  Regression models for continuous outcomes often require a transformation of
the outcome, which the user either specify {\it a priori} or estimate from a
parametric family. Cumulative probability models (CPMs) nonparametrically
estimate the transformation and are thus a flexible analysis approach for
continuous outcomes. However, it is difficult to establish asymptotic
properties for CPMs due to the potentially unbounded range of the
transformation. Here we show asymptotic properties for CPMs when applied to
slightly modified data where the outcomes are censored at the ends. We prove
uniform consistency of the estimated regression coefficients and the estimated
transformation function over the non-censored region, and describe their joint
asymptotic distribution. We show with simulations that results from this
censored approach and those from the CPM on the original data are similar when
a small fraction of data are censored. We reanalyze a dataset of HIV-positive
patients with CPMs to illustrate and compare the approaches.
