Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003. Imprecisely or incompletely observed data often appear in engineering, epidemiology and economic studies, observations on certain variables may be grouped or measured with errors, which poses challenges to the usual statistical methods. This thesis consists of three studies in this general area. First, we study linear calibration of a crude device to a more accurate one. Second, we use the Markov Chain Monte Carlo (MCMC) method to handle a grouped independent variable in a linear model as motivated by a residential energy study. The third study is concerned with an approximate minimum Hellinger distance estimator (AMHDE) under appropriate grouping of data from a continuous variable. The estimator is shown to be asymptotically normal with good efficiency and robustness. U of I Only Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs