Statistics Seminar: John Robinson (USyd) -- Nonparametric Tests for Multi-parameter M-estimators

Abstract 

Tests of hypotheses concerning subsets of multivariate means or coefficients in linear
or generalized linear models depend on parametric assumptions which may not hold.  One
nonparametric approach to these problems uses the standard nonparametric bootstrap using
the test statistics derived from some parametric model but basing inferences on
bootstrap approximations.  We derive different test statistics based on empirical
exponential families and use a tilted bootstrap to give inferences.The bootstrap
approximations can be accurately approximated to relative second order accuracy by a
saddlepoint approximation.  This generalises earlier work in two ways.  First, we
generalise from bootstraps based on resampling vectors of both response and explanatory
variables to include bootstrapping residuals for fixed explanatory variables, and
second, we obtain a theorem for tail probabilities under weak conditions justifying
approximation to bootstrap results for both cases.