Is this the least squares estimate?

It is shown that the sum of squares can have several local minima with a positive probability for any intrinsically nonlinear regression with infinite tails. Therefore, the availability of global criteria is crucial. The concept of the local convexity level for the sum of squares in nonlinear regression models is introduced. A general formula for this local convexity level is derived and it is shown that the local convexity level is equal to the minimum of the squared radius of the full curvature of the expectation surface of the nonlinear regression. Two general global criteria are formulated. The ideas are illustrated by four types of nonlinear model, namely polylinear, power, linear M-regression and exponential regression models. The suggested global criteria are shown to work well for real-life data.