Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Approximate MSE Expression for Maximum Likelihood and Other
  Implicitly Defined Estimators of Non-Random Parameters (extended version)   An approximate mean square error (MSE) expression for the performance
analysis of implicitly defined estimators of non-random parameters is proposed.
An implicitly defined estimator (IDE) declares the minimizer/maximizer of a
selected cost/reward function as the parameter estimate. The maximum likelihood
(ML) and the least squares estimators are among the well known examples of this
class. In this paper, an exact MSE expression for implicitly defined estimators
with a symmetric and unimodal objective function is given. It is shown that the
expression reduces to the Cramer-Rao lower bound (CRLB) and misspecified CRLB
in the large sample size regime for ML and misspecified ML estimation,
respectively. The expression is shown to yield the Ziv-Zakai bound (without the
valley filling function) when it is used in a Bayesian setting, that is, when
an a-priori distribution is assigned to the unknown parameter. In addition,
extension of the suggested expression to the case of nuisance parameters is
studied and some approximations are given to ease the computations for this
case. Numerical results indicate that the suggested MSE expression not only
predicts the estimator performance in the asymptotic region; but it is also
applicable for the threshold region analysis, even for IDEs whose objective
functions do not satisfy the symmetry and unimodality assumptions. Advantages
of the suggested MSE expression are its conceptual simplicity and its
relatively straightforward numerical calculation due to the reduction of the
estimation problem to a binary hypothesis testing problem, similar to the usage
of Ziv-Zakai bounds in random parameter estimation problems.

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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg