A DATA DRIVEN SMOOTH TEST FOR CIRCULAR UNIFORMITY

M. BOGDAN^{1}, K. BOGDAN^{1} AND A. FUTSCHIK^{2}

1Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27,

50-370 Wrocław, Poland

2Institute of Statistics, University of Wien, Universitätsstr. 5/9, A-1010 Vienna, Austria

(Received December 14, 1999; revised October 16, 2000)

Abstract. We propose a new omnibus test for uniformity on the circle. The new test is based upon the idea of data driven smooth tests as presented in Ledwina (1994, J. Amer. Statist. Assoc., 89, 1000–1005). Our simulations indicate that the test performs very well for multifarious alternatives. In particular, it seems to outperform other known omnibus tests when testing against multimodal alternatives. We also investigate asymptotic properties of our test and we prove that it is consistent against every departure from uniformity.

Key words and phrases: Schwarz’s BIC criterion, goodness-of-fit, score test, smooth test, Neyman’s test, Monte Carlo simulations.