arXiv Open Access 2019

Estimating the Random Effect in Big Data Mixed Models

Michael Law Ya'acov Ritov

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Abstrak

We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero, derive an asymptotic confidence interval for a single random effect at the parametric rate $\sqrt{n}$, and propose an empirical Bayes estimator for a part of the mean vector in ANOVA type models that performs asymptotically as well as the oracle Bayes estimator. We support our results with numerical simulations and provide comparisons with oracle estimators. The procedures developed are applied to the Trends in International Mathematics and Sciences Study (TIMSS) data.

Topik & Kata Kunci

math.ST stat.ME

Penulis (2)

Michael Law

Ya'acov Ritov

Format Sitasi

APA MLA BibTeX

Law, M., Ritov, Y. (2019). Estimating the Random Effect in Big Data Mixed Models. https://arxiv.org/abs/1907.11958

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Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓