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A new approach to statistical efficiency of weighted least squares fitting algorithms for reparameterization of nonlinear regression models |
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| Authors: | Shimin Zheng A.K. Gupta |
| Affiliation: | a Department of Biostatistics and Epidemiology, East Tennessee State University, Box 70259, Johnson City, TN 37614, USA b Department of Finance, Nanjing Audit University, Nanjing, PR China c Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA |
| Abstract: | We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao-Cramer lower bound) in the limit of small noise. |
| Keywords: | Nonlinear regression Small sigma asymptotic Reparameterization Weighted least squares Efficiency Rao-Cramer bound |
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