Estimation and Testing on Independent Not Identically Distributed Observations Based on Rényi’s Pseudodistances

Castilla, Elena; Jaenada, María; Pardo, Leonardo

doi:10.1109/tit.2022.3158308

Cited by 6 publications

(5 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From this perspective, the density power divergence (DPD) family, leading to the minimum density power divergence estimators (MDPDEs) (see Basu et al [7]), as well as the Rényi's pseudodistance (RP), leading to the minimum Rényi's pseudodistance estimators (MRPE) (see Broniatowski et al [8]) between others, play an important role. The results presented in Broniatowski et al [8] in the context of independent and identically distributed random variables were extended for the case of independent but not identically distributed random variables by Castilla et al [9].…”

Section: Introductionmentioning

confidence: 81%

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

Jaenada

Miranda

Pardo

2022

Entropy

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 81%

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

Jaenada

Miranda

Pardo

2022

Entropy

View full text Add to dashboard Cite

show abstract

“…We can observe that the influence function of θ τ G , obtained in (31), will be bounded if the influence function of the MDPDGE, θ τ G , given in ( 29) is bounded. In general, it is not easy to see if it is bounded or not, but in particular situations, this can be solved.…”

Section: Influence Function For the Rmdpdgementioning

confidence: 98%

“…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.…”

Section: Rao-type Tests Based On Rmdpdgementioning

confidence: 99%

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

et al. 2023

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in this case constrained estimators to inherent restrictions of the underlying distribution. Furthermore, we derive robust Rao-type test statistics based on the MDPDGE for testing a simple null hypothesis, and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study.

show abstract

“…The resulting degenerate distribution of the multinomial model concentrates all probability at one cell and so, varying over all possible such outlier cells, we get all possible counting errors. The influence function given in Equation ( 15) then represents the bias in the estimator caused by infinitesimal amount of such errors, and robustness should be better examined it terms of gross error sensitivity of the functional, as discussed in Castilla et al (2022). This view of considering outliers in multinomial sampling as classification errors is in line with the general literature on robust analysis of categorical data, including different types of logistic regressions having finite supports for the model densities (Johnson (1985), Croux and Haesbroeck (2003), Bondell (2008), Basu et al (2017), Castilla et al (2021)).…”

Section: Robustness Analysismentioning

confidence: 99%

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

Jaenada¹,

Pardo²

2022

Building Bridges Between Soft and Statistical Methodologies for Data Science

View full text Add to dashboard Cite

One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is before the test time. Some kind of one-shot units do not get destroyed when tested, and then survival units can continue within the test providing extra information for inference. This not-destructiveness is a great advantage when the number of units under test are few. On the other hand, one-shot devices may last for long times under normal operating conditions and so accelerated life tests (ALTs), which increases the stress levels at which units are tested, may be needed. ALTs relate the lifetime distribution of an unit with the stress level at which it is tested via log-linear relationship, so inference results can be easily extrapolated to normal operating conditions. In particular, the step-stress model, which allows the experimenter to increase the stress level at pre-fixed times gradually during the life-testing experiment is specially advantageous for non-destructive one-shot devices. In this paper, we develop robust Raotype test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive one-shot devices under the stepstress ALTs with exponential lifetime distributions. We theoretically study their asymptotic and robustness properties, and empirically illustrates such properties through a simulation study.

show abstract

Estimation and Testing on Independent Not Identically Distributed Observations Based on Rényi’s Pseudodistances

Cited by 6 publications

References 31 publications

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

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

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

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

Contact Info

Product

Resources

About