Robust approach for comparing two dependent normal populations through Wald-type tests based on Rényi’s pseudodistance estimators

Abstract

Since the two seminal papers by Fisher (Biometrika 10:507–521, 1915; Metron 1:1–32, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of asymptotic robust statistics, it remains being a topic of great interest to be investigated. For this and other tests, focused on paired correlated normal random samples, Rényi’s pseudodistance estimators are proposed, their asymptotic distribution is established and an iterative algorithm is provided for their computation. From them the Wald-type test statistics are constructed for different problems of interest and their influence function is theoretically studied. For testing null correlation in different contexts, an extensive simulation study and two real data based examples support the robust properties of our proposal.

Restricted Distance-Type Gaussian Estimators Based on Density Power Divergence and Their Applications in Hypothesis Testing

“…Distance-based test statistics are essentially of two types: Wald-type tests and Rao-type tests. Some applications of these tests can be seen at [8,[20][21][22][23][29][30][31][32][33][34][35][36][37] and references therein. In this section, we introduce the Rao-type tests based on RMDPDGE, and we study their asymptotic properties, proving the consistency of the tests.…”

“…, and consider the testing problem defined in (32). The Rao-type test statistic based on RMDPDGE is defined by…”

“…Theorem 3. Let Y 1 , ..., Y n be independent and identically distributed observations from an mdimensional random vector (32), and let us assume that E θ [Y τ (θ 0 )] = 0 d . Then,…”

“…In particular, the simple null hypothesis in (32) can be written as a composite null hypothesis with g(θ) = θ − θ 0 . In this case, G(θ) reduces to the identity matrix of dimension p and the restricted estimator θ τ G coincides with θ 0 .…”

An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances

“…In [27], Castilla et al introduced a family of Wald-type tests for testing the parameters in linear regression models, and these results were later extended for generalized linear regression models in [32,33]. Wald-type tests based on minimum RP estimators in bidimensional normal populations were considered in [34]. Jaenada et al [35] introduced and studied the minimum RP estimators under restricted parameter spaces, which are of great statistical interest in many practical applications such as hypothesis testing.…”