C. R. Henderson, the statistician; and his contributions to variance components estimation

Area of Science:

• Statistics
• Population Genetics
• Animal Breeding

Background:

• The 1953 Biometrics paper by C. R. Henderson pioneered methods for estimating variance components using unbalanced data.
• This research addressed complex scenarios beyond the one-way classification, enabling the use of more varied datasets.

Discussion:

• Henderson's work facilitated the application of selection theory and index techniques in population genetics and animal breeding.
• The paper stimulated significant interest in random effects, mixed models, and variance components estimation among statisticians.
• Later developments, including maximum likelihood (ML) and restricted maximum likelihood (REML), built upon Henderson's foundational work, with his mixed model equations playing a key role.

Key Insights:

• Provided the first methods to estimate variance components from unbalanced data in complex classifications.
• Demonstrated the practical utility of these methods in fields like animal breeding and population genetics.
• Catalyzed further research and development in statistical modeling for complex data structures.

Outlook:

• Henderson's methods and subsequent advancements continue to influence statistical modeling in genetics and breeding.
• The development of feasible computing procedures, alongside Henderson's mixed model equations, made advanced statistical techniques more accessible.
• The foundational nature of this work ensures its continued relevance in statistical research and application.