Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large scale reduction principle and application to hypothesis testing   Consider a non--linear function $G(X_t)$ where $X_t$ is a stationary Gaussian
sequence with long--range dependence. The usual reduction principle states that
the partial sums of $G(X_t)$ behave asymptotically like the partial sums of the
first term in the expansion of $G$ in Hermite polynomials. In the context of
the wavelet estimation of the long--range dependence parameter, one replaces
the partial sums of $G(X_t)$ by the wavelet scalogram, namely the partial sum
of squares of the wavelet coefficients. Is there a reduction principle in the
wavelet setting, namely is the asymptotic behavior of the scalogram for
$G(X_t)$ the same as that for the first term in the expansion of $G$ in Hermite
polynomial? The answer is negative in general. This paper provides a minimal
growth condition on the scales of the wavelet coefficients which ensures that
the reduction principle also holds for the scalogram. The results are applied
to testing the hypothesis that the long-range dependence parameter takes a
specific value.

36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph