The Combination of the Sign and Wilcoxon Tests for Symmetry and Their Pitman Efficiency
G. Burgio, Ya. Yu. Nikitin · Birkhäuser Boston eBooks · 2001
We consider the efficiency properties of the test of symmetry based on the sequence of statistics Gn = aS n +bW n , where S n and W n are the classical sign and Wilcoxon statistics and a and b are some constants. Pitman efficiency of this test with respect to the student test in the case of location alternatives and its maximum with respect to a and b are calculated. This generalizes the classical results of Hodges and Lehmann (1956). We also find the form of the alternative distributions under which the new test is Pitman optimal.