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Local linear approach: conditional density estimate for functional and censored data

Benkhaled Abdelkader, Madani Fethi

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

315--327

EN

Let Y be a random real response, which is subject to right censoring by another random variable C . In this paper, we study the nonparametric local linear estimation of the conditional density of a scalar response variable and when the covariable takes values in a semi-metric space. Our main aim is to prove under some regularity conditions both the pointwise and the uniform almost-sure consistencies with convergence rates of the conditional density estimator related by this estimation procedure.

2

Learning novelty detection outside a class of random curves with application to COVID-19 growth

Rafajłowicz Wojciech

Journal of Artificial Intelligence and Soft Computing Research

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2021

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Vol. 11, No. 3

195--215

EN

Let a class of proper curves is specified by positive examples only. We aim to propose a learning novelty detection algorithm that decides whether a new curve is outside this class or not. In opposite to the majority of the literature, two sources of a curve variability are present, namely, the one inherent to curves from the proper class and observations errors’. Therefore, firstly a decision function is trained on historical data, and then, descriptors of each curve to be classified are learned from noisy observations.When the intrinsic variability is Gaussian, a decision threshold can be established from T2 Hotelling distribution and tuned to more general cases. Expansion coefficients in a selected orthogonal series are taken as descriptors and an algorithm for their learning is proposed that follows nonparametric curve fitting approaches. Its fast version is derived for descriptors that are based on the cosine series. Additionally, the asymptotic normality of learned descriptors and the bound for the probability of their large deviations are proved. The influence of this bound on the decision threshold is also discussed.The proposed approach covers curves described as functional data projected onto a finite-dimensional subspace of a Hilbert space as well a shape sensitive description of curves, known as square-root velocity (SRV). It was tested both on synthetic data and on real-life observations of the COVID-19 growth curves.

3

Use of functional cluster analysis of CPTU data for assessment of a subsoil rigidity

Młynarek Z., Wierzbicki J., Wołyński W.

Studia Geotechnica et Mechanica

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2018

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Vol. 40, nr 2

117--124

EN

This paper shows an example of the grouping of piezocone penetration test (CPTU) characteristics using functional data analysis, together with the results of clustering, in the form of a subsoil rigidity model. The subsoil rigidity model was constructed based on layer separation using the proposed method, as well as the k-means method. In the construction of the subsoil rigidity model, the constrained modulus M was applied. These moduli were determined from empirical relationships for overconsolidated and normally consolidated soils from Poland based on cone tip resistance.