RESIDUAL'S INFLUENCE INDEX (RINFIN), BAD LEVERAGE AND UNMASKING IN HIGH DIMENSIONAL L2-REGRESSION

Yannis G. Yatracos

No 2018-060, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: 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.

Keywords: Big Data; Data Science; Influence Function; Leverage; Masking; Residual's Influence Index (RINFIN) (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2018
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