Regression, parameter estimation local optimization

In a strict sense parameter estimation is the procedure of computing the estimates by localizing the extremum point of an objective function. A further advantage of the least squares method is that this step is well supported by efficient numerical techniques. Its use is particularly simple if the response function (3.1) is linear in the parameters, since then the estimates are found by linear regression without the inherent iteration in nonlinear optimization problems. 

The diagonal elements iv usually are some atomic physico-chemical properties or local vertex invariants however, diagonal elements can also be atom-type variable parameters (x, y, z,. ..) that are optimized to enhance the estimate of the studied property by regression analysis [Randic and Pompe, 2001b Lucic, Milicevic et al., 2003]. 

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