arXiv subjects

Yoichi Arai

Publications and source records attributed to Yoichi Arai.

4 recordsLinked to original sources

arXiv2024

GLS under Monotone Heteroskedasticity

The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requires a restrictive functional form assumption for parametric estimation or smoothing parameters for nonparametric estimation. In this paper, we propose an alternative approach to estimate the conditional variance function under nonparametric monotonicity constraints by utilizing the isotonic regression method. Our GLS estimator is shown to be asymptotically equivalent to the infeasible GLS estimator with knowledge of the conditional error variance, and involves only some tuning to trim boundary observations, not only for point estimation but also for interval estimation or hypothesis testing. Our analysis extends the scope of the isotonic regression method by showing that the isotonic estimates, possibly with generated variables, can be employed as first stage estimates to be plugged in for semiparametric objects. Simulation studies illustrate excellent finite sample performances of the proposed method. As an empirical example, we revisit Acemoglu and Restrepo's (2017) study on the relationship between an aging population and economic growth to illustrate how our GLS estimator effectively reduces estimation errors.

econ.EM↗

arXiv2021

Regression Discontinuity Design with Potentially Many Covariates

This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform stably regardless of the number of covariates. The proposed methods combine the local approach using kernel weights with $\ell_{1}$-penalization to handle high-dimensional covariates. We provide theoretical and numerical results which illustrate the usefulness of the proposed methods. Theoretically, we present risk and coverage properties for our point estimation and inference methods, respectively. Under certain special case, the proposed estimator becomes more efficient than the conventional covariate adjusted estimator at the cost of an additional sparsity condition. Numerically, our simulation experiments and empirical example show the robust behaviors of the proposed methods to the number of covariates in terms of bias and variance for point estimation and coverage probability and interval length for inference.

econ.EM↗

arXiv2015

Optimal Bandwidth Selection for the Fuzzy Regression Discontinuity Estimator

A new bandwidth selection method for the fuzzy regression discontinuity estimator is proposed. The method chooses two bandwidths simultaneously, one for each side of the cut-off point by using a criterion based on the estimated asymptotic mean square error taking into account a second-order bias term. A simulation study demonstrates the usefulness of the proposed method.

stat.ME↗

arXiv2015

Simultaneous Selection of Optimal Bandwidths for the Sharp Regression Discontinuity Estimator

A new bandwidth selection rule that uses different bandwidths for the local linear regression estimators on the left and the right of the cut-off point is proposed for the sharp regression discontinuity estimator of the mean program impact at the cut-off point. The asymptotic mean squared error of the estimator using the proposed bandwidth selection rule is shown to be smaller than other bandwidth selection rules proposed in the literature. An extensive simulation study shows that the proposed method's performances for the sample sizes 500, 2000, and 5000 closely match the theoretical predictions.

stat.ME↗