arXiv subjects

Maria Jaenada

Publications and source records attributed to Maria Jaenada.

4 recordsLinked to original sources

arXiv2023

Robust inference for an interval-monitored step-stress experiment with competing risks for failure

Accelerated life-tests (ALTs) are used for inferring lifetime characteristics of highly reliable products. In particular, step-stress ALTs increase the stress level at which units under test are subject at certain pre-fixed times, thus accelerating the product's wear and inducing its failure. In some cases, due to cost or product nature constraints, continuous monitoring of devices is infeasible, and so the units are inspected for failures at particular inspection time points. In a such setup, the ALT response is interval-censored. Furthermore, when a test unit fails, there are often more than one fatal cause for the failure, known as competing risks. In this paper, we assume that all competing risks are independent and follow exponential distributions with scale parameters depending on the stress level. Under this setup, we present a family of robust estimators based on density power divergence, including the classical maximum likelihood estimator (MLE) as a particular case. We derive asymptotic and robustness properties of the Minimum Density Power Divergence Estimator (MDPDE), showing its consistency for large samples. Based on these MDPDEs, estimates of the lifetime characteristics of the product as well as estimates of cause-specific lifetime characteristics are then developed. Direct asymptotic, transformed and, bootstrap confidence intervals for the mean lifetime to failure, reliability at a mission time and, distribution quantiles are proposed, and their performance is then compared through Monte Carlo simulations. Moreover, the performance of the MDPDE family has been examined through an extensive numerical study and the methods of inference discussed here are finally illustrated with a real-data example concerning electronic devices.

math.ST↗

arXiv2023

Model Selection for independent not identically distributed observations based on R\'enyi's pseudodistances

Model selection criteria are rules used to select the best statistical model among a set of candidate models, striking a trade-off between goodness of fit and model complexity. Most popular model selection criteria measure the goodness of fit trough the model log-likelihood function, yielding to non-robust criteria. This paper presents a new family of robust model selection criteria for independent but not identically distributed observations (i.n.i.d.o.) based on the R\'enyi's pseudodistance (RP). The RP-based model selection criterion is indexed with a tuning parameter $\alpha$ controlling the trade-off between efficiency and robustness. Some theoretical results about the RP criterion are derived and the theory is applied to the multiple linear regression model, obtaining explicit expressions of the model selection criterion. Moreover, restricted models are considered and explicit expressions under the multiple linear regression model with nested models are accordingly derived. Finally, a simulation study empirically illustrates the robustness advantage of the method.

math.ST↗

arXiv2021

Estimation and testing on independent not identically distributed observations based on Rényi's pseudodistances

In real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) without random covariates. While the classical methods are based on the maximum likelihood estimator (MLE), it is well known its lack of robustness to small deviations from the assumed conditions. In this paper, and based on the Rényi's pseudodistance (RP), we introduce a new family of estimators in case our information about the unknown parameter is given for i.n.i.d.o.. This family of estimators, let say minimum RP estimators (as they are obtained by minimizing the RP between the assumed distribution and the empirical distribution of the data), contains the MLE as a particular case and can be applied, among others, to the MLRM without random covariates. Based on these estimators, we introduce Wald-type tests for testing simple and composite null hypotheses, as an extension of the classical MLE-based Wald test. Influence functions for the estimators and Wald-type tests are also obtained and analysed. Finally, a simulation study is developed in order to asses the performance of the proposed methods and some real-life data are analysed for illustrative purpose.

math.ST↗

arXiv2020

Robust adaptive variable selection in ultra-high dimensional linear regression models

We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive penalty functions are used in this regard to achieve the oracle variable selection property along with easier computational burden. However, the usual adaptive procedures (e.g., adaptive LASSO) based on the squared error loss function is extremely non-robust in the presence of data contamination which are quite common with large-scale data (e.g., noisy gene expression data, spectra and spectral data). In this paper, we present a regularization procedure for the ultra-high dimensional data using a robust loss function based on the popular density power divergence (DPD) measure along with the adaptive LASSO penalty. We theoretically study the robustness and the large-sample properties of the proposed adaptive robust estimators for a general class of error distributions; in particular, we show that the proposed adaptive DPD-LASSO estimator is highly robust, satisfies the oracle variable selection property, and the corresponding estimators of the regression coefficients are consistent and asymptotically normal under easily verifiable set of assumptions. Numerical illustrations are provided for the mostly used normal error density. Finally, the proposal is applied to analyze an interesting spectral dataset, in the field of chemometrics, regarding the electron-probe X-ray microanalysis (EPXMA) of archaeological glass vessels from the 16th and 17th centuries.

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