Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regression estimation from an individual stable sequence   We consider univariate regression estimation from an individual (non-random)
sequence $(x_1,y_1),(x_2,y_2), ... \in \real \times \real$, which is stable in
the sense that for each interval $A \subseteq \real$, (i) the limiting relative
frequency of $A$ under $x_1, x_2, ...$ is governed by an unknown probability
distribution $\mu$, and (ii) the limiting average of those $y_i$ with $x_i \in
A$ is governed by an unknown regression function $m(\cdot)$.
  A computationally simple scheme for estimating $m(\cdot)$ is exhibited, and
is shown to be $L_2$ consistent for stable sequences $\{(x_i,y_i)\}$ such that
$\{y_i\}$ is bounded and there is a known upper bound for the variation of
$m(\cdot)$ on intervals of the form $(-i,i]$, $i \geq 1$. Complementing this
positive result, it is shown that there is no consistent estimation scheme for
the family of stable sequences whose regression functions have finite
variation, even under the restriction that $x_i \in [0,1]$ and $y_i$ is
binary-valued.

20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int