Type: Seminar

Distribution: World

Expiry: 16 Sep 2016

CalTitle1: Nonparametric Tests for Multi-parameter M-estimators

Auth: jormerod@pjormerod5.pc (assumed)

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.