This paper examines the problem of system identification from frequency response data. Recent approaches to this problem, known collectively as ＇Estimation in H-infinity＇, involve deterministic descriptions of noise corruptions to the data. In order to provide ＇worst-case＇ convergence with respect to these deterministic noise descriptions, non-linear data algorithms are required. In contrast, this paper examines ＇worst-case＇ estimation in H-infinity when the disturbances are subject to mild stochastic assumptions and linearity in the data algorithms is employed. Issues of convergence, error bounds, and model order selection are considered.