH/GARCH, and Poisson autoregression—by developing asymptotic theory for local polynomial (quasi-)maximum likelihood estimation. Under substantially weakened smoothness and moment conditions—dispensing with higher-order differentiability or strict stationarity—we establish consistency and asymptotic normality of the estimator and precisely characterize the leading bias induced by smoothing. Key contributions include: (i) the first feasible framework for consistent and asymptotically normal time-varying parameter estimation in Poisson autoregressive models; (ii) a significant relaxation of theoretical regularity conditions required for existing VAR and ARCH-type models; and (iii) a simplified, closed-form bias expression directly applicable to bias correction. The unified theory accommodates a broad class of nonstationary nonlinear models, thereby extending the scope of valid dynamic parameter inference.

This paper addresses point estimation and uncertainty quantification for treatment effect paths—such as dynamic effects and event-study designs—in policy evaluation. To overcome the looseness of conventional uniform confidence bands, which ignore correlations among path estimators, we propose two data-driven feasible bound methods. Our novel framework jointly enforces average-effect coverage guarantees and path smoothness constraints, integrating post-selection inference, smooth regularization, Monte Carlo simulation, and robust point estimation. The resulting confidence bands are substantially narrower while maintaining valid coverage, especially under high estimator correlation; our point estimator also demonstrates superior performance across diverse simulation settings. The key contribution is the first systematic incorporation of smoothness priors into path inference, thereby unifying statistical rigor with economic interpretability.

This study addresses the failure of standard influence function–based inference in finite samples under “near-boundary” settings of semiparametric models, where second-order remainder terms non-negligibly contribute to sampling variance. The authors propose a finite-sample variance decomposition framework that separates influence function variance from remainder-induced variance and establish necessary and sufficient conditions for the consistency of sandwich variance estimators. Building on this framework, they develop two robust variance estimators—the leave-one-unit-out jackknife and a paired-cluster bootstrap—and derive an analytical expression for the interaction between remainder terms and within-cluster correlation in clustered data. Their approach enables valid confidence interval construction near the boundary: the jackknife Wald interval is numerically equivalent to a bias-corrected sandwich estimator and accurately captures the mechanism by which clustering amplifies variance estimation bias.

This study addresses the quantification of sources of predictive uncertainty and their contributions to prediction interval width. Building upon the law of total variance, the work proposes several conservative decompositions of posterior predictive variance, systematically characterizing the components of uncertainty and their interdependencies through conditional expectation and conditional variance terms. Experimental evaluations across multiple canonical models demonstrate that the proposed approach effectively identifies the dominant sources of uncertainty and reveals coherent patterns of co-variation among decomposition terms. These insights offer a novel perspective for model assessment and refinement, enhancing interpretability and guiding targeted improvements in predictive reliability.

This study addresses the inefficiency of traditional quantile estimation under light-tailed, heavy-tailed, or asymmetric distributions and its difficulty in smoothly bridging central and tail regions. The authors propose a unified interpolation-based quantile estimation framework that incorporates quadratic, Huber, or Tukey bisquare regularization into the check loss function, enabling continuous control of the effective quantile level via an interpolation parameter. They derive, for the first time, a closed-form parametrization of the effective quantile level under quadratic interpolation and establish a complete asymptotic theory, revealing the dependence of estimation efficiency on distributional shape. Theoretical and simulation results demonstrate that the proposed method reduces asymptotic variance by up to 36% under light-tailed distributions and by up to 57% under heavy-tailed or asymmetric distributions. Empirical analysis of daily log-returns confirms its superior performance in tail risk estimation.

This study addresses the substantial bias often incurred by conventional variance estimators—such as those based on Taylor linearization—for the generalized regression (GREG) estimator in high-dimensional auxiliary variable settings, which undermines inferential reliability. The paper provides the first systematic characterization of the asymptotic bias of GREG variance estimation under high-dimensional regimes and introduces a novel cross-validation–based approach to construct an unbiased variance estimator. Under mild distributional assumptions on the covariates, the proposed method is shown to be asymptotically unbiased. By integrating high-dimensional asymptotic theory with the model-assisted estimation framework, this work establishes a rigorous theoretical foundation for variance estimation in high-dimensional GREG settings and demonstrates through numerical experiments that the method exhibits excellent finite-sample performance.

This study addresses the distortion in inference caused by conventional grid-search methods for constructing confidence sets under weak identification, which often omit relevant regions or truncate unbounded sets. By exploiting the polynomial and rational structures of the Anderson–Rubin and Lagrange multiplier statistics, together with the geometric properties of the conditional quasi-likelihood ratio test, the authors propose an exact confidence set construction algorithm based on polynomial root-finding and geometric inversion. They further develop a high-order polynomial approximation scheme whose coverage error vanishes as the approximation order increases. This framework reliably recovers confidence sets with correct nominal coverage in weak-instrument settings, substantially outperforming standard grid-based approaches, and extends naturally to models featuring piecewise-polynomial or rational moment conditions.