Memorandum 1504
W. Albers, W.C.M. Kallenberg & F. Martini
Abstract:
Tail alternatives describe the frequent occurrence of a
non-constant shift in the two-sample problem with a shift function
increasing in the tail. The classes of shift functions can be built up
using Legendre polynomials. It is important to rightly choose the number
of polynomials involved. Here this choice is based on the data, using a
modification of Schwarz's selection rule. Given the data driven choice of
the model, appropriate rank tests are applied. Simulations show that the
new data driven rank tests work very well. While other tests for
detecting shift alternatives as Wilcoxon's test may completely break
down for important classes of tail alternatives, the new tests have high
and stable power. The new tests have also higher power than data driven
rank tests for the unconstrained two-sample problem. Theoretical support
is obtained by proving consistency of the new tests against very large
classes of alternatives, including all common tail alternatives. A
simple but accurate approximation of the null distribution makes
application of the new tests easy.
Keywords:
Shift function, model selection, Monte Carlo
study, consistency, Legendre polynomials
Mathematics Subject Classification: 62G10, 62E25, 62G20