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

Performance lower bounds are known to be a fundamental design tool in parametric estimation theory. A plethora of deterministic exist the literature, ranging from general Barankin bound well-known Cramér-Rao (CRB), latter providing optimal mean square error performance locally unbiased estimators. In this contribution, we interested mixed real- and integer-valued parameter vectors. We propose closed-form expression leveraging on CRB formulation, being limiting form McAulay-Seidman bound. Such formulation is key point take into account parameters. As particular case form, provide expressions for Gaussian observation model. One noteworthy assessment asymptotic efficiency maximum likelihood estimator linear regression model with vectors noise covariance matrix, thus complementing rather rich literature that topic. representative carrier-phase based precise positioning example provided support discussion show usefulness proposed