Abstract
Canonical correlation assesses the relationship between two groups of variables. Although it has been a useful tool in a wide variety of research areas, it is not well known that weaker canonical correlations require larger sample sizes to be correctly inferred. In this article, we investigate small sample bias in canonical correlation analysis and apply the jackknife bias correction to the estimation of canonical correlations. We use bootstrap samples to obtain a better confidence interval for the jackknife canonical correlation estimator.
Mathematics Subject Classification:
Acknowledgment
The author thanks Dr. Myunghee Cho Paik, Professor in Biostatistics at Columbia University, for suggestions that led to improvements in this article.
Notes
γ10: true correlation; bias(γ1) = γ1 − γ10; : standard estimator; : jackknife estimator; : bootstrap estimator
Pairs: number of pairs; γ10: true maximum canonical correlation; ASV: asymptotic variance estimator; SJKV: standard jackknife variance estimator; 95% CR: coverage rate of 95% confidence interval
Pairs: number of pairs; γ10: true maximum canonical correlation; ASV(γ1): asymptotic variance estimator; SJKV: standard jackknife variance estimate; 95% CR: coverage rate of 95% confidence interval
Pairs: number of pairs; γ10: true maximum canonical correlation; BJKV: bootstrap jackknife variance estimate; 95% CR: coverage rate of 95% confidence interval; Length: average length of confidence interval; Boot-t: using standardized pivotal distribution of bootstrap jackknife estimates; Boot-%: using distribution of bootstrap jackknife estimates
Pairs: number of pairs; γ10: true maximum canonical correlation; BJKV: bootstrap jackknife variance estimate; 95% CR: coverage rate of 95% confidence interval; Length: average length of confidence interval; Boot-t: using standardized pivotal distribution of bootstrap jackknife estimates; Boot-%: using distribution of bootstrap jackknife estimates