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On standardness and the non-estimability of certain functionals of a set

Sun, 01 Jan 2023 00:00:00 GMT

Título: On standardness and the non-estimability of certain functionals of a set Autor: Cholaquidis, Alejandro; Moreno, Leonardo; Pateiro-López, Beatriz Resumen: Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that satisfies the standard assumption. Relevant results in this field, such as rates of convergence and confidence sets, depend on the standardness parameter, which in practice may be unknown. In this paper, we review the notion of standardness and its connection to other geometrical restrictions. We prove the almost sure consistency of a plug-in type estimator for the so-called standardness constant, already studied in the literature. We propose a method to correct the bias of the plug-in estimator and corroborate our theoretical findings through a small simulation study. We also show that it is not possible to determine, based on a finite sample, whether a probability measure satisfies the standard assumption.

Conformal inference for regression on Riemannian Manifolds

Sun, 01 Jan 2023 00:00:00 GMT

Título: Conformal inference for regression on Riemannian Manifolds Autor: Cholaquidis, Alejandro; Gamboa, Fabrice; Moreno, Leonardo Resumen: Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for this type of data. Circular data is a classic example, but so is data in the space of covariance matrices, data on the Grassmannian manifold obtained as a result of principal component analysis, among many others. In this work we investigate prediction sets for regression scenarios when the response variable, denoted by Y, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space. This extends the concepts delineated in [Lei and Wasserman, 2014] to this novel context. Aligning with traditional principles in conformal inference, these prediction sets are distribution-free, indicating that no specific assumptions are imposed on the joint distribution of (X, Y ), and they maintain a non-parametric character. We prove the asymptotic almost sure convergence of the empirical version of these regions on the manifold to their population counterparts. The efficiency of this method is shown through a comprehensive simulation study and an analysis involving real-world data.

Dependency change with aging and associated factors in Uruguay: a cohort study

Fri, 01 Jan 2021 00:00:00 GMT

Título: Dependency change with aging and associated factors in Uruguay: a cohort study Autor: Marroig, Alejandra; Machado, Maximiliano; Muniz-Terrera, Graciela Resumen: Objectives: To assess the heterogeneity of transitions toward dependency in older adults and to explore the robustness of results to different operationalizations of dependency. Method: Using data from people aged 60 years and older from a national representative study in Uruguay (Encuesta Longitudinal de Protección Social, N= 5071), we fitted multinomial regressions adjusted by sociodemographic and health characteristics to model transitions into dependency and death. We used a harder operationalization with basic activities of daily living (Katz-dependency) and Comprehensive-dependency with basic, instrumental, and advanced activities. Results: Increasing age (RRR = 1.08, CI = [1.05; 1.12], p< .001) and having comorbidities (RRR = 2.16,CI = [1.31; 3.57], p= .003) increased the risk of transition from nondependent to dependent using Katz-dependency. Women with at least two chronic conditions have increased risk of Comprehensive-dependency (RRR = 1.79, CI = [1.15; 2.80], p=.010). Discussion: Inconsistencies in findings emerged when evaluating transitions into dependency with the different measures, which may have social care implications. Descripción: Postprint (versión arbitrada por pares aceptada para publicar)

Cognitive dispersion is not associated with cerebrospinal fluid biomarkers of Alzheimer’s disease: results from the European Prevention of Alzheimer’s Dementia (EPAD) v500.0 Cohort

Wed, 01 Jan 2020 00:00:00 GMT

Título: Cognitive dispersion is not associated with cerebrospinal fluid biomarkers of Alzheimer’s disease: results from the European Prevention of Alzheimer’s Dementia (EPAD) v500.0 Cohort Autor: Watermeyer, Tam; Marroig, Alejandra; Ritchie, Craig W.; Ritchie, Karen; Blennow, Kaj; Muniz-Terrera, Graciela Resumen: Background: Cognitive dispersion, variation in performance across cognitive domains, is posited as a non-invasive and cost-effective marker of early neurodegeneration. Little work has explored associations between cognitive dispersion and Alzheimer’s disease (AD) biomarkers in healthy older adults. Even less is known about the influence or interaction of biomarkers reflecting brain pathophysiology or other risk factors on cognitive dispersion scores. Objective: The main aim of this study was to examine whether higher cognitive dispersion was associated with cerebrospinal fluid (CSF) levels of amyloid β (Aβ42), total tau (t-tau), phosphorylated tau (p-tau) and amyloid positivity in a cohort of older adults at various severities of AD. A secondary aim was to explore which AD risk factors were associated with cognitive dispersion scores. Method: Linear and logistic regression analyses explored the associations between dispersion and CSF levels of Aβ42, t-tau and p-tau and amyloid positivity (Aβ42<1000pg/ml). Relationships between sociodemographics, APOEɛ4 status, family history of dementia and levels of depression and dispersion were also assessed. Results: Dispersion did not emerge as associated with any of the analytes nor amyloid positivity. Older (𝛽=−0.007,𝑆𝐸=0.002, p=0.001) and less educated (𝛽=−0.009,𝑆𝐸=0.003, p =0.009) individuals showed greater dispersion. Conclusion: Dispersion was not associated with AD pathology, but was associated with age and years of education, highlighting individual differences in cognitive ageing. The use of this metric as a screening tool for existing AD pathology is not supported by our analyses. Follow-up work will determine if dispersion scores can predict changes in biomarker levels and/or positivity status longitudinally. Descripción: Postprint (versión revisada por pares y aceptada para su publicación).