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 in the 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 linear in the data algorithms are employed. Issues of convergence, error bounds, and model order selection are considered.