A geometer's view of the the Cramér-Rao bound on estimator variance

Anthony D. Blaom

Home/Archive/arXiv

arXiv · 1710.01598

A geometer's view of the the Cramér-Rao bound on estimator variance

Anthony D. Blaom

View original source ↗Read source document ↗Export metadata ↓

Abstract

The classical Cramér-Rao inequality gives a lower bound for the variance of a unbiased estimator of an unknown parameter, in some statistical model of a random process. In this note we rewrite the statment and proof of the bound using contemporary geometric language.

Explore related subjects

stat.OT math.ST stat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Anthony D. Blaom. 2017-10-25. A geometer's view of the the Cramér-Rao bound on estimator variance. https://arxiv.org/abs/1710.01598

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

See You at the Posterior Line: Learning Bayesian Modeling Through a Car Racing Game

We present an interactive classroom activity designed to address a central challenge in teaching introductory Bayesian statistics: how to formalize subjective knowledge and available information into prior distributions and then update them with empirical data. Role-playing as data analysts for a racing team, students evaluate candidate tires by converting qualitative engineering reports into prior distributions, collecting primary data via a virtual racing game, and using a Beta-Binomial model to inform team strategy. This discovery-based exercise allows small groups to observe directly how different prior choices and sample data jointly shape posterior inference. Student feedback ($n=32$) highlights high enjoyment, engagement and improved conceptual clarity. Open-access materials to implement the activity are provided, alongside recommendations for adapting it to other teaching contexts.

stat.OT↗

arXiv2026

Why is Regularization Underused? An Empirical Study on Trust and Adoption of Statistical Methods

Statistical practice does not automatically follow methodological innovation. Regularization methods, widely advocated to reduce overfitting and stabilize inference, are readily available in modern software, but are not consistently used by data analysts. We investigate this implementation gap in a large-scale empirical study of trust in, and acceptance of, regularization techniques, based on $N = 606$ data analysts. Drawing on measurement frameworks from technology acceptance research, we survey practitioners and embed a randomized experiment to test whether written recommendation of regularization methods increases trust or intended use. We find no evidence of such an effect. Instead, adoption intentions are strongly associated with analysts' perceptions of ease of implementation and practical benefit, such as improved bias control or interpretability. Perceived social norms also emerge as a central driver. These results indicate that uptake of statistical methodology depends less on formal recommendations than on usability, perceived utility, and community practice.

stat.OT↗

arXiv2026

Exact analysis of a split--merge queue with latent Erlang-factor dependent subtask times

This paper studies a two-server split--merge queue with positively dependent subtask service times modeled through a latent-factor bivariate Erlang construction. An exact characterization of the split--merge completion time is obtained, including explicit formulas for its first two moments and the resulting mean waiting time. Under fixed marginal service-time distributions, independence is shown to stochastically increase the completion time and hence overestimate mean waiting time. Numerical illustrations show that this benchmark gap can be substantial.

stat.OT↗