Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Autoregressive Functions Estimation in Nonlinear Bifurcating
  Autoregressive Models   Bifurcating autoregressive processes, which can be seen as an adaptation of
au-toregressive processes for a binary tree structure, have been extensively
studied during the last decade in a parametric context. In this work we do not
specify any a priori form for the two autoregressive functions and we use
nonparametric techniques. We investigate both nonasymp-totic and asymptotic
behavior of the Nadaraya-Watson type estimators of the autoregressive
functions. We build our estimators observing the process on a finite subtree
denoted by Tn, up to the depth n. Estimators achieve the classical rate |Tn|
--$\beta$/(2$\beta$+1) in quadratic loss over H{\"o}lder classes of smoothness.
We prove almost sure convergence, asymptotic normality giving the bias
expression when choosing the optimal bandwidth and a moderate deviations
principle. Our proofs rely on specific techniques used to study bifurcating
Markov chains. Finally, we address the question of asymmetry and develop an
asymptotic test for the equality of the two autoregressive functions.

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The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci