Distribution-agnostic Linear Unbiased Estimation with Saturated Weights for Heterogeneous Data

The challenging problem of distribution-agnostic linear (weighted) unbiased estimation a global parameter from heterogeneous and unbalanced data is addressed. This setup may originate in different signal processing contexts involving the joint non-homogeneous groups whose statistical distribution unknown, with (possibly highly) diverse sample sizes. Since estimators local variances are inaccurate low-sample regime, suitable weighting schemes required. For this problem, we study family based on idea trimmed weights, i.e., proportional to size but proper saturation. Such an approach theoretically analyzed, showing that it can be linked Maximum Entropy principle under uncertainty generative model (as well as broader class cost functions). Different criteria for setting “cut-off” threshold between saturated regions also obtaining reduced-complexity approximation optimal minimum-variance estimator generalized mixed-effect model. To aim, further contribution several hyperparameter derived analyzed. proposed analyzed its performance assessed against state-of-the-art estimators. An illustrative application real-world COVID-19 finally developed.