Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Consistency of M estimates for separable nonlinear regression models   Consider a nonlinear regression model : y_{i}=g(x_{i},{\theta})+e_{i},
i=1,...,n, where the x_{i} are random predictors x_{i} and {\theta} is the
unknown parameter vector ranging in a set {\Theta}\subsetR^{p}. All known
results on the consistency of the least squares estimator and in general of M
estimators assume that either {\Theta} is compact or g is bounded, which
excludes frequently employed models such as the Michaelis-Menten, logistic
growth and exponential decay models. In this article we deal with the so-called
separable models, where p=p_{1}+p_{2}, {\theta}=({\alpha},{\beta}) with
{\alpha}\inA\subsetR^{p_{1}}, {\beta}\inB\subsetR^{p_{2},}and g has the form
g(x,{\theta})={\beta}^{T}h(x,{\alpha}) where h is a function with values in
R^{p_{2}}. We prove the strong consistency of M estimators under very general
assumptions, assuming that h is a bounded function of {\alpha}, which includes
the three models mentioned above. Key words and phrases: Nonlinear regression,
separable models, consistency, robust estimation.

35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th