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Biometrika 1987 74(4):679-685; doi:10.1093/biomet/74.4.679
© 1987 by Biometrika Trust
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Asymmetry of estimators in nonlinear regression

RICHARD MORTON

CSIRO Division of Mathematics and Statistics Canberra, ACT2601, Australia

The least-squares estimators of nonlinear regression parameters are partitioned into three terms. Only the first is symmetrically distributed. Measures of asymmetry are derived from the other two which are valid for any sample size in that, if they are both zero for a given parameter, then its estimator is exactly symmetrically distributed. Asymptotic results are derived and we find that all odd central moments have a common factor when evaluated to first order. This factor relates to the second term only, as does the bias. To first order, the second term consists of ‘parameter effects’, in that it may be removed by transformation, whereas the third term is intrinsic.

Key Words: Asymmetric distribution • Least-squares estimator • Measure of asymmetry • Nonlinear regression


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