Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of variance, coefficient of determination and $F$-test for
  local polynomial regression   This paper provides ANOVA inference for nonparametric local polynomial
regression (LPR) in analogy with ANOVA tools for the classical linear
regression model. A surprisingly simple and exact local ANOVA decomposition is
established, and a local R-squared quantity is defined to measure the
proportion of local variation explained by fitting LPR. A global ANOVA
decomposition is obtained by integrating local counterparts, and a global
R-squared and a symmetric projection matrix are defined. We show that the
proposed projection matrix is asymptotically idempotent and asymptotically
orthogonal to its complement, naturally leading to an $F$-test for testing for
no effect. A by-product result is that the asymptotic bias of the ``projected''
response based on local linear regression is of quartic order of the bandwidth.
Numerical results illustrate the behaviors of the proposed R-squared and
$F$-test. The ANOVA methodology is also extended to varying coefficient models.

15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat