706 research outputs found
The rabbinic interpretation of the eighth century prophets
Thesis (M.A.)--Boston University, 1932. This item was digitized by the Internet Archive
Non-Bayesian Post-Model-Selection Estimation as Estimation Under Model Misspecification
In many parameter estimation problems, the exact model is unknown and is
assumed to belong to a set of candidate models. In such cases, a predetermined
data-based selection rule selects a parametric model from a set of candidates
before the parameter estimation. The existing framework for estimation under
model misspecification does not account for the selection process that led to
the misspecified model. Moreover, in post-model-selection estimation, there are
multiple candidate models chosen based on the observations, making the
interpretation of the assumed model in the misspecified setting non-trivial. In
this work, we present three interpretations to address the problem of
non-Bayesian post-model-selection estimation as an estimation under model
misspecification problem: the naive interpretation, the normalized
interpretation, and the selective inference interpretation, and discuss their
properties. For each of these interpretations, we developed the corresponding
misspecified maximum likelihood estimator and the misspecified
Cramr-Rao-type lower bound. The relations between the
estimators and the performance bounds, as well as their properties, are
discussed. Finally, we demonstrate the performance of the proposed estimators
and bounds via simulations of estimation after channel selection. We show that
the proposed performance bounds are more informative than the oracle
Cramr-Rao Bound (CRB), where the third interpretation
(selective inference) results in the lowest mean-squared-error (MSE) among the
estimators.Comment: This work has been submitted to the IEEE for possible publication.
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