The Biases and Mean Squared Errors of Estimators of Multinormal Squared Multiple Correlation

Joseph F. Lucke and Susan Embretson Whitely

Journal of Educational and Behavioral Statistics, 1984, vol. 9, issue 3, 183-192

Abstract: The sample squared multiple correlation coefficient, R 2 , is known to have certain unsatisfactory properties as an estimator of the population squared multiple correlation. Hence, numerous adjusted estimators based on functions of 1 – R 2 have been proposed. We examine the biases and mean squared errors of five adjusted estimators as well as R 2 . General results are given for estimators linear in 1 – R 2 , and four such estimators are examined in detail. In addition, a quadratic estimator and the minimum variance unbiased estimator are examined. Comparisons among these estimators are made in terms of absolute bias and mean squared error.

Keywords: Squared multiple correlation; correlation; adjusted estimators; shrinkage (search for similar items in EconPapers)
Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:9:y:1984:i:3:p:183-192

DOI: 10.3102/10769986009003183

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