Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inferring the mixing properties of an ergodic process   We propose strongly consistent estimators of the $\ell_1$ norm of the
sequence of $\alpha$-mixing (respectively $\beta$-mixing) coefficients of a
stationary ergodic process. We further provide strongly consistent estimators
of individual $\alpha$-mixing (respectively $\beta$-mixing) coefficients for a
subclass of stationary $\alpha$-mixing (respectively $\beta$-mixing) processes
with summable sequences of mixing coefficients. The estimators are in turn used
to develop strongly consistent goodness-of-fit hypothesis tests. In particular,
we develop hypothesis tests to determine whether, under the same summability
assumption, the $\alpha$-mixing (respectively $\beta$-mixing) coefficients of a
process are upper bounded by a given rate function. Moreover, given a sample
generated by a (not necessarily mixing) stationary ergodic process, we provide
a consistent test to discern the null hypothesis that the $\ell_1$ norm of the
sequence $\boldsymbol{\alpha}$ of $\alpha$-mixing coefficients of the process
is bounded by a given threshold $\gamma \in [0,\infty)$ from the alternative
hypothesis that $\left\lVert \boldsymbol{\alpha} \right\rVert> \gamma$. An
analogous goodness-of-fit test is proposed for the $\ell_1$ norm of the
sequence of $\beta$-mixing coefficients of a stationary ergodic process.
Moreover, the procedure gives rise to an asymptotically consistent test for
independence.

24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc