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Notes
See also FØrsund (1980, p. 12) “If a specific distribution is assumed for u, and if the parameters of this distribution can be derived from its higher-order (second, third, etc.) central moments, then we can estimate these parameters consistently from the moments of the OLS residuals. Since \(\mu \) is a function of these parameters, it too can be estimated consistently, and this estimate can be used to ‘correct’ the OLS constant term, which is a consistent estimate of \((\alpha -\mu )\). COLS thus provides consistent estimates of all of the parameters of the frontier.”
The corresponding statement in Aigner et al. (1977, pp. 28–29) is “We note in passing that if estimation of \(\varvec{\beta }\) alone is desired, all but the coefficient in \(\varvec{\beta }\) corresponding to a column of ones in X is estimated unbiasedly and consistently by least squares. Moreover, the components of \(\sigma ^2\) can be extracted (i.e., consistent estimators for them can be found) based on the least squares results by utilizing Eq. (9) for \(V(\varepsilon )\) in terms of \(\sigma ^2_u\) and \(\sigma ^2_v\) and a similar relationship for a higher-order moment of \(\varepsilon \), since \(V(\varepsilon )\) and higher order mean-corrected moments of \(\varepsilon \) are themselves consistently estimable from the computed least-squares residuals.”
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Communicated by Pierre R. L. Dutilleul.
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Papadopoulos, A., Parmeter, C.F. A skewed sense of newness. Environ Ecol Stat 28, 861–863 (2021). https://doi.org/10.1007/s10651-021-00518-z
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DOI: https://doi.org/10.1007/s10651-021-00518-z