Research

This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our theory accommodates growing and heterogeneous cluster sizes. We derive asymptotic conditional bias and variance, establish uniform consistency, and prove asymptotic normality. Our findings reveal that under heterogeneous cluster sizes, the asymptotic variance includes a new term reflecting within-cluster dependence, which is overlooked when cluster sizes are presumed to be bounded. We propose valid approaches for bandwidth selection and inference, introduce estimators of the asymptotic variance, and demonstrate their consistency. In simulations, we verify the effectiveness of the cluster-robust bandwidth selection and show that the derived cluster-robust confidence interval improves the coverage ratio. We illustrate the application of these methods using a policy-targeting dataset in development economics.

This paper studies optimal hypothesis testing for nonregular statistical models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on the likelihood ratio process. The proposed one-sided test involves randomization to achieve asymptotic size control, some tuning constant to avoid discontinuities in the limiting likelihood ratio process, and a user-specified alternative hypothetical value to achieve the asymptotic optimality. Our two-sided test becomes asymptotically uniformly most powerful without imposing further restrictions such as unbiasedness. Simulation results illustrate desirable power properties of the proposed tests.

OLS estimators are widely used in network experiments to estimate spillover effects via regressions on exposure mappings that summarize treatment and network structure. We study the causal interpretation and inference of such OLS estimators when both design-based uncertainty in treatment assignment and sampling-based uncertainty in network links are present. We show that correlations among elements of the exposure mapping can contaminate the OLS estimand, preventing it from aggregating heterogeneous spillover effects for clear causal interpretation. We derive the estimator's asymptotic distribution and propose a network-robust variance estimator. Simulations and an empirical application reveal sizable contamination bias and inflated spillover estimates.