Wald tests of singular hypotheses

Wald tests of singular hypotheses

Motivated by the problem of testing tetrad constraints in factor analysis, we study the large-sample distribution of Wald statistics at parameter points at which the gradient of the tested constraint vanishes. When based on an asymptotically normal estimator, the Wald statistic converges to a rational function of a normal random vector. The rational function is determined by a homogeneous polyn...

Robust Wald - Type Tests of One - Sided Hypotheses in the Linear Model

ABSTRACf Let us consider the linear model Y = XO + E in the usual matrix notation, where the errors are independent and identically distributed. Our main objective is to develop robust Wald-type tests for a large class of hypotheses on OJ by 'robust' we mean robustness in terms of size and power against long tailed error distributions. First, assume that the error distribution is symmetric abou...

Generalised Score and Wald Tests

Influence analysis of robust Wald-type tests

We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the influence functions as well as the chi-square infla...

Rao and Wald Tests for Nonhomogeneous Scenarios

In this paper, we focus on the design of adaptive receivers for nonhomogeneous scenarios. More precisely, at the design stage we assume a mismatch between the covariance matrix of the noise in the cell under test and that of secondary data. Under the above assumption, we show that the Wald test is the adaptive matched filter, while the Rao test coincides with the receiver obtained by using the ...