arXiv subjects

Shuvashree Mondal

Publications and source records attributed to Shuvashree Mondal.

10 recordsLinked to original sources

arXiv2026

An Exponential-Polynomial Divergence-based Robust Information Criterion for Linear Panel Data Models and Neural Networks

Model selection is a cornerstone of statistical inference, where information criteria are widely employed to balance model fit and complexity. However, classical likelihood-based criteria are often highly sensitive to contamination, outliers, and model misspecification. In this paper, we develop a robust alternative based on the Exponential-Polynomial Divergence, a flexible extension of existing divergence measures that enhances adaptability to diverse data irregularities. The proposed Exponential-Polynomial Divergence Information Criterion preserves the objective of approximating the discrepancy between the true model and candidate models while incorporating robustness against anomalous observations. Its theoretical properties are established, and robustness is examined through influence function analysis, demonstrating controlled sensitivity to extreme data points. For practical implementation, a data-driven tuning parameter selection strategy based on generalized score matching is employed, ensuring improved computational stability and efficiency. The effectiveness of the proposed method is demonstrated through extensive simulation studies under varying contamination levels, as well as real data applications involving linear mixed-effects panel data models and neural network-based prediction tasks. The results consistently show improved stability and reliability compared to classical likelihood and density power divergence-based information criteria. The proposed framework thus provides a practical and unified approach for model selection in complex and contaminated data settings.

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arXiv2025

Inequality Constrained Minimum Density Power Divergence Estimation in Panel Count Data

The analysis of panel count data has garnered considerable attention in the literature, leading to the development of multiple statistical techniques. In inferential analysis, most works focus on leveraging estimating equation-based techniques or conventional maximum likelihood estimation. However, the robustness of these methods is largely questionable. In this paper, we present a robust density power divergence estimation method for panel count data arising from non-homogeneous Poisson processes correlated through a latent frailty variable. To cope with real-world incidents, it is often desirable to impose certain inequality constraints on the parameter space, leading to the constrained minimum density power divergence estimator. Being incorporated with inequality restrictions, coupled with the inherent complexity of our objective function, standard computational algorithms are inadequate for estimation purposes. To overcome this, we adopt sequential convex programming, which approximates the original problem through a series of subproblems. Further, we study the asymptotic properties of the resultant estimator, making a significant contribution to this work. The proposed method ensures high efficiency in the model estimation while providing reliable inference despite data contamination. Moreover, the density power divergence measure is governed by a tuning parameter $γ$, which controls the trade-off between robustness and efficiency. To effectively determine the optimal value of $γ$, this study employs a generalized score-matching technique, marking considerable progress in the data analysis. Simulation studies and real data examples are provided to illustrate the performance of the estimator and to substantiate the theory developed.

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arXiv2025

Robust Bayesian approach for reliability prognosis of nondestructive one-shot devices under cumulative risk model

The present study aims to determine the lifetime prognosis of highly durable nondestructive one-shot devices (NOSD) units under a step-stress accelerated life testing (SSALT) experiment applying a cumulative risk model (CRM). In an SSALT experiment, CRM retains the continuity of hazard function by allowing the lag period before the effects of stress change emerge. When prior information about the model parameters is available, Bayesian inference is crucial. In a Bayesian analysis of such lifetime data, conventional likelihood-based Bayesian estimation frequently fails in the presence of outliers in the dataset. This work incorporates a robust Bayesian approach utilizing a robustified posterior based on the density power divergence measure. The order restriction on shape parameters has been incorporated as a prior assumption to reflect the decreasing expected lifetime with increasing stress levels. In testing of hypothesis, a Bayes factor is implemented based on the robustified posterior. In Bayesian estimation, we exploit Hamiltonian Monte Carlo, which has certain advantages over the conventional Metropolis-Hastings algorithms. Further, the influence functions are examined to evaluate the robust behaviour of the estimators and the Bayes factor. Finally, the analytical development is validated through a simulation study and a real data analysis.

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arXiv2025

Exponential-polynomial divergence based inference for nondestructive one-shot devices under progressive stress model

Nondestructive one-shot device (NOSD) testing plays a crucial role in engineering, particularly in the reliability assessment of high-stakes systems such as aerospace components, medical devices, and semiconductor technologies. Accurate reliability prognosis of NOSD testing data is essential for ensuring product durability, safety, and performance optimization. The conventional estimation methods like maximum likelihood estimation (MLE) are sensitive to data contamination, leading to biased results. Consequently, this study develops robust inferential analysis for NOSD testing data under a progressive stress model. The lifetime of NOSD is assumed to follow Log-logistic distribution. The estimation procedure addresses robustness by incorporating Exponential-polynomial divergence (EPD). Equipped with three tuning parameters, EPD based estimation is proven to be more flexible than density power divergence estimation frequently used for one-shot device testing data analysis. Further, we explore the asymptotic behaviour of minimum EPD estimator (MEPDE) for large sample size. The robustness of MEPDE is analytically studied through influence function. Since tradeoff between efficiency and robustness of EPD based estimation is governed by three tuning parameters, a novel approach leveraging Concrete Score Matching (CSM) is introduced to optimize the tuning parameters of MEPDE. Moreover, a comparative study with the existing methods of finding tuning parameters is conducted through extensive simulation experiment and data analysis. Another aspect of this study is determining an optimal plan to ensure a successful ALT experiment within specified budget and time constraints. It is designed on A-optimality criteria subject to the given constraints and is executed using the constraint particle swarm optimization (CPSO) algorithm.

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arXiv2025

Robust Bayesian inference for nondestructive one-shot device testing data under competing risk using Hamiltonian Monte Carlo method

The prevalence of one-shot devices is quite prolific in engineering and medical domains. Unlike typical one-shot devices, nondestructive one-shot devices (NOSD) may survive multiple tests and offer additional data for reliability estimation. This study aims to implement the Bayesian approach of the lifetime prognosis of NOSD when failures are subject to multiple risks. With small deviations from the assumed model conditions, conventional likelihood-based Bayesian estimation may result in misleading statistical inference, raising the need for a robust Bayesian method. This work develops Bayesian estimation by exploiting a robustified posterior based on the density power divergence measure for NOSD test data. Further, the testing of the hypothesis is carried out by applying a proposed Bayes factor derived from the robustified posterior. A flexible Hamiltonian Monte Carlo approach is applied to generate posterior samples. Additionally, we assess the extent of resistance of the proposed methods to small deviations from the assumed model conditions by applying the influence function (IF) approach. In testing of hypothesis, IF reflects how outliers impact the decision-making through Bayes factor under null hypothesis. Finally, this analytical development is validated through a simulation study and a data analysis based on cancer data.

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arXiv2023

One-Shot Device Testing Data Analysis under Logistic-Exponential Lifetimes with an Application to SEER Gallbladder Cancer Data

In the literature, the reliability analysis of one-shot devices is found under accelerated life testing in the presence of various stress factors. The application of one-shot devices can be extended to the bio-medical field, where we often evidence that inflicted with a certain disease, survival time would be under different stress factors like environmental stress, co-morbidity, the severity of disease etc. This work is concerned with a one-shot device data analysis and applies it to SEER Gallbladder cancer data. The two-parameter logistic exponential distribution is applied as a lifetime distribution. For robust parameter estimation, weighted minimum density power divergence estimators (WMDPDE) is obtained along with the conventional maximum likelihood estimators (MLE). The asymptotic behaviour of the WMDPDE and the robust test statistic based on the density power divergence measure are also studied. The performances of estimators are evaluated through extensive simulation experiments. Later those developments are applied to SEER Gallbladder cancer data. Citing the importance of knowing exactly when to inspect the one-shot devices put to the test, a search for optimum inspection times is performed. This optimization is designed to minimize a defined cost function which strikes a trade-off between the precision of the estimation and experimental cost. The search is accomplished through the population-based heuristic optimization method Genetic Algorithm.

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arXiv2022

Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals

Recently, a growing amount interest is quite evident in modelling dependent competing risks in life time prognosis problem. In this work, we propose to model the dependent competing risks by Marshal-Olkin bivariate exponential distribution. The observable data consists of number of failures due to different causes across different time intervals. The failure count data is common in instances like one shot devices where state of the subjects are inspected at different inspection times rather than the exact failure times. The point estimation of the life time distribution in presence of competing risk has been studied through divergence based robust estimation method called minimum density power divergence estimation (MDPDE). The testing of hypothesis is performed based on a Wald type test statistic. The influence function is derived both for the point estimator and the test statistic, which reflects the degree of robustness. Another, key contribution of this work is to determine the optimal set of inspection times based on some predefined objectives. This article presents determination of multi criteria based optimal design. Population based heuristic algorithm non-dominated sorting-based multiobjective Genetic algorithm is exploited to solve this optimization problem.

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arXiv2018

Inference on Weibull Parameters Under a Balanced Two Sample Type-II Progressive Censoring Scheme

The progressive censoring scheme has received considerable amount of attention in the last fifteen years. During the last few years joint progressive censoring scheme has gained some popularity. Recently, the authors Mondal and Kundu ("A new two sample Type-II progressive censoring scheme", arXiv:1609.05805) introduced a balanced two sample Type-II progressive censoring scheme and provided the exact inference when the two populations are exponentially distributed. In this article we consider the case when the two populations follow Weibull distributions with the common shape parameter and different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators cannot be obtained in explicit forms, hence, we propose approximate maximum likelihood estimators, which can be obtained in explicit forms. We construct the asymptotic and bootstrap confidence intervals of the population parameters. Further we derive an exact joint confidence region of the unknown parameters. We propose an objective function based on the expected volume of this confidence set and using that we obtain the optimum progressive censoring scheme. Extensive simulations have been performed to see the performances of the proposed method, and one real data set has been analyzed for illustrative purposes.

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arXiv2017

Point and Interval Estimation of Weibull Parameters Based on Joint Progressively Censored Data

The analysis of progressively censored data has received considerable attention in the last few years. In this paper we consider the joint progressive censoring scheme for two populations. It is assumed that the lifetime distribution of the items from the two populations follow Weibull distribution with the same shape but different scale parameters. Based on the joint progressive censoring scheme first we consider the maximum likelihood estimators of the unknown parameters whenever they exist. We provide the Bayesian inferences of the unknown parameters under a fairly general priors on the shape and scale parameters. The Bayes estimators and the associated credible intervals cannot be obtained in closed form, and we propose to use the importance sampling technique to compute the same. Further, we consider the problem when it is known apriori that the expected lifetime of one population is smaller than the other. We provide the order restricted classical and Bayesian inferences of the unknown parameters. Monte Carlo simulations are performed to observe the performances of the different estimators and the associated confidence and credible intervals. One real data set has been analyzed for illustrative purpose.

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arXiv2016

A New Two Sample Type-II Progressive Censoring Scheme

Progressive censoring scheme has received considerable attention in recent years. In this paper we introduce a new type-II progressive censoring scheme for two samples. It is observed that the proposed censoring scheme is analytically more tractable than the existing joint progressive type-II censoring scheme proposed by Rasouli and Balakrishnan \cite{RB:2010}. It has some other advantages also. We study the statistical inference of the unknown parameters based on the assumptions that the lifetime distribution of the experimental units for the two samples follow exponential distribution with different scale parameters. The maximum likelihood estimators of the unknown parameters are obtained and their exact distributions are derived. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals are also constructed. For comparison purposes we have used bootstrap confidence intervals also. It is observed that the bootstrap confidence intervals work very well and they are very easy to implement in practice. Some simulation experiments are performed to compare the performances of the proposed method with the existing one, and the performances of the proposed method are quite satisfactory. One data analysis has been performed for illustrative purposes. Finally we propose some open problems.

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