Memorandum 1548
W.C.M. Kallenberg
Abstract:
Data driven Neyman's tests are based on two elements: Neyman's smooth tests
in finite dimensional submodels and a selection rule to choose the ``right''
submodel. As selection rule usually (a modification of) Schwarz's rule is
applied. In this paper we consider data driven Neyman's tests with selection
rules allowing also other penalties than the one in Schwarz's rule. It is
shown that the nice properties of consistency against very large classes of
alternatives and the more deep result of asymptotic optimality in the sense
of vanishing shortcoming continue to hold for other penalties as well,
including the one corresponding to Akaike's selection rule.
Keywords:
Goodness-of-fit, model selection, Schwarz's criterion, Akaike's criterion,
penalty, data driven test, consistency, vanishing shortcoming, intermediate
efficiency, moderate deviations.
Mathematics Subject Classification: 62G10, 62G20