Graduation Year
2026
Date of Submission
4-2026
Document Type
Campus Only Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematical Sciences
Reader 1
Evan Rosenman
Abstract
The James–Stein and Bock estimators improve upon the maximum likelihood estimator of a multivariate normal mean under squared-error loss. Their dominance properties have been established analytically, but the shape of the risk function across parameter space is less thoroughly characterized, particularly under non-spherical covariance. This thesis develops closed- form risk expressions for both estimators through Stein’s unbiased risk identity and uses them to trace performance curves across three covariance regimes: spherical, heteroscedastic, and AR(1)-correlated. The analysis identifies the effective dimension 𝑝∗ = tr(𝚺)/𝜆max(𝚺) as the central object governing the shape of these curves, and shows how the curves reshape as the covariance moves away from sphericity, including a directional dependence absent in the spherical case and a continuous transition through the dominance boundary 𝑝∗ = 2.
Recommended Citation
Fang, Yishu, "Performance Curve Analysis of Shrinkage Estimators under General Covariance" (2026). CMC Senior Theses. 4068.
https://scholarship.claremont.edu/cmc_theses/4068
This thesis is restricted to the Claremont Colleges current faculty, students, and staff.
