اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDepth-based reconstruction method for incomplete functional data
91
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its eigendecomposition, a task that may be difficult. In particular, the accuracy of the estimation might be affected by the complexity of the covariance function and the poor availability of complete functional data. We introduce a non-parametric alternative based on a novel concept of depth for partially observed functional data. Our simulations point out that the available methods are unbeatable when the covariance function is stationary, and there is a large proportion of complete data. However, our approach was superior when considering non-stationary covariance functions or when the proportion of complete functions is scarce. Moreover, even in the most severe case of having all the functions incomplete, our method performs well meanwhile the competitors are unable. The methodology is illustrated with two real data sets: the Spanish daily temperatures observed in different weather stations and the age-specific mortality by prefectures in Japan.
قيم البحث
اقرأ أيضاً
A data depth measures the centrality of a point with respect to an empirical distribution. Postulates are formulated, which a depth for functional data should satisfy, and a general approach is proposed to construct multivariate data depths in Banach
spaces. The new approach, mentioned as Phi-depth, is based on depth infima over a proper set Phi of R^d-valued linear functions. Several desirable properties are established for the Phi-depth and a generalized version of it. The general notions include many new depths as special cases. In particular a location-slope depth and a principal component depth are introduced.
Smart metering infrastructures collect data almost continuously in the form of fine-grained long time series. These massive time series often have common daily patterns that are repeated between similar days or seasons and shared between grouped mete
rs. Within this context, we propose a method to highlight individuals with abnormal daily dependency patterns, which we term evolution outliers. To this end, we approach the problem from the standpoint of Functional Data Analysis (FDA), by treating each daily record as a function or curve. We then focus on the morphological aspects of the observed curves, such as daily magnitude, daily shape, derivatives, and inter-day evolution. The proposed method for evolution outliers relies on the concept of functional depth, which has been a cornerstone in the literature of FDA to build shape and magnitude outlier detection methods. In conjunction with our evolution outlier proposal, these methods provide an outlier detection toolbox for smart meter data that covers a wide palette of functional outliers classes. We illustrate the outlier identification ability of this toolbox using actual smart metering data corresponding to photovoltaic energy generation and circuit voltage records.
One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from multivariate
data analysis: the data depth plot (DD-plot). This DD-plot is a generalization of theunivariate Q-Q plot (quantile-quantile plot). We propose some statistics based onthese DD-plots, and we use bootstrapping techniques to estimate their distributions.We estimate the finite-sample size and power of our test via simulation, obtainingbetter results than other homogeneity test proposed in the literature. Finally, weillustrate the procedure in samples of real heterogeneous data and get consistent results.
We develop a novel exploratory tool for non-Euclidean object data based on data depth, extending the celebrated Tukeys depth for Euclidean data. The proposed metric halfspace depth, applicable to data objects in a general metric space, assigns to dat
a points depth values that characterize the centrality of these points with respect to the distribution and provides an interpretable center-outward ranking. Desirable theoretical properties that generalize standard depth properties postulated for Euclidean data are established for the metric halfspace depth. The depth median, defined as the deepest point, is shown to have high robustness as a location descriptor both in theory and in simulation. We propose an efficient algorithm to approximate the metric halfspace depth and illustrate its ability to adapt to the intrinsic data geometry. The metric halfspace depth was applied to an Alzheimers disease study, revealing group differences in the brain connectivity, modeled as covariance matrices, for subjects in different stages of dementia. Based on phylogenetic trees of 7 pathogenic parasites, our proposed metric halfspace depth was also used to construct a meaningful consensus estimate of the evolutionary history and to identify potential outlier trees.
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data, which has rec
eived the most attention in the literature, in this paper we will review how Bayesian networks can model dynamic data and data with incomplete observations. Such data are the norm at the forefront of research and in practical applications, and Bayesian networks are uniquely positioned to model them due to their explainability and interpretability.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
