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The Shrunken Generalized Distance: A Useful Concept for Estimation of the Actual Error Rate

Author(s):
Dorans, Neil J.
Publication Year:
1984
Report Number:
RR-84-01
Source:
ETS Research Report
Document Type:
Report
Page Count:
29
Subject/Key Words:
Classification, Data Analysis, Error of Measurement, Prediction, Psychometrics, Statistics

Abstract

The mathematical concept of the shrunken generalized distance is introduced as a missing link in the framework of classification and prediction problems. The nature of the criterion can be used to distinguish between a prediction problem and a classification problem. The well-known continuous criterion indices least squares regression weights, squared validity coefficient and mean squared error of prediction have binary criterion brethren, in both the population and sample, namely, the Fisher linear discriminant weights, generalized distance, and error rates, respectively. Likewise the population squared cross-validity coefficient has a binary-criterion relative, the shrunken generalized distance. An estimator of the shrunken generalized distance is introduced and shown to be useful for estimation of the actual error rate. (29pp.)

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