model calibration

Instrumental variable (IV) estimation suffers from severe finite-sample bias when the number of instruments $p$ far exceeds the sample size $n$. This paper systematically introduces random matrix theory to high-dimensional IV settings, revealing the implicit bias–variance trade-off advantage of ridge regularization under dense first-stage regressions—and extending this analysis to the $p > n$ regime. By reconstructing the finite-sample bias structure of two-stage least squares (2SLS), we propose a unified correction framework grounded in random matrix asymptotics, substantially improving second-stage estimation accuracy. We establish theoretical consistency of the proposed estimator under both high-dimensional sparse and dense first-stage designs. Empirically, the method reduces estimation error by over 30% on average across benchmark specifications. Our approach unifies and generalizes existing bias approximation and correction theories for high-dimensional IV estimation.

Single-parameter regularization in polynomial function regression lacks flexibility and struggles to adapt to heterogeneous data. Method: This paper proposes a multi-parameter Tikhonov-type regularization framework, enabling the first decoupled modeling and joint optimization of regularization parameters. It introduces an adaptive parameter selection criterion grounded in the bias–variance trade-off and designs an ensemble-based model aggregation strategy for robust fusion of models trained under varying regularization strengths. Contribution/Results: Theoretically, we establish learnability guarantees and generalization bounds for the multi-parameter regularized estimator. Empirically, on both synthetic and clinical medical datasets, the proposed method reduces average prediction error by 18.7% compared to single-parameter baselines, demonstrating improved generalization performance and clinical applicability.

This study addresses the fundamental trade-off between bias in a narrow model and variance in a wider model under moderate misspecification—where the true data-generating process includes one additional parameter beyond the fitted narrow model. The authors introduce the concept of a “tolerance radius” to quantify the range of misspecification within which the narrow model yields superior performance. Building on large-sample theory, likelihood-based estimation, and bias–variance decomposition, they develop a novel estimator that achieves robustness and efficiency across both model classes. Theoretical analysis and extensive numerical experiments across multiple model settings demonstrate that the proposed estimator significantly improves estimation accuracy within the tolerance radius, offering a principled balance between robustness to misspecification and statistical efficiency.

Existing surrogate models primarily focus on identifying a single optimal parameter set, neglecting the broader distribution of parameters that satisfy a given target output. Method: We propose a joint input-output space density estimation framework that integrates neural surrogate modeling, feature likelihood estimation, and Bayesian inference to construct a confidence-aware parameter prior. This enables efficient sampling and visualization of plausible parameter sets in high-dimensional spaces. Contribution/Results: Our key innovation lies in unifying density estimation with inverse inference to support interactive exploration of multi-solution parameter distributions. Evaluated on three scientific simulation datasets, the method demonstrates effectiveness in goal-directed parameter analysis, significantly enhancing users’ understanding of and ability to control the parameter-feature mapping relationship.

This paper addresses identification issues in skill formation structural models arising from standard normalization constraints, demonstrating that conventional scale and location normalization—particularly under CES utility—distorts key policy parameters, induces estimation bias, and undermines policy recommendations. Methodologically, it integrates structural identification analysis, characterization of identified sets, counterfactual inference, and statistical testing and correction of normalization constraints. The study establishes, for the first time, necessary and sufficient conditions for “true normalization,” achieving point identification of policy parameters under weaker assumptions than existing approaches; it further identifies and rectifies over-identification induced by scale constraints in CES models. A practical correction framework is proposed that preserves compatibility with standard estimators, ensures robustness of investment strategies to unit changes, and enhances the credibility of counterfactual predictions and policy evaluations.

This work addresses the lack of intuitive, immediate feedback on fitting errors in existing model-fitting approaches. It proposes an interactive fitting framework that integrates visual and auditory feedback: as users manipulate parametric curves, the system synthesizes audio in real time, with greater model-data discrepancies producing louder and more dissonant sounds. This is the first approach to incorporate auditory cues into model exploration, enabling multisensory assessment of fit quality. Combining interactive visualization, real-time audio synthesis, and Gaussian process regression, the method demonstrates effectiveness and generalizability across four diverse case studies—golf putting, dilution experiments, cosmological parameter estimation, and temperature data fitting—significantly enhancing users’ intuitive perception of model misfit.

This work addresses the high computational cost of traditional spline regression, which relies on grid search and cross-validation to select resolution hyperparameters. By leveraging approximation theory and ANOVA decomposition, the authors derive—for the first time—a closed-form analytical solution for the optimal resolution, thereby eliminating costly hyperparameter tuning. The proposed method, KORE, estimates bias and noise via two pilot fits and rapidly computes leave-one-out error using the PRESS identity. KORE reveals a Kolmogorov-optimal scaling law dependent solely on effective density and independent of input dimensionality, and it integrates multiple model selection criteria—including GCV, Cp, AIC, and BIC—for efficient modeling. On additive and sparse pairwise functions up to 80 dimensions, KORE achieves the accuracy of exhaustive cross-validation with only about one-eighth of the fitting effort; across 36 real-world tabular datasets, it attains the highest accuracy per unit computation among 21 competing methods.

This study addresses the ad hoc division between calibrated and estimated parameters in structural modeling, which often lacks a systematic foundation and can induce substantial bias due to calibration errors. For the first time, the partitioning problem is formalized as an optimization task, and a sensitivity-minimization criterion is proposed for selecting the optimal split. Specifically, a sensitivity statistic—constructed from local derivatives—quantifies how target estimates respond to perturbations in calibrated parameters. The method selects the partition that minimizes this statistic, thereby reducing worst-case local bias. Notably, it avoids repeated re-estimation and is applicable across a broad class of structural models. An application to a New Keynesian model demonstrates that the chosen partition significantly enhances estimation robustness and credibility under sizable calibration errors.

This study addresses the challenge of optimizing data collection to enhance social welfare in policy learning when unobserved heterogeneity is present. Accounting for latent individual differences in policy responses, the authors propose a repeated-measurement design based on proxy variables for latent traits and derive minimax regret bounds for policy rules that either incorporate or omit these latent variables. The theoretical analysis uncovers a novel trade-off between policy class complexity and estimation accuracy, leading to an optimal data collection strategy that allocates resources efficiently between measurement precision and sample size. In a development economics application, incorporating a proxy for entrepreneurs’ managerial ability increases social welfare by 5% and reduces the probability of welfare loss by 50%.

This work addresses the computational inefficiency in Bayesian semiparametric regression arising from complex design matrix structures. To mitigate this challenge, the authors propose an orthogonalization preprocessing step applied to the design日晚间 matrix prior to iterative inference, combined with a hybrid algorithm integrating Gibbs sampling and coordinate ascent variational inference. This approach reduces computational complexity to quadratic in the number of covariates, substantially accelerating both model fitting and posterior inference. Empirical evaluations across diverse experimental settings demonstrate speedups ranging from 5× to 60× compared to conventional methods, effectively alleviating the computational bottleneck induced by high-dimensional covariates.