In linear regression of Y on X(2 Rp) with parameters (2 Rp+1); statistical inference is unreliable when observations are obtained from gross-error model, F;G = (1??)F +G; instead of the assumed probability F;G is gross-error probability, 0 < < 1: When G is unit mass at (x; y); Residual's Inuence Index, RINFIN(x; y; ; ), measures the dierence in small x-perturbations of L2-residual, r(x; y); for model F and for F;G via r's x-partial derivatives. Asymptotic properties are presented for sample RINFIN that is successful in extracting indications for inuential and bad leverage cases in microarray data and simulated, high dimensional data. Its performance improves as p increases and can also be used in multiple response linear regression. RINFIN's advantage is that, whereas in inuence functions of L2-regression coecients each x-coordinate and r(x; y) appear in a sum as product with moderate size when (x; y) is bad leverage case and masking makes r(x; y) nearly vanish, RINFIN's x-partial derivatives convert the product in sum allowing for unmasking.
Big Data Data Science Influence Function Leverage Masking Residual's Influence Index (RINFIN)