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A new class of change point test statistics is proposed that utilizes aweighting and trimming scheme for the cumulative sum (CUSUM) process inspiredby R\'enyi (1953). A thorough asymptotic analysis and simulations bothdemonstrate that this new class of statistics possess superior power comparedto traditional change point statistics based on the CUSUM process when thechange point is near the beginning or end of the sample. Generalizations ofthese "R\'enyi" statistics are also developed to test for changes in theparameters in linear and non-linear regression models, and in generalizedmethod of moments estimation. In these contexts we applied the proposedstatistics, as well as several others, to test for changes in the coefficientsof Fama-French factor models. We observed that the R\'enyi statistic was themost effective in terms of retrospectively detecting change points that occurnear the endpoints of the sample.

A new class of change point test statistics of R\'enyi type