Leverage and subset efficiencies in regression

Leverages and coleverages comprise the matrix H in regression. These traditionally serve to gauge (i) the remoteness of regressors, (ii) the impact of responses on fitted values, (iii) the predictive efficiency of an observation YiYi, (iv) powers of tests for outliers, and (v) limits on critical features of deletion diagnostics. This study goes beyond traditional usage in developing leverage efficiency diagnostics   to quantify the leverage exerted by subsets of data on efficiency in estimation, specifically, to identify parameters impacted adversely on subset deletions, or enhanced through augmentations, and to quantify altered efficiencies of their estimators. These topics are not covered by conventional regression diagnostics. Instead, our objectives emerge here through spectral analyses of blocks of H, independently of observed responses. Case studies utilize the methodology to evaluate comparative efficiencies among small nested second-order designs.