Fixed effects models often rely on the within transformation, which constructs demeaned
arrays prior to forming cross-products. This paper develops an estimator that avoids the for-
mation of demeaned arrays by exploiting grouped summaries built from per-unit sufficient
statistics. A complete derivation shows that the grouped Gram representation reproduces the
classical estimator exactly. The difference lies in memory access patterns and byte movement.
The grouped estimator concentrates operations into unit-level accumulations, avoiding the
writes associated with array centering. Gains arise once the panel reaches a scale where mem-
ory traffic governs run time. Simulations examine coefficient accuracy, bootstrap dispersion,
run time, and memory use.