A note on a sequential signed-rank test for symmetry^†

^†Research supported in part by NSF Grant No. MPS74–07295 AMS 1970 subject classifications. Primary 62L10; Secondary 60J10

Abstract

Reynolds has proposed a sequential procedure for testing the hypothesis that the distribution of a sequence of i.i.d. random variables is symmetric about zero. The critical region and expected sample size of the test are approximated by using the fact that the test statistic behaves asymptotically like a Brownian motion process. In this paper we propose to use approximations based on a continuous non-homogeneous Markov chain. Monte Carlo studies show this approach to be much more accurate in determining appropriate critical regions and in finding expected sample size.

Keywords:

• Sequential test
• signed-rank statistic
• Markov chain

^†Research supported in part by NSF Grant No. MPS74–07295 AMS 1970 subject classifications. Primary 62L10; Secondary 60J10

^†Research supported in part by NSF Grant No. MPS74–07295 AMS 1970 subject classifications. Primary 62L10; Secondary 60J10

Notes

^†Research supported in part by NSF Grant No. MPS74–07295 AMS 1970 subject classifications. Primary 62L10; Secondary 60J10