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Cramér-Rao bound for a mixture of real- and integer-valued parameter vectors and its application to the linear regression model

Abstract : Performance lower bounds are known to be a fundamental design tool in parametric estimation theory. A plethora of deterministic bounds exist in the literature, ranging from the general Barankin bound to the well-known Cramér-Rao bound (CRB), the latter providing the optimal mean square error performance of locally unbiased estimators. In this contribution, we are interested in the estimation of mixed real- and integer-valued parameter vectors. We propose a closed-form lower bound expression leveraging on the general CRB formulation, being the limiting form of the McAulay-Seidman bound. Such formulation is the key point to take into account integer-valued parameters. As a particular case of the general form, we provide closed-form expressions for the Gaussian observation model. One noteworthy point is the as- sessment of the asymptotic efficiency of the maximum likelihood estimator for a linear regression model with mixed parameter vectors and known noise covariance matrix, thus complementing the rather rich literature on that topic. A representative carrier-phase based precise positioning example is provided to support the discussion and show the usefulness of the proposed lower bound.
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Submitted on : Wednesday, October 21, 2020 - 1:49:20 PM
Last modification on : Thursday, October 22, 2020 - 8:51:23 AM
Long-term archiving on: : Friday, January 22, 2021 - 6:42:45 PM

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Daniel Medina, Jordi Vilà Valls, Eric Chaumette, François Vincent, Pau Closas. Cramér-Rao bound for a mixture of real- and integer-valued parameter vectors and its application to the linear regression model. Signal Processing, Elsevier, 2021, 179, pp.107792. ⟨10.1016/j.sigpro.2020.107792⟩. ⟨hal-02973927⟩

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