The motivation for this article comes from our development of soft sensors for chemical processes where several challenges are encountered. For example, quality variables in chemical processes are often measured off-line through laboratory analysis. Collection of samples and subsequent analyses inevitably introduce uncertain time delays associated with the irregularly sampled quality variables, which add significant difficulty in identification of process with multirate (MR) data. Considering the MR system with random sampling delays described by a finite impulse response (FIR) model, an Expectation-Maximization (EM)-based algorithm to estimate its parameters along with the time delays is developed. Based on the identified FIR model, two algorithms are proposed to recover the approximate output error (OE) or transfer function model. Two simulation examples as well as a pilot-scale experiment are provided to illustrate the effectiveness of the proposed methods. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 4124-4132, 2013