Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic near-efficiency of the ''Gibbs-energy (GE) and
  empirical-variance'' estimating functions for fitting Mat{\'e}rn models --
  II: Accounting for measurement errors via ''conditional GE mean''   Consider one realization of a continuous-time Gaussian process $Z$ which
belongs to the Mat\' ern family with known ``regularity'' index $\nu >0$. For
estimating the autocorrelation-range and the variance of $Z$ from $n$
observations on a fine grid, we studied in Girard (2016) the GE-EV method which
simply retains the empirical variance (EV) and equates it to a candidate
``Gibbs energy (GE)'' i.e.~the quadratic form ${\bf z}^T R^{-1} {\bf z}/n$
where ${\bf z}$ is the vector of observations and $R$ is the autocorrelation
matrix for ${\bf z}$ associated with a candidate range. The present study
considers the case where the observation is ${\bf z}$ plus a Gaussian white
noise whose variance is known. We propose to simply bias-correct EV and to
replace GE by its conditional mean given the observation. We show that the
ratio of the large-$n$ mean squared error of the resulting CGEM-EV estimate of
the range-parameter to the one of its maximum likelihood estimate, and the
analog ratio for the variance-parameter, have the same behavior than in the
no-noise case: they both converge, when the grid-step tends to $0$, toward a
constant, only function of $\nu$, surprisingly close to $1$ provided $\nu$ is
not too large. We also obtain, for all $\nu$, convergence to 1 of the analog
ratio for the microergodic-parameter.

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc