Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parametric and nonparametric probability distribution estimators of
  sample maximum   Extreme value theory has constructed asymptotic properties of the sample
maximum under some parametric assumptions. This study concerns probability
distribution estimation of the sample maximum. The traditional approach is
parametric fitting to the limiting distribution - the generalized extreme value
distribution; however, the model in finite cases is misspecified to a certain
extent. We propose a plug-in type of nonparametric estimator that does not need
model specification. Asymptotic properties of the distribution estimator are
derived. The numerical performances of the parametric estimator and the
nonparametric estimator are compared in this study. A simulation experiment
demonstrates the obtained asymptotic convergence rates and clarifies the
influence of misspecification in the context of probability distribution
estimation.
  This study assumes that the underlying distribution of the original sample
belongs to one of the Hall class, the Weibull class and the bounded class,
whose types of the limiting distributions are all different: the Frechet,
Gumbel and Weibull. It is proven that the convergence rate of the parametric
fitting estimator depends on both the tail index and the second-order parameter
and gets slow as the tail index tends to zero. The simulation results are
generally consistent with the obtained convergence rates. Finally, we report
two real case studies: the Potomac River peak stream flow (cfs) data and the
Danish Fire Insurance data.

23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ