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Robust estimation of fixed effect parameters and variances of linear mixed models: the minimum density power divergence approach
No full textMany real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measures the discrepancy between two probability density functions, has been successfully used to build robust estimators with high stability associated with minimal loss in efficiency. Here, we develop the minimum DPD estimator (MDPDE) for independent but non-identically distributed observations for LMMs according to the variance components model. We prove that the theoretical properties hold, including consistency and asymptotic normality of the estimators. The influence function and sensitivity measures are computed to explore the robustness properties. As a data-based choice of the MDPDE tuning parameter α is very important, we propose two candidates as “optimal” choices, where optimality is in the sense of choosing the strongest downweighting that is necessary for the particular data set. We conduct a simulation study comparing the proposed MDPDE, for different values of α, with S-estimators, M-estimators and the classical maximum likelihood estimator, considering different levels of contamination. Finally, we illustrate the performance of our proposal on a real-data example
Robust singular value decomposition with application to video surveillance background modelling
No full textThe traditional method of computing singular value decomposition (SVD) of a data matrix is based on the least squares principle and is, therefore, very sensitive to the presence of outliers. Hence, the resulting inferences across different applications using the classical SVD are extremely degraded in the presence of data contamination. In particular, background modelling of video surveillance data in the presence of camera tampering cannot be reliably solved by the classical SVD. In this paper, we propose a novel robust singular value decomposition technique based on the popular minimum density power divergence estimator. We have established the theoretical properties of the proposed estimator such as convergence, equivariance and consistency under the high-dimensional regime where both the row and column dimensions of the data matrix approach infinity. We also propose a fast and scalable algorithm based on alternating weighted regression to obtain the estimate. Within the scope of our fairly extensive simulation studies, our method performs better than existing robust SVD algorithms. Finally, we present an application of the proposed method on the video surveillance background modelling problem
Self-organized bistability on globally coupled higher-order networks
No full textSelf-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints. By applying Ott-Antonsen dimensionality reduction in the thermodynamic limit to the higher-order network, we derive SOB requirements under coupling limits that are in good agreement with numerical simulations on systems of finite size. We use continuous synchronization diagrams and statistical data from spontaneous synchronized events to demonstrate the crucial role SOB plays in initiating and terminating temporary synchronized events. We show that under weak-coupling consumption, these spontaneous occurrences closely resemble the statistical traits of the epileptic brain functioning
Self-testing of genuine multipartite entangled states without network assistance
No full textWe study the self-testing problem of quantum correlations in the context of a multipartite scenario, a task that becomes increasingly complex compared to the bipartite systems. Recently, [Šupić, Nat. Phys. 19, 670 (2023)10.1038/s41567-023-01945-4] introduced a novel self-testing method for pure multipartite entangled states, which leverages network assistance and relies on bipartite entangled measurements. Hence, their scheme loses the ideal device-independent nature of self-testing. To address this, we provide a self-testing scheme for genuine multipartite entanglement in the true sense. Our approach utilizes a generalized Hardy-type nonlocality argument and requires only local operations, eliminating the need for network assistance or bipartite entangled measurements. Furthermore, we establish a device-independent bound for the maximum probability of success for a generalized Hardy-type argument. This paves the way for reliable and efficient self-testing of quantum correlations without relying on additional resources
Sequential Estimation of Conditional Odds Ratio
No full textThis paper deals with fixed-width confidence interval of conditional odds ratio in the context of clinical trial experiment with matched pair-type of data structure. Some related asymptotic result is also obtained. The procedure is evaluated by simulation followed by a data study
Stochastic comparisons of coherent systems with active redundancy at the component or system levels and component lifetimes following the accelerated life model
No full textAn effective way to increase system reliability is to use redundancies (spares) into the systems either in component level or in system level. In this prospect, it is a significant issue that which set of available spares providing better system reliability in some stochastic sense. In this paper, we derive sufficient conditions under which a coherent system with a set of active redundancy at the component level or the system level provide better system reliability than that of the system with another set of redundancy, with respect some stochastic orders. We have derived the results for the component lifetimes following accelerated life (AL) model. The results obtained help us to design more reliable systems by allocating appropriate redundant components from the set of available options for the same. Various examples satisfying the sufficient conditions of the theoretical results are provided. Some results are illustrated with real-world data
Stochastic comparisons of largest claim and aggregate claim amounts
No full textIn this paper, we establish some stochastic comparison results for largest claim amounts of two sets of independent and also for interdependent portfolios under the setup of the proportional odds model. We also establish stochastic comparison results for aggregate claim amounts of two sets of independent portfolios. Further, stochastic comparisons for largest claim amounts from two sets of independent multiple-outlier claims have also been studied. The results we obtained apply to the whole family of extended distributions, also known as the Marshall-Olkin family of distributions. We have given many numerical examples to illustrate the results obtained
The distal-proximal relationships among the human moonlighting proteins: Evolutionary hotspots and Darwinian checkpoints
No full textMoonlighting proteins, known for their ability to perform multiple, often unrelated functions within a single polypeptide chain, challenge the traditional “one gene, one protein, one function” paradigm. As organisms evolved, their genomes remained relatively stable in size, but the introduction of post-translational modifications and sub-strategies like protein promiscuity and intrinsic disorder enabled multifunctionality. Enzymes, in particular, exemplify this phenomenon, engaging in unrelated processes alongside their primary catalytic roles. This study employs a systematic, quantitative informatics approach to shed light on human moonlighting protein sequences. Phylogenetic analyses of human moonlighting proteins are presented, elucidating the distal-proximal relationships among these proteins based on sequence-derived quantitative features. The findings unveil the captivating world of human moonlighting proteins, urging further investigations in the emerging field of moonlighting proteomics, with the potential for significant contributions to our understanding of multifunctional proteins and their roles in diverse cellular processes and diseases
The influence of bottom disturbances on wave generation in a viscous liquid in the presence of uniform current
No full textIn the present paper, the effect of bottom disturbances on wave generation in a viscous liquid in the presence of uniform current is studied. The wave potential and Stokes stream function are used to formulate this problem. Multiple integrals representing the free surface elevation are obtained by mathematical analysis using the Laplace transform in time and the Fourier transform in space. This is divided into various multiple integrals, using the steepest descent method to evaluate them asymptotically for a large time and distance. There are three types of ground disturbances taken into consideration: D0(x)=e(−x2/2), D0(x)=e−|x|, and D0(x)=δ(x). The effect of uniform current speed (U) and viscosity (ν) on the free surface elevation is illustrated for the three forms of ground disturbances. It is observed that the presence of current often amplifies the energy of the propagating wave and also increases its amplitude. Moreover, as viscosity increases, the amplitude of free surface elevation decreases with respect to time, and further, the period of oscillation of surface elevation becomes smaller for a large time
The multi-objective economic statistical design of the p-chart: NSGA II approach
No full textA control chart is a crucially important tool in statistical process control that is essentially used to differentiate between assignable and chance causes of variation. With the advent of Six Sigma in the parlance of quality management, the control chart assumes more significance to hold the gain in the control phase after attaining process improvement in the improve phase. The sample size, sampling interval, and control limits’ multiplier are three important parameters required to design an effective as well as efficient control chart. Many approaches like economic design, statistical design, and economic statistical design of control charts have been studied by several researchers. All these approaches consider a single objective function. In this paper, we have proposed a multi-objective design of the p-chart, where we are minimizing both out-of-control Average Run Length ((Formula presented.)) and the expected cost per cycle ((Formula presented.)). Non-dominated Sorting Genetic Algorithm II (NSGA II) is used to solve the proposed multi-objective model. The proposed approach is demonstrated with the help of two numerical examples and the corresponding results are found to be quite encouraging for minimizing both objectives in comparison to another pertinent model given in the literature. Sensitivity analysis has been carried out to give credence to the worth of the proposed approach