arXiv subjects

Leandro Pardo

Publications and source records attributed to Leandro Pardo.

At least 19 recordsLinked to original sources

arXiv2026

Robust inference for cyclic-stress accelerated life tests under interval monitoring with lognormal lifetimes

Highly reliable products are often tested under accelerated conditions to provoke failures within a feasible timeframe. For products whose service life involves repeated alternation between two stress levels, such as automotive air-conditioners, batteries, and aerospace components, cyclic-stress accelerated life testing (CyALT) provides a more realistic loading profile than conventional accelerated tests. In practice, failures are often recorded only at scheduled inspection times, leading to interval-censored counts rather than exact lifetimes. Moreover, traditional maximum likelihood estimation is sensitive to data contamination, which is a genuine concern in small-sample industrial experiments. This paper develops robust inferential procedures for CyALT models with lognormal lifetimes under interval monitoring. Robust estimators are obtained by minimizing a weighted density power divergence (WDPD), leading to the weighted minimum density power divergence estimator (WMDPDE). We establish the asymptotic distribution of the WMDPDE, derive influence function expressions to characterize the robustness, and present asymptotic and bootstrap confidence intervals for important lifetime characteristics. A simulation study confirms that the WMDPDE provides substantial protection against outliers while retaining high efficiency under clean data. The methodology is illustrated through the analysis of an air-conditioner reliability dataset, demonstrating the practical advantages of robust inference in the CyALT framework.

stat.ME↗

arXiv2026

Robust Estimation in Step-Stress Experiments under Weibull Lifetime Distributions

Many modern products are highly reliable, often exhibiting long lifetimes. As a result, conducting experiments under normal operating conditions can be prohibitively time-consuming to collect sufficient failure data for robust statistical inference. Accelerated life tests (ALTs) offer a practical solution by inducing earlier failures, thereby reducing the required testing time. In step-stress experiments, a stress factor that accelerates product degradation is identified and systematically increased at predetermined time points, while remaining constant between intervals. Failure data collected under these elevated stress levels is analyzed, and the results are then extrapolated to normal operating conditions. Traditional estimation methods for such data, such as the maximum likelihood estimator (MLE), are highly efficient under ideal conditions but can be severely affected by outlying or contaminated observations. To address this, we propose the use of Minimum Density Power Divergence Estimators (MDPDEs) as a robust alternative, offering a balanced trade-off between efficiency and resistance to contamination. The MDPDE framework is extended to mixed distributions and its theoretical properties, including the asymptotic distribution of the model parameters, are derived assuming Weibull lifetimes. The effectiveness of the proposed approach is illustrated through extensive simulation studies, and its practical applicability is further demonstrated using real-world data.

stat.ME↗

arXiv2026

Cosmological constraints on viable $f(R)$ models using weak lensing

The accelerated expansion of the Universe remains one of the central open problems in modern cosmology. While the $\Lambda$CDM model successfully describes a wide range of observations, the physical nature of dark energy is still unknown, motivating the study of alternative theories of gravity. Among these, $f(R)$ models provide a well-established extension of General Relativity, capable of reproducing a $\Lambda$CDM-like background evolution without introducing an explicit dark energy component. However, they can induce deviations in the growth of cosmic structures, making them testable through observables sensitive to cosmological perturbations. In this work, we use weak gravitational lensing to constrain several viable $f(R)$ gravity models. We analyze their impact on the matter power spectrum, as well as on the convergence and cosmic shear power spectra. Our analysis is carried out within a Bayesian framework using the \textit{Cobaya} code and its modified gravity extension, \textit{MGCobaya}, which enables consistent theoretical predictions and their comparison with current weak lensing and CMB lensing data. We find that standard cosmological parameters remain consistent with the $\Lambda$CDM scenario for all models considered, as expected from their background degeneracy. Nevertheless, we obtain non-trivial and model-dependent constraints on the characteristic parameters of several $f(R)$ theories.

astro-ph.CO↗

arXiv2025

Robust Estimation in Step-Stress Experiments under Exponential Lifetime Distributions

Many modern products exhibit high reliability, often resulting in long times to failure. Consequently, conducting experiments under normal operating conditions may require an impractically long duration to obtain sufficient failure data for reliable statistical inference. As an alternative, accelerated life tests (ALTs) are employed to induce earlier failures and thereby reduce testing time. In step-stress experiments a stress factor that accelerates product degradation is identified and systematically increased to provoke early failures. The stress level is increased at predetermined time points and maintained constant between these intervals. Failure data observed under increased levels of stress is statistically analyzed, and results are then extrapolate to normal operating conditions. Classical estimation methods such analysis rely on the maximum likelihood estimator (MLE) which is know to be very efficient, but lack robustness in the presence of outlying data. In this work, Minimum Density Power Divergence Estimators (MDPDEs) are proposed as a robust alternative, demonstrating an appealing compromise between efficiency and robustness. The MDPDE based on mixed distributions is developed, and its theoretical properties, including the expression for the asymptotic distribution of the model parameters, are derived under exponential lifetime assumptions. The good performance of the proposed method is evaluated through simulation studies, and its applicability is demonstrated using real data.

stat.ME↗

arXiv2025

Robust statistical inference for accelerated life-tests with one-shot devices under log-logistic distributions

A one-shot device is a unit that operates only once, after which it is either destroyed or needs to be rebuilt. For this type of device, the operational status can only be assessed at a specific inspection time, determining whether failure occurred before or after it. Consequently, lifetimes are subject to left- or right-censoring. One-shot devices are usually highly reliables. To analyze the reliability of such products, an accelerated life test (ALT) plan is typically employed by subjecting the devices to increased levels of stress factors, thus allowing life characteristics observed under high-stress conditions to be extrapolated to normal operating conditions. By accelerating the degradation process, ALT significantly reduces both the time required for testing and the associated experimental costs. Recently, robust inferential methods have gained considerable interest in statistical analysis. Among them, weighted minimum density power divergence estimators (WMDPDEs) are widely recognized for their robust statistical properties with small loss of efficiency. In this work, robust WMDPDE and associated statistical tests are developed under a log-logistic lifetime distribution with multiple stresses. Explicit expressions for the estimating equations and asymptotic distribution of the estimators are obtained. Further, a Monte Carlo simulation study is presented to evaluate the performance of the WMDPDE in practical applications.

math.ST↗

arXiv2024

Robust estimators for the log-logistic model based on ranked set sampling

In this paper we introduce a new family of estimators for the parameters of shape and scale of the log-logistic distribution being robust when rank set sample method is used to select the data. Rank set sampling arises as a way to reduce the impact of extremal data. Log-logistic distribution is an important distribution suitable for modeling many different situations ranging from Economy to Engineering and Hydrology. This new family of estimators is based on density power divergences. The choice of this family of divergence measures is motivated by the fact that they have shown a very good behavior in terms of robustness at a reduced cost in efficiency. This new family recovers the classical maximum likelihood estimator as a special case. We have developed the form of these estimators and derived their corresponding asymptotic distribution. A simulation study is carried out, suggesting that these new estimators are very robust when contamination arises and are competitive with classical estimators in terms of efficiency.

math.ST↗

arXiv2024

Robust inference for an interval-monitored step-stress experiment under proportional hazards

Accelerated life tests (ALTs) play a crucial role in reliability analyses, providing lifetime estimates of highly reliable products. Among ALTs, step-stress design increases the stress level at predefined times, while maintaining a constant stress level between successive changes. This approach accelerates the occurrence of failures, reducing experimental duration and cost. While many studies assume a specific form for the lifetime distribution, in certain applications instead a general form satisfying certain properties should be preferred. Proportional hazard model assumes that applied stresses act multiplicatively on the hazard rate, so the hazards function may be divided into two factors, with one representing the effect of the stress, and the other representing the baseline hazard. In this work we examine two particular forms of baseline hazards, namely, linear and quadratic. Moreover, certain experiments may face practical constraints making continuous monitoring of devices infeasible. Instead, devices under test are inspected at predetermined intervals, leading to interval-censoring data. On the other hand, recent works have shown an appealing trade-off between the efficiency and robustness of divergence-based estimators. This paper introduces the step-stress ALT model under proportional hazards and presents a robust family of minimum density power divergence estimators (MDPDEs) for estimating device reliability and related lifetime characteristics such as mean lifetime and distributional quantiles. The asymptotic distributions of these estimates are derived, providing approximate confidence intervals. Empirical evaluations through Monte Carlo simulations demonstrate their performance in terms of robustness and efficiency. Finally, an illustrative example is provided to demonstrate the usefulness of the model and associated methods developed.

math.ST↗

arXiv2024

Robust Rao-type tests for step-stress accelerated life-tests under interval-monitoring and Weibull lifetime distributions

Many products in engineering are highly reliable with large mean lifetimes to failure. Performing lifetests under normal operations conditions would thus require long experimentation times and high experimentation costs. Alternatively, accelerated lifetests shorten the experimentation time by running the tests at higher than normal stress conditions, thus inducing more failures. Additionally, a log-linear regression model can be used to relate the lifetime distribution of the product to the level of stress it experiences. After estimating the parameters of this relationship, results can be extrapolated to normal operating conditions. On the other hand, censored data is common in reliability analysis. Interval-censored data arise when continuous inspection is difficult or infeasible due to technical or budgetary constraints. In this paper, we develop robust restricted estimators based on the density power divergence for step-stress accelerated life-tests under Weibull distributions with interval-censored data. We present theoretical asymptotic properties of the estimators and develop robust Rao-type test statistics based on the proposed robust estimators for testing composite null hypothesis on the model parameters.

stat.ME↗

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

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.

stat.ME↗

arXiv2023

Model Selection for independent not identically distributed observations based on Rényi'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 Rényi's pseudodistance (RP). The RP-based model selection criterion is indexed with a tuning parameter $α$ 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↗

arXiv2023

Robust adaptive Lasso in high-dimensional logistic regression

Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the existing methods based on the likelihood loss function are sensitive to data contamination and other noise and, hence, robust methods are needed for stable and more accurate inference. In this paper, we propose a family of robust estimators for sparse logistic models utilizing the popular density power divergence based loss function and the general adaptively weighted LASSO penalties. We study the local robustness of the proposed estimators through its influence function and also derive its oracle properties and asymptotic distribution. With extensive empirical illustrations, we demonstrate the significantly improved performance of our proposed estimators over the existing ones with particular gain in robustness. Our proposal is finally applied to analyse four different real datasets for cancer classification, obtaining robust and accurate models, that simultaneously performs gene selection and patient classification.

stat.ME↗

arXiv2023

Restricted distance-type Gaussian estimators based on density power divergence and their applications in hypothesis testing

Zhang (2019) presented a general estimation approach based on the Gaussian distribution for general parametric models where the likelihood of the data is difficult to obtain or unknown, but the mean and variance-covariance matrix are known. Castilla and Zografos (2021) extended the method to density power divergence-based estimators, which are more robust than the likelihood-based Gaussian estimator against data contamination. In this paper we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. Also, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, in special in testing composite null hypothesis, and provide here constrained estimators to inherent restrictions of the underlying distribution. Further, we derive robust Rao-type test statistics based on the MDPDGE for testing 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.

math.ST↗

arXiv2022

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

Since the two seminal papers by Fisher (1915, 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.

math.ST↗

arXiv2022

Robust inference for intermittently-monitored step-stress tests under Weibull lifetime distributions

Many modern products exhibit high reliability under normal operating conditions. Conducting life tests under these conditions may result in very few observed failures, insufficient for accurate inferences. Instead, accelerated life tests (ALTs) must be performed. One of the most popular ALT designs is the step-stress test, which shortens the product's lifetime by progressively increasing the stress level at which units are subjected to at some pre-specified times. Classical estimation methods based on the maximum likelihood estimator (MLE) enjoy suitable asymptotic properties but they lack robustness. That is, data contaminationcan significantly impact the statistical analysis. In this paper, we develop robust inferential methods for highly reliable devices based on the density power divergence (DPD) for estimating and testing under the step-stress model with intermittent monitoring and Weibull lifetime distributions. We theoretically and empirically examine asymptotic and robustness properties of the minimum DPD estimators and associated Wald-type test statistics. Moreover, we develop robust estimators and confidence intervals for some important lifetime characteristics. The effect of temperature in solar lights, medium power silicon bipolar transistors and LED lights using real data arising from an step-stress ALT is analyzed applying the robust methods proposed.

stat.AP↗

arXiv2022

The restricted minimum density power divergence estimator for non-destructive one-shot device testing the under step-stress model with exponential lifetimes

One-shot devices data represent an extreme case of interval censoring.Some kind of one-shot units do not get destroyed when tested, and so, survival units can continue within the test providing extra information about their lifetime. Moreover, one-shot devices may last for long times under normal operating conditions, and so accelerated life tests (ALTs) may be used for inference. ALTs relate the lifetime distribution of an unit with the stress level at which it is tested via log-linear relationship.Then, mean lifetime of the devices are reduced during the test by increasing the stress level and inference results on increased stress levels can be easily extrapolated to normal operating conditions. In particular, the step-stress ALT model increases the stress level at pre-fixed times gradually during the life-testing experiment, which may be specially advantageous for non-destructive one-shot devices. However, when the number of units under test are few, outlying data may greatly influence the parameter estimation. In this paper, we develop robust restricted estimators based on the density power divergence (DPD) under linearly restricted subspaces, for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distributions. We theoretically study the asymptotic and robustness properties of the restricted estimators and we empirically illustrate such properties through a simulation study.

math.ST↗

arXiv2022

Robust inference for non-destructive one-shot device testing under step-stress model with exponential lifetimes

One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one-shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step-stress tests allow the experimenter to increase the stress levels at pre-fixed times gradually during the life-testing experiment. The cumulative exposure model is commonly assumed for step-stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper,vwe develop robust estimators and Z-type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and confidence intervals for different lifetime characteristic such as reliability, distribution quantiles and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real-life data sets are analyzed finally for illustrative purpose.

stat.ME↗

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↗