arXiv subjects

Toshiki Tsuda

Publications and source records attributed to Toshiki Tsuda.

4 recordsLinked to original sources

arXiv2026

A Uniform Confidence Band for the Marginal Treatment Effect Function

This paper presents a method for constructing uniform confidence bands for the marginal treatment effect (MTE) function. The shape of the MTE function provides insight into how the unobserved propensity to receive treatment relates to the treatment effect. Our approach visualizes the statistical uncertainty of an estimated function, facilitating inferences about the function's shape. The proposed method is computationally inexpensive and requires only minimal information: sample size, standard errors, kernel function, and bandwidth. We derive a Gaussian approximation for a local quadratic estimator and consider the approximation of the distribution of its supremum in polynomial order. Monte Carlo simulations demonstrate that our bands provide the desired coverage and are less conservative than those based on the Gumbel approximation. An empirical application based on the rural electrification program is included.

econ.EM↗

arXiv2025

Universality of estimators for high-dimensional linear models with block dependency

We study the universality property of estimators for high-dimensional linear models, which implies that the distribution of estimators is independent of whether the covariates follow a Gaussian distribution. Recent developments in high-dimensional statistics typically require covariates to strictly follow a Gaussian distribution to precisely characterize the properties of estimators. To relax this Gaussianity requirement, the existing literature has examined conditions under which estimators achieve universality. In particular, independence among the elements of the high-dimensional covariates has played a critical role. In this study, we focus on high-dimensional linear models with covariates exhibiting block dependence, where covariate elements can only be dependent within each block, and show that estimators for such models retain universality. Specifically, we prove that the distribution of estimators with Gaussian covariates can be approximated by the distribution of estimators with non-Gaussian covariates having the same moments under block dependence. To establish this result, we develop a generalized Lindeberg principle suitable for handling block dependencies and derive new error bounds for correlated covariate elements. We further demonstrate the universality result across several different estimators.

math.ST↗

arXiv2024

Treatment Effects with Multidimensional Unobserved Heterogeneity: Identification of the Marginal Treatment Effect

This paper establishes sufficient conditions for the identification of the marginal treatment effects with multivalued treatments. Our model is based on a multinomial choice model with utility maximization. Our MTE generalizes the MTE defined in Heckman and Vytlacil (2005) in binary treatment models. As in the binary case, we can interpret the MTE as the treatment effect for persons who are indifferent between two treatments at a particular level. Our MTE enables one to obtain the treatment effects of those with specific preference orders over the choice set. Further, our results can identify other parameters such as the marginal distribution of potential outcomes.

econ.EM↗

arXiv2023

Benign Overfitting of Non-Sparse High-Dimensional Linear Regression with Correlated Noise

We investigate the high-dimensional linear regression problem in the presence of noise correlated with Gaussian covariates. This correlation, known as endogeneity in regression models, often arises from unobserved variables and other factors. It has been a major challenge in causal inference and econometrics. When the covariates are high-dimensional, it has been common to assume sparsity on the true parameters and estimate them using regularization, even with the endogeneity. However, when sparsity does not hold, it has not been well understood to control the endogeneity and high dimensionality simultaneously. This study demonstrates that an estimator without regularization can achieve consistency, that is, benign overfitting, under certain assumptions on the covariance matrix. Specifically, our results show that the error of this estimator converges to zero when the covariance matrices of correlated noise and instrumental variables satisfy a condition on their eigenvalues. We consider several extensions relaxing these conditions and conduct experiments to support our theoretical findings. As a technical contribution, we utilize the convex Gaussian minimax theorem (CGMT) in our dual problem and extend CGMT itself.

math.ST↗