First derivatives at the optimum analysis (fdao): An approach to estimate the uncertainty in nonlinear regression involving stochastically independent variables
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An important problem of optimization analysis surges when parameters such as {θ_i}_i=1, ... ,k , determining a function y=f(x | {θ_i}) , must be estimated from a set of observables { x_j,y_j}_j=1, ... ,m . Where {x_i} are independent variables assumed to be uncertainty-free. It is known that analytical solutions are possible if y=f(x | θ_i) is a linear combination of {θ_i=1, ... ,k}. Here it is proposed that determining the uncertainty of parameters that are not linearly independent may be achieved from derivatives ∂ f(x | {θ_i})∂θ_i at an optimum, if the parameters are stochastically independent.
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