Cramér-Rao Bound for Estimation After Model Selection and Its Application to Sparse Vector Estimation

In many practical parameter estimation problems, such as coefficient of polynomial regression, the true model is unknown and thus, a selection step performed prior to estimation. The data-based affects subsequent particular, oracle Cramér-Rao bound (CRB), which based on knowledge model, inappropriate for post-model-selection performance analysis system design outside asymptotic region. this paper, we investigate vector with an support set, where set represents model. We analyze coherent estimators that force unselected parameters zero. use mean-squared-selected-error (MSSE) criterion introduce concept selective unbiasedness in sense Lehmann unbiasedness. derive non-Bayesian Cramér-Rao-type MSSE mean-squared-error (MSE) any estimator specific selective-bias function sense. implement CRB special case sparse set. Finally, demonstrate simulations proposed informative lower maximum selected likelihood general linear generalized information one thresholding. It shown these cases outperforms Sando-Mitra-Stoica (SMS-CRB) [1].