0619694 20260224155458.620250515235959.9 105005102546 001488394600001 10.1007/s13171-025-00389-7 21 s. P cav_un_epca*06196930976-836X Errors in variables Asymptotic relative efficiency cav_un_auth*0368969 Jurečková Jana UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI CZ 50% S Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0488462 Koul H. L. US https://library.utia.cas.cz/separaty/2025/SI/jureckova-0619694.pdf GA22-03636S GA ČR CZ cav_un_auth*0435411 This note proves the asymptotic uniform linearity of a weighted empirical process of residual signed ranks and a class of linear residual signed rank statistics with bounded scores in nonlinear parametric regression models when covariates are random and independent of the errors. This result is used to derive limiting distributions of a class of signed rank estimators of the underlying regression parameters in these models. The latter result is applied to the errors in variables linear regression model to show that these estimators are robust against large measurement error in the sense that the asymptotic relative efficiency of a class of signed rank estimators against the bias corrected least square estimator tends to infinity as the measurement error variance tends to infinity (in some cases monotonically), when covariates and regression and measurement errors have Gaussian distributions. 2027 BB WOS 10000 10100 10103 2 BB RVO:67985556 https://hdl.handle.net/11104/0366806 cav_un_auth*0487717 Michigan State University, East Lansing, USA MSU S A STATISTICS&PROBABILITY 0.7 0.6 26.7 0.00061 0.361 752 12 0.309 31.22 0.78 97 Q3 0.500 37 Q4 8.6 0.38 Q4 8.6 2026 105005102546 SCOPUS PUBMED 001488394600001 WOS cav_un_epca*0619693 Sankhy_A : The Indian Journal of Statistics 2026 0976-836X 0976-8378