Moments of the Least Squares Estimators in a Non-Linear Regression Model
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1980 · Volume 42 · Issue 2
DOI: 10.1111/j.2517-6161.1980.tb01124.x
Abstract
The least squares estimates of the parameters of a non-linear regression model with normal and independent errors are expanded as a power series in independent standardized normal variables. From this expansion, expressions are derived for the variances and covariances which include one term beyond the usual approximation by the inverse of the information matrix. Similarly, expressions for the biases are found and overall relationships between the biases, variances and Beale's measures of non-linearity. Data following the Richards' Function are used in an example.
Keywords
bias, measures of non-linearity, non-linear regression, richards' function, variance
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