Impact of Relying on Sample Variance-Covariance Estimate on Prediction Accuracy and Statistical Power of Hypothesis Testing When n << p

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Peter H. Hu*+ and Yue Wang and Jared Lunceford
• Companies: Merck & Co., Inc. and Merck & Co., Inc. and Merck & Co., Inc.
• Keywords: shrinkage estimator ; variance-covariance estimator ; linear combination ; high-dimensionality ; discriminant analysis ; power analysis

Abstract

Among 3 different variance-covariance estimators, the one using sample covariance shows the worst performance in prediction during a discriminant analysis with a high-dimensionality data. Comparison in the distributions of eigen values of these estimates in a simulation study suggests that their performances depend on how large the sample size n is relative to the feature size p. Comparison among 3 estimates with two real data for the variance of a composite score derived from a pre-specified linear combination of multi-variate data consistently shows that the variance estimate ignoring between-feature correlation performs the best. In a simulation study with similar setting, the sample variance of the composite score performs the worst among the 3 estimators. These results imply other estimators for the covariance matrix than using sample covariance should be considered when n << p.