kNN estimation in functional partial linear modeling

Ling, Nengxiang; Aneiros, Germán; Vieu, Philippe

doi:10.1007/s00362-017-0946-0

Cited by 26 publications

(14 citation statements)

References 35 publications

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“…KNN is a nonparametric prediction algorithm. It searches for k most similar eigenvectors in the historical database to predict the future value [20]. e model has simple structure and high computational efficiency.…”

Section: Vmdmentioning

confidence: 99%

Fault Diagnosis of Rolling Bearing Based on Improved VMD and KNN

Shen

Wang

et al. 2021

Mathematical Problems in Engineering

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Variational modal decomposition (VMD) has the end effect, which makes it difficult to efficiently obtain fault eigenvalues from rolling bearing fault signals. Inspired by the mirror extension, an improved VMD is proposed. This method combines VMD and mirror extension. The mirror extension is a basic algorithm to inhibit the end effect. A comparison is made with empirical mode decomposition (EMD) for fault diagnosis. Experiments show that the improved VMD outperforms EMD in extracting the fault eigenvalues. The performance of the new algorithm is proven to be effective in real-life mechanical fault diagnosis. Furthermore, in this article, combining with singular value decomposition (SVD), fault eigenvalues are extracted. In this way, fault classification is realized by K-nearest neighbor (KNN). Compared with EMD, the proposed approach has advantages in the recognition rate, which can accurately identify fault types.

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Section: Vmdmentioning

confidence: 99%

Fault Diagnosis of Rolling Bearing Based on Improved VMD and KNN

Shen

Wang

et al. 2021

Mathematical Problems in Engineering

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“… Estimation procedures: there are different methods and studies for estimation procedures of SFPLR model such as: fully automatic estimation procedure with the data-driven method and cross-validation for bandwidth selection of the smoothing parameter of nonparametric component [7], the asymptotic normality of linear part is studied [8], in a situations when the observation number of each subject is completely flexible and studying the convergence rate of the nonparametric part [9], the spline estimator of nonparametric part with studying their convergence rate [10], the two estimation procedure: 1-functional principal components regression (FPCR) and 2-functional ridge regression (FRR) based on the Tikhonov regularization [11][12][13], the new estimators for the parametric component called semiparametric least squares estimator (SLSE) [14], the nonparametric component approximated by a B-spline function [15], polynomial spline [16] and the slope function is estimated with the functional principal component basis [15,16], the k-nearest-neighbours (kNN) estimates with the local adaptive property that is better in the practice than kernel methods and some computations properties of this estimator [17][18][19], the Functional Semiparametric Additive Model via COmponent Selection and Smoothing Operator (FSAM-COSSO) in sparse setting [20], the sufficient dimension reduction methods such as sliced inverse regression (SIR) and sliced average variance estimation (SAVE) [21], the estimations are from the reproducing kernel Hilbert spaces (RKHS) [22], the frequentist and optimal model averaging [23], the latent group structure with K-means clustering [24], the joint asymptotic framework called joint Bahadur representation [25], the empirical likelihood estimation for non-functional high-dimension covariates [26], Sparse and penalized least-squares estimators [27] and the software for doing this analysis is available [28] .  Confidence Regions: Some papers have some sections for calculating confidence regions ,and we do not repeat them.…”

Section: Other Extensionsmentioning

confidence: 99%

A Literature Review of Semi-functional Partial Linear Regression Models

Fayaz¹

2021

Preprint

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Background: In the functional data analysis (FDA), the hybrid or mixed data are scalar and functional datasets. The semi-functional partial linear regression model (SFPLR) is one of the first semiparametric models for the scalar response with hybrid covariates. Various extensions of this model are explored and summarized. Methods: Two first research articles, including “semi-functional partial linear regression model”, and “Partial functional linear regression” have more than 300 citations in Google Scholar. Finally, only 106 articles remained according to the inclusion and exclusion criteria such as 1) including the published articles in the ISI journals and excluding 2) non-English and 3) preprints, slides, and conference papers. We use the PRISMA standard for systematic review. Results: The articles are categorized into the following main topics: estimation procedures, confidence regions, time series, and panel data, Bayesian, spatial, robust, testing, quantile regression, varying Coefficient Models, Variable Selection, Single-index model, Measurement error, Multiple Functions, Missing values, Rank Method and Others. There are different applications and datasets such as the Tecator dataset, air quality, electricity consumption, and Neuroimaging, among others. Conclusions: SFPLR is one of the most famous regression modeling methods for hybrid data that has a lot of extensions among other models.

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“…Remark 1 Condition C1-C9 are not the weakest possible conditions, but they are imposed to facilitate the proof of Theorem. Conditions C1-C6 are required in the context of semi-functional partial linear model (see Ling et al, 2017). They are also a direct extension of Aneiros-Pérez and Vieu (2006).…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

“…Aneiros-Pérez and Vieu (2008) extended the model to time series area. Ling et al (2017) proposed a k-nearest-neighbours (kNN) procedure and derived the asymptotic performances of kNN estimators. Aneiros et al (2015) extend the model to high-dimensional framework.…”

Section: Introductionmentioning

confidence: 99%

Semi-functional partial linear quantile regression

Ding

Zhang

et al. 2018

Statistics & Probability Letters

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Semi-functional partial linear model is a flexible model in which a scalar response is related to both functional covariate and scalar covariates. We propose a quantile estimation of this model as an alternative to the least square approach. We also extend the proposed method to kNN quantile method. Under some regular conditions, we establish the asymptotic normality of quantile estimators of regression coefficient. We also derive the rates of convergence of nonparametric function. Finite-sample performance of our estimation is compared with least square approach via a Monte Carlo simulation study. The simulation results indicate that our method is much more robust than the least square method. A real data example about spectrometric data is used to illustrate that our model and approach are promising.

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kNN estimation in functional partial linear modeling

Cited by 26 publications

References 35 publications

Fault Diagnosis of Rolling Bearing Based on Improved VMD and KNN

Fault Diagnosis of Rolling Bearing Based on Improved VMD and KNN

A Literature Review of Semi-functional Partial Linear Regression Models

Semi-functional partial linear quantile regression

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