Optimal Testing for Serial Correlation in a Large Number of Small Samples

In recent years, there has been an increased awareness of the potential one‐sided nature of many testing problems in applied sciences. Usually, these testing problems can be reduced, either by conditioning on sufficient statistics or by invariant techniques. COX and SOLOMON (1988) considered testing the serial correlation coefficient of a stationary first order autoregressive process and concentrated on four independent samples, with each of size three. We outline a general method for testing the serial correlation coefficient, using locally best invariant, point optimal invariant and locally most mean powerful invariant test procedures. The first procedure optimizes power near the null hypothesis, the second optimizes it at a pre‐determined point away from the null while the third optimizes the average curvature of the power hypersurface in the neighbourhood of the null hypothesis.