3,761 research outputs found
Nonparametric methods for complex spatial domains: density estimation and hypothesis testing
Full text linkThe analysis of not only big, but increasingly complex data represents a thriving branch of statistics. Modern applications ranging from neuroscience, geo-sciences, astronomy and engineering pose stimulating challenges to classical statistics and require the development of novel methodologies. In this thesis we propose nonparametric approaches to density estimation and hypothesis testing over multidimensional domains with complex shapes. The synergy of ideas and techniques from applied mathematics, numerical analysis and statistics allows us to obtain flexible and efficient tools. The thesis is organized in three main threads. The first considers the problem of density estimation over multidimensional domains with complex shapes. Here we combine a nonparametric likelihood approach with a regularization involving partial differential operators. The second thread examines two sample hypothesis testing. Inspired by the first part, we take advantage of permutation procedures to develop high dimensional
multinomial tests for distributions defined over complex domain. The last thread moves toward a parallel direction, that is the study of hypothesis testing procedures for semiparametric spatial regression models. After a careful analysis of their theoretical properties, we propose a nonparametric randomization approach to test the linear
components of such models
Modal clustering of matrix-variate data
Full text linkThe nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation allows for a natural, yet not trivial, generalization of the approach to the matrix-valued setting, increasingly widespread, for example, in longitudinal and multivariate spatio-temporal studies. In this work we introduce nonparametric estimators of matrix-variate distributions based on kernel methods, and analyze their asymptotic properties. Additionally, we propose a generalization of the mean-shift procedure for the identification of the modes of the estimated density. Given the intrinsic high dimensionality of matrix-variate data, we discuss some locally adaptive solutions to handle the problem. We test the procedure via extensive simulations, also with respect to some competitors, and illustrate its performance through two high-dimensional real data applications
Nonparametric test for density modes
No full textA nonparametric resampling procedure is proposed to test the significance of a mode, with the aim of evaluating whether a region of relatively high observed density reflects the actual presence of a mode in the true distribution underlying a set of data. The method leverages on Morse theory and stochastic gradient methods to characterize the local properties of the modes. This allows the definition of an asymptotic test, based on the concept of gradient ascent paths and relying on resampling methods, to approximate the distribution of the test statistic under the null hypothesis
On testing the significance of a mode
No full textWe propose a nonparametric test for the significance of a mode, with the
aim of evaluating whether a region of relatively high observed density reflects the
actual presence of a mode in the true distribution underlying a set of data. The
method leverages on Morse theory to characterize the local properties of the modes
and the gradient. This allows the definition of an asymptotic test, based on the concept of gradient ascent paths and relying on resampling methods, to approximate
the distribution of the test statistic under the null hypothesis. The performances of
the proposed test statistic and the control of the Type-I error are shown via multiple
simulation studies
A spatial epidemic model with contact and mobility restrictions
No full textSeveral spatiotemporal epidemic models have described how contact and mobility restrictions have a dynamic effect on morbidity and mortality of fast transmitting pathogens in epidemics. Despite this, there have been rather limited contributions looking at policy optimization. This work combines a new spatiotemporal epidemic model of a heterogeneous mixed population located at different places with an optimal control approach to show the effects of contact and mobility restrictions under policy optimization. The objective of optimization not only includes epidemiological but also socio-economic implications of the restrictions. Several scenarios are numerically investigated, and the dependence of the optimal policy on some basic epidemiological parameters is analysed. The results illustrate the strong impact of spatial heterogeneity on optimal policy measures. An analysis of the stability of the disease-free equilibrium of the model is also presented
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