Records Tests for Trend in Location

The number of upper and lower records in both directions of the series is considered for testing the hypothesis that a sequence of random variables is independently and identically distributed, against the alternative of a polynomial trend in location. The asymptotic relative efficiency of the records tests, originally suggested by Foster and Stuart (1954), is derived. It is shown that the efficiency of these tests is raised distinctly by splitting the series of observations and by weighting the records according to their position in the series.