  A new class of change point test statistics is proposed that utilizes a
weighting and trimming scheme for the cumulative sum (CUSUM) process inspired
by R\'enyi (1953). A thorough asymptotic analysis and simulations both
demonstrate that this new class of statistics possess superior power compared
to traditional change point statistics based on the CUSUM process when the
change point is near the beginning or end of the sample. Generalizations of
these "R\'enyi" statistics are also developed to test for changes in the
parameters in linear and non-linear regression models, and in generalized
method of moments estimation. In these contexts we applied the proposed
statistics, as well as several others, to test for changes in the coefficients
of Fama-French factor models. We observed that the R\'enyi statistic was the
most effective in terms of retrospectively detecting change points that occur
near the endpoints of the sample.
