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Chen-Chien Wang

2011-10-07
12:50:00 - 14:30:00

400-1 , Mathematics Research Center Building (ori. New Math. Bldg.)

For nonlinear regression models, we often simply use asymptotic normality of the parameter estimators (a linear approximation) to construct ellipsoidal shape confidence regions. This straightforward method, however, can be misleading especially when sample size is small. In this talk, we first illustrate how nonlinearity leads to inaccurate confidence regions when adopting simple linear approximation. Then, we give a brief review of Hamilton's works (David Hamilton, Biometrika, 73, 57—64, 1986), in which he considers a well-chosen coordinate system to eliminate parameter-effect nonlinearity. The author then took the second order approximation of the solution locus into account in the construction of confidence region. A real data example, amino acid data, will be further used to demonstrate its performance visually.