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To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...
To validate pollution data, subject-matter experts in Airpl (an organization
that maintains a network of air pollution monitoring stations in western
France) daily perform visual examinations of the data and check their
consistency. In this paper, we describe these visual examinations and
propose a formalization for this problem. The examinations consist
in comparisons of so-called shorth intervals so we build a statistical
test that compares such intervals in a nonparametric regression model.
This...
The paper is concerned with the asymptotic distributions of estimators for
the length and the centre of the so-called -shorth interval in a
nonparametric regression framework. It is shown that the estimator of the
length converges at the
-rate to a Gaussian law and that the
estimator of the centre converges at the
-rate to the location
of the maximum of a Brownian motion with parabolic drift.
Bootstrap procedures are proposed and shown to be consistent.
They...
We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis : “” against the composite alternative : “” under the assumption that the true regression function is decreasing. The test statistic is based on the -distance between the isotonic estimator of and the function , since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under . We study the asymptotic...
We consider the problem of hypothesis testing within a monotone
regression model. We propose a new test of the hypothesis
: “” against the composite alternative
: “” under the assumption that the true regression function
is decreasing. The test statistic is based on the
-distance between the isotonic estimator of and the
function
, since it is known that a properly centered and
normalized version of this distance is asymptotically standard
normally...
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