arXiv subjects

Akira Shinkyu

Publications and source records attributed to Akira Shinkyu.

3 recordsLinked to original sources

arXiv2026

Uniform Consistency of Generalized Cross-Validation for Ridge Regression in High-Dimensional Misspecified Linear Models

This study examines generalized cross-validation for the tuning parameter selection for ridge regression in high-dimensional misspecified linear models. The set of candidates for the tuning parameter includes not only positive values but also zero and negative values. We demonstrate that if the second moment of the specification error converges to zero, generalized cross-validation is still a uniformly consistent estimator of the out-of-sample prediction risk. This implies that generalized cross-validation selects the tuning parameter for which ridge regression asymptotically achieves the smallest prediction risk among the candidates if the degree of misspecification for the regression function is small. Our simulation studies show that ridge regression tuned by generalized cross-validation exhibits a prediction performance similar to that of optimally tuned ridge regression and outperforms the Lasso under correct and incorrect model specifications.

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arXiv2022

Testing Heteroskedasticity in High-Dimensional Linear Regression

We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that our test statistic has asymptotic normality under the null hypothesis of homoskedasticity. Simulation results show that the proposed testing procedure obtains accurate empirical sizes and powers. We also present results of real economic data applications.

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arXiv2022

Small Tuning Parameter Selection for the Debiased Lasso

In this study, we investigate the bias and variance properties of the debiased Lasso in linear regression when the tuning parameter of the node-wise Lasso is selected to be smaller than in previous studies. We consider the case where the number of covariates $p$ is bounded by a constant multiple of the sample size $n$. First, we show that the bias of the debiased Lasso can be reduced without diverging the asymptotic variance by setting the order of the tuning parameter to $1/\sqrt{n}$.This implies that the debiased Lasso has asymptotic normality provided that the number of nonzero coefficients $s_0$ satisfies $s_0=o(\sqrt{n/\log p})$, whereas previous studies require $s_0 =o(\sqrt{n}/\log p)$ if no sparsity assumption is imposed on the precision matrix. Second, we propose a data-driven tuning parameter selection procedure for the node-wise Lasso that is consistent with our theoretical results. Simulation studies show that our procedure yields confidence intervals with good coverage properties in various settings. We also present a real economic data example to demonstrate the efficacy of our selection procedure.

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