Facilitating the Calculation of the Efficient Score Using Symbolic Computing

• Activity Number: 300
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Education
• Author(s): Alexander Sibley*+ and Zhiguo Li and Yu Jiang and Cliburn Chan and Andrew Allen and Kouros Owzar
• Companies: Duke Cancer Institute and Duke University and Duke University and Duke University and Duke University and Duke University
• Keywords: efficient score ; symbolic computing ; computer algebra

Abstract

The score function (Rao, 1948) continues to serve a fundamental role in statistical inference. In the context of analyzing data from high-throughput genomic assays, inference on the basis of the score, as opposed to the asymptotically equivalent Wald or likelihood ratio tests, usually enjoys greater stability, considerably higher computational efficiency, and lends itself more readily to the use of resampling methods. While the score function often depends on a set of unknown nuisance parameters, which have to be replaced by estimators, the efficient score accounts for the variability induced by estimating these parameters. We illustrate using symbolic computing with computer algebra systems to facilitate the derivation of the efficient score. We demonstrate this process within the context of a standard example, and observe that this approach removes the burden of calculation and is less prone to error than manual derivations. In addition, the resulting symbolic expressions can be readily ported to compiled languages for the purpose of developing fast numerical algorithms for high throughput genomic analysis. We conclude by considering extensions of this approach.