Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First derivatives at the optimum analysis (\textit{fdao}): An approach
  to estimate the uncertainty in nonlinear regression involving stochastically
  independent variables   An important problem of optimization analysis surges when parameters such as
$ \{\theta_j\}_{j=1,\, \dots \,,k }$, determining a function $
y=f(x\given\{\theta_j\}) $, must be estimated from a set of observables $ \{
x_i,y_i\}_{i=1,\, \dots \,,m} $. Where $ \{x_i\} $ are independent variables
assumed to be uncertainty-free. It is known that analytical solutions are
possible if $ y=f(x\given\theta_j) $ is a linear combination of $
\{\theta_{j=1,\, \dots \,,k} \}.$ Here it is proposed that determining the
uncertainty of parameters that are not \textit{linearly independent} may be
achieved from derivatives $ \tfrac{\partial f(x \given \{\theta_j\})}{\partial
\theta_j} $ at an optimum, if the parameters are \textit{stochastically
independent}.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th