In many practical parameter estimation problems, such as medical experiments and cognitive radio communications, parameter selection is performed prior to estimation. The selection process has a major impact on subsequent estimation by introducing a selection bias and creating coupling between decoupled parameters. As a result, classical estimation theory may be inappropriate and inaccurate and a new methodology is needed. In this study, the problem of estimating a preselected unknown deterministic parameter, chosen from a parameter set based on a predetermined data-based selection rule, Ψ, is considered. In this talk, I will present a general non-Bayesian estimation theory for estimation after parameter selection, includes estimation methods, performance analysis, and adaptive sampling strategies. The new theory is based on the post-selection mean-square-error (PSMSE) criterion as a performance measure instead of the commonly used mean-square-error (MSE). We derive the corresponding Cramér-Rao-type bound on the PSMSE of any Ψ-unbiased estimator, where the Ψ -unbiasedness is in the Lehmann-unbiasedness sense. Then, the post-selection maximum-likelihood (PSML) estimator is presented and its Ψ–efficiency properties are demonstrated. Practical implementations of the PSML estimator are proposed as well. As time permits, I will discuss the similar ideas that can be applied to estimation after model selection and to estimation in Good-Turing models.
Tirza Routtenberg (S'07-M'13-SM'18) received the B.Sc. degree (magna cum laude) in bio-medical engineering from the Technion Israel Institute of Technology, Haifa, Israel in 2005 and the M.Sc. (magna cum laude) and Ph.D. degrees in electrical engineering from the Ben-Gurion University of the Negev, Beer-Sheva, Israel, in 2007 and 2012, respectively. She was a postdoctoral fellow with the School of Electrical and Computer Engineering, Cornell University, in 2012-2014. Since October 2014, she is a faculty member at the Department of Electrical and Computer Engineering, and Ben-Gurion University of the Negev, Beer-Sheva, Israel. Her research interests include signal processing in smart grid, statistical signal processing, estimation and detection theory, and signal processing on graphs. She was a recipient of the Best Student Paper Award in International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2011, in IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) 2013 (coauthor), in ICASSP 2017 (coauthor), and in IEEE Workshop on Statistical Signal Processing (SSP) 2018 (coauthor).