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Ordering results between extreme order statistics in models with dependence defined by Archimedean [survival] copulas
No full textMotivated by recent works about stochastic comparisons between extreme order statistics arising from heterogeneous and dependent random variables, where the dependency structure is defined by the family of Archimedean copulas and the marginal distributions follow some specific parametric distributions, in this work, we investigate the case in which the marginal distributions can have arbitrary distribution functions depending on some parameter. Such parameter can be a shape, scale or location parameter, but other kinds of parameters, as frailty, resilience or tilt parameters can be also considered. Hence, the modified proportional hazard rate scale (MPHRS) and the modified proportional reversed hazard rate scale (MPRHRS) models, among others, belong to the wide parametric model studied here. Under this setup, we provide some general results for the usual stochastic order, when the parameter vectors verify the p-larger order or the reciprocally majorization order, generalizing some of the existing results in the literature. Besides this, extreme order statistics arising from the dependent MPHRS and MPRHRS models are compared in the sense of the reversed hazard rate order and the hazard rate order as well
Osteology and revised diagnosis of Cherninia denwai from the Middle Triassic Denwa Formation, Satpura Gondwana Basin, Central India
No full textThe Middle Triassic Denwa Formation located within the Satpura Gondwana basin of Central India exhibits a significant presence of temnospondyl amphibians classified under the family Mastodonsauridae. Prior investigations have documented two taxa of the Mastodonsauridae family, namely Cherninia denwai and Paracyclotosaurus crookshanki, from the Denwa Formation. These prior accounts were predominantly predicated upon two holotype skull specimens, thereby neglecting other specimens contained within the collection as well as various associated post-cranial materials. Recently, a diverse assortment of novel specimens pertaining to C. denwai has been unearthed from the Denwa Formation. Utilizing both the newly acquired specimens and previously overlooked specimens, this study presents a redescription of C. denwai. The newly discovered specimens comprise a partial skull, a mandible, clavicles, interclavicles, vertebrae, neural arches and spines, ulnae, an ilium, a femur, and a fibula, all of which are described herein for the first time. An extensive osteological analysis of the skull and mandible is conducted. It is noted that C. denwai coexists temporally with C. megarhina, and both taxa exhibit distinct synapomorphies; however, they are recognized as separate and unique species
Prevalence of major depressive disorder and its determinants among young married women and unmarried girls: Findings from the second round of UDAYA survey
No full textIntroduction Depression is a prevalent and debilitating mental illness affecting young women worldwide. This study aimed to identify psychosocial determinants of major depressive disorder (MDD) among young women in Bihar and Uttar Pradesh, India. Methods Data from Understanding the Lives of Adolescents and Young Adults (UDAYA) study (2018-19) for young women aged 12-23 years, both married and unmarried was used for this paper. MDD was evaluated using the Patient Health Questionnaire PHQ-9 with a cut-off score of ≤10. The determinants of MDD were identified through multilevel binary logistic regression analysis. Results The prevalence of MDD was 13.6% (95% CL 12.2-15.2) and 5.1% (95% CL 4.2-6.1) for young married women and unmarried girls, respectively. Among the young married women, community-level variables like dowry-related humiliation (1.74, 95% CI 1.15-2.64), and sexual assaults (2.15, 95% CI 1.24-3.73) were significantly associated with MDD. For unmarried girls, reporting of family violence \u3c10% of participants (0.45, 95% CI 0.24-0.85), family violence (≥10% of participants) % (0.35 95% CI 0.19-0.68) and interpartner violence (\u3e25% of participants) (0.42; 95% CI 0.23-0.74) remain significant predictors of MDD. At individual level, for both the groups, age, participation in decision making (on education), social capital (currently attending school/educational course and number of friends), self-efficacy, telephonic harassment, and physical activity were associated with MDD. Wealth index, job seeking, participation in decision making (on health-seeking), parental interactions and physical abuse (for unmarried girls only) and education, reported last sexual intercourse, pressure from the in-laws’ to conceive (for young married women only) were associated with MDD. Conclusions For young married women, community level targeted interventions should focus on the social ecology to foster a sense of safe community environment. For unmarried girls, additionally, interventions should aim to optimize their family environment for effective mental health outcomes
Process incapability index for autocorrelated data in the presence of measurement errors
No full textProcess incapability index is a useful tool for measuring the performance of a process to maintain the quality of products. In this article, we discuss some statistical properties of the estimator of process incapability index when process observations are autocorrelated and contaminated by measurement errors. In many industry, it has been proven that observed quality characteristics for consecutive items are autocorrelated. Moreover, some amount of measurement errors is always present in the observed data. Therefore, it is important to analyze the statistical properties of the estimator under the combined effect of autocorrelation and measurement error for commenting approximately on the ability of a manufacturing process
Quantifying fluid pressure events using shallow crustal veins
No full textReactivation of pre-existing fractures is attributed to fluid pressure conditions and orientation of fractures with respect to the tectonic stress field. In most cases, multiple fluid pressure events reactivate fracture networks. However, it is difficult to perceive and quantify the number of such fluid pressure events directly from a heterogeneous vein data distribution. In the present study, we undertake a statistical approach, well known and extensively used for fuzzy clustering of planar data to approximate the minimum number of fluid pressure events which formed/reactivated fractures. We have also combined the deterministic method for quantifying the minimum number of such fluid pressure events with the traditional method of scaling 3D Mohr circles to determine the absolute fluid pressure magnitudes. The method has been applied to published data of the Gadag-Chitradurga greenstone belt, a prominent Archean greenstone belt of the western Dharwar Craton, south India, to understand the mechanism behind shallow crustal emplacement of auriferous quartz veins within a transtensional tectonic regime. Further, we provide field evidence of fracture reactivation and estimate their reactivation potential, which play a significant role in the spatial variation of fluid pressure along the greenstone belt. Graphical abstract: Identifying data clusters using Bingham statistics for Pf determination. [Figure not available: see fulltext.]
Robust adaptive LASSO in high-dimensional logistic regression: Robust adaptive LASSO in high-dimensional logistic regression: A. Basu et al.
No full textPenalized 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
Robust Principal Component Analysis: A Median of Means Approach
No full textPrincipal component analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in statistics, machine learning, computer vision, and related fields. However, PCA is well-known to fall prey to outliers and often fails to detect the true underlying low-dimensional structure within the dataset. Following the Median of Means (MoM) philosophy, recent supervised learning methods have shown great success in dealing with outlying observations without much compromise to their large sample theoretical properties. This article proposes a PCA procedure based on the MoM principle. Called the MoMPCA, the proposed method is not only computationally appealing but also achieves optimal convergence rates under minimal assumptions. In particular, we explore the nonasymptotic error bounds of the obtained solution via the aid of the Rademacher complexities while granting absolutely no assumption on the outlying observations. The derived concentration results are not dependent on the dimension because the analysis is conducted in a separable Hilbert space, and the results only depend on the fourth moment of the underlying distribution in the corresponding norm. The proposal\u27s efficacy is also thoroughly showcased through simulations and real data applications
Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order
No full textIn this paper, we focus on studying the Cauchy problem for semilinear damped wave equations involving the sub-Laplacian L on the Heisenberg group Hn with power type nonlinearity |u|p and initial data taken from Sobolev spaces of negative order homogeneous Sobolev space H˙L-γ(Hn),γ\u3e0, on Hn. In particular, in the framework of Sobolev spaces of negative order, we prove that the critical exponent is the exponent pcrit(Q,γ)=1+4Q+2γ, for γ∈(0,Q2), where Q:=2n+2 is the homogeneous dimension of Hn. More precisely, we establish A global-in-time existence of small data Sobolev solutions of lower regularity for p\u3epcrit(Q,γ) in the energy evolution space; A finite time blow-up of weak solutions for 1crit(Q,γ) under certain conditions on the initial data by using the test function method. Furthermore, to precisely characterize the blow-up time, we derive sharp upper bound and lower bound estimates for the lifespan in the subcritical case
Solving superconducting quantum circuits in Dirac\u27s constraint analysis framework
No full textIn this work we exploit Dirac\u27s Constraint Analysis (DCA) in Hamiltonian formalism to study different types of Superconducting Quantum Circuits (SQC) in a unified way. The Lagrangian of a SQC reveals the constraints, that are classified in a Hamiltonian framework, such that redundant variables can be removed to isolate the canonical degrees of freedom for subsequent quantization of the Dirac Brackets via a generalized Correspondence Principle. This purely algebraic approach makes the application of concepts such as graph theory, null vector, loop charge, etc that are in vogue, (each for a specific type of circuit), completely redundant. The universal validity ofDCAscheme in SQC, proposed by us, is demonstrated by correctly re-deriving existing results for different SQCs, obtained previously exploiting different formalisms each applicable for a specific SQC. Furthermore, we have also analysed and predicted new results for a generic form of SQC - it will be interesting to see its validation in an explicit circuit implementation