Robust Test Statistics Based on Restricted Minimum Rényi’s Pseudodistance Estimators

Abstract

The Rao’s score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order equivalent and asymptotically optimal. Conversely, these three classical tests present serious robustness problems, as they are based on the maximum likelihood estimator, which is highly non-robust. To overcome this drawback, some test statistics have been introduced in the literature based on robust estimators, such as robust generalized Wald-type and Rao-type tests based on minimum divergence estimators. In this paper, restricted minimum Rényi’s pseudodistance estimators are defined, and their asymptotic distribution and influence function are derived. Further, robust Rao-type and divergence-based tests based on minimum Rényi’s pseudodistance and restricted minimum Rényi’s pseudodistance estimators are considered, and the asymptotic properties of the new families of tests statistics are obtained. Finally, the robustness of the proposed estimators and test statistics is empirically examined through a simulation study, and illustrative applications in real-life data are analyzed.

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

“…In [19], the theoretical robustness properties of the RMDPDE were studied. In [20,21], the restricted Rényi pseudodistance estimator is considered, and robust Rao-type tests are derived from it and developed. More recently, in [22], the RMDPD under normal distributions is studied, and independence tests under the normal assumption are developed, and in [23] the RMDPDE is applied in the context of independent but not identically distributed variables under heterocedastic linear regression models.…”

“…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.…”

Robust Rao-Type Tests for Non-destructive One-Shot Device Testing Under Step-Stress Model with Exponential Lifetimes

“…To overcome the robustness drawback with a small loss of efficiency, Basu et al (2018) developed robust parametric tests for composite hypotheses based on RMDPDEs. Later, Basu et al (2022) generalizes the Rao test using the RMDPD for general statistical models, and Jaenada et al (2022) studied Rényi pseudodistancebased restricted estimators for the same purpose. For interval-censored step-stress ALTs, Balakrishnan et al (2023b) developed RMDPDE under exponential lifetimes, and derived explicit expressions of the Rao-type tests for the exponential lifetime distribution and linear null hypothesis.…”

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

“…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. Under the name of γ-entropy, Fujisawa and Eguchi [36] applied RP to introduce robust estimators of general parametric families.…”