Some Geometrical Aspects of the Nonlinear Least Squares Method

Results on the geometry of a nonlinear regression model and their statistical consequences are presented in a condensed form. The least squares method is considered here as a projection onto the expectation surface, which allows to explain the problem of uniqueness of the parameter estimates, and overcomes the danger of a false interpretation of the least squares in case of very curved or statistically overlapping models. Measures of nonlinearity (curvatures), and the Riemannian curvature tensor are presented briefly, and statistical consequences of having zero curvatures are given. In particular, the earlier author's results on the probability density of the estimator are discussed briefly, in relation to curvatures (Author)