Giummolè, Federica and Ventura, Laura (2001) Improved maximum likelihood estimation in heteroscedastic nonlinear regression models. [Working Paper] WORKING PAPER SERIES, 15/2001 . , PADOVA (Inedito)
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Nonlinear heteroscedastic regression models are a widely used class of models in applied statistics, with applications especially in biology, medicine or chemistry. Nonlinearity and variance heterogeneity can make likelihood estimation for a scalar parameter of interest rather inaccurate for small or moderate samples. In this paper, we suggest a new approach to point estimation based on estimating equations obtained from higher-order pivots for the parameter of interest. In particular, we take as an estimating function the modified directed likelihood. This is a higher-order pivotal quantity that can be easily computed in practice for nonlinear heteroscedastic models with normally distributed errors , using a recently developed S-PLUS library (HOA, 2000) . The estimators obtained from this procedure are a refinement of the maximum likelihood estimators, improving their small sample properties and keeping equivariance under reparameterisation. Two applications to real data sets are discussed.
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