semiparametric projection method

This study addresses the estimation bias arising from endogeneity in regression models by proposing a general and computationally efficient semiparametric projection method. The approach constructs endogenous instrumental variables by projecting and expanding the conditional mean function of the structural error onto the space of explanatory variables, thereby avoiding reliance on conventional exogenous instruments or specific parametric model forms. It is applicable to linear, nonlinear, and semiparametric settings alike. By integrating LASSO-based variable selection with asymptotic theory, the paper establishes identification conditions and asymptotic properties of the resulting estimator. Extensive simulations and empirical analyses demonstrate the method’s strong finite-sample performance, confirming its practical utility in mitigating endogeneity bias across diverse modeling contexts.

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.

This study addresses the estimation of average impulse response functions in macroeconomic structural dynamic models featuring pervasive nonlinearities—such as nonlinearly transformed regressors, state-dependent coefficients, and nonlinear interactions between shocks and state variables—and proposes the first semiparametric local projection estimator tailored to this class of models. The method relies on doubly robust moment conditions, expressing the target functional as a linear functional of a nonparametric conditional mean, and incorporates a density ratio to characterize the effect of counterfactual shock variations. Cross-fitting is employed to effectively handle serial dependence. The resulting estimator achieves √T-consistency and asymptotic normality, demonstrates robustness across diverse nonlinear data-generating processes, and is validated through two empirical applications.

This study addresses the challenge of constructing Neyman-orthogonal scores for robust causal inference in semiparametric models with infinite-dimensional nuisance parameters. The authors propose a general framework that, for the first time, explicitly constructs orthogonal scores for a broad class of such models, yielding estimators of the target parameter that are asymptotically normal and require only a convergence rate of $o_p(n^{-1/4})$ or better for the nuisance parameter estimates. The approach seamlessly integrates with machine learning algorithms and is applied to estimate causal effects under binary instrumental variables. Numerical experiments demonstrate substantial finite-sample improvements over naive estimators, and an empirical analysis of the Oregon Health Insurance Experiment confirms the method’s robustness and practical utility in real-world settings.

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 study addresses policy evaluation when the outcome variable is non-Gaussian—exhibiting skewness or heavy tails—and the error distribution is unknown. Under a structural model assuming a low-dimensional parametric form for the mean function and independence between errors and both treatment assignment and covariates, the authors derive the semiparametric efficiency bound and the corresponding efficient influence function. They propose a targeted maximum likelihood estimator based on cross-fitting and efficient regression scores. The method substantially outperforms Gaussian working models, Bayesian additive regression trees, and augmented inverse probability weighting in settings with correctly specified mean structures and imbalanced treatment allocation, yielding lower root mean squared error and shorter confidence intervals. Its practical advantages are further demonstrated through an application to earnings data from the National Supported Work program.

This study addresses the critical challenge of reliably estimating sharp lower bounds for the standard errors of moment condition estimators when cross-sample correlation information is either absent or only partially available. By leveraging geometric inequalities, the authors derive explicit and tight lower bounds on standard errors and show that the general problem can be reformulated as a semidefinite programming (SDP) problem amenable to efficient computation. This approach yields the first sharp error bounds in settings with no knowledge of cross-sample correlations. Integrating insights from moment condition estimation and statistical inference theory, the method demonstrates both validity and practical utility across several applications, including menu cost models, heterogeneous-agent New Keynesian frameworks, and two-sample instrumental variable settings.

This study addresses the challenge of specification testing in conditional moment models under high-dimensional nuisance parameters, where conventional approaches relying on asymptotically linear estimators struggle to accommodate modern machine learning methods. The authors propose a kernel-based locally robust testing framework that uniquely integrates Neyman-orthogonal moments, cross-fitting, and reproducing kernel Hilbert space techniques to achieve first-order insensitivity to estimation errors in nuisance parameters. Under mild convergence rates for nuisance estimators, the method ensures oracle equivalence between feasible and infeasible tests and precisely characterizes local power. Employing a fast multiplier bootstrap, the framework demonstrates excellent finite-sample performance across diverse applications—including specification tests for high-dimensional linear and logistic regression, significance testing in machine learning regression, and tests for constant conditional treatment effects—as validated by Monte Carlo simulations and empirical analysis.

This study addresses the bias arising from estimation errors in nuisance parameters within parametric moment condition models. To mitigate this issue, the paper proposes a high-order debiasing method that constructs moment functions exhibiting Neyman orthogonality of a specified order with respect to the nuisance parameters, thereby substantially reducing the sensitivity of the estimator to such errors. The approach is both unified and computationally tractable, with a key innovation being that the number of additional nuisance parameters required for orthogonality does not grow with the order of orthogonality—indeed, it can be reduced to a single scalar. Theoretical analysis and empirical evidence demonstrate that this method effectively diminishes estimation bias and significantly enhances robustness and precision across a broad class of econometric models.