FDA: theoretical and practical efficiency of the local linear estimation based on the <i>k</i>NN smoothing of the conditional distribution when there are missing data

Rachdi, Mustapha; Laksaci, Ali; Almanjahie, Ibrahim M.; Chikr-Elmezouar, Zouaoui

doi:10.1080/00949655.2020.1732378

Cited by 5 publications

(7 citation statements)

References 27 publications

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“…This LC estimation combined with kNN (LLE-kNN) is new in Nonparametric Functional data analysis (NFDA). As far as we know, expected Chikr-Elmezouar, Almanjahie, Laksaci, and Rachdi (2019) for the conditional density estimation or Rachdi, Laksaci, Almanjahie, and Chikr-Elmezouar (2020) for the cumulative distribution function estimation there are no results on the LLE-kNN in NFDA. The present contribution may be considered as the first study in this direction.…”

Section: Introductionmentioning

confidence: 94%

“…In particular, the proofs of Lemmas 5 and 6 and the Corollaries 1 and 2 are omitted. In fact, proofs for these results can be obtained by combining the ideas of Baillo and Grane (2009), Burba et al (2009), and Rachdi et al (2020). The main challenge is how to handle the unlimited variable Y and the variable .…”

Section: Appendixmentioning

confidence: 99%

“…Proof of Lemma 2. Using arguments similar to those of Rachdi et al (2020), the proof would be based on the behaviors of the following quantities, for all j ≥ 0…”

Section: Appendixmentioning

confidence: 99%

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k‐Nearest neighbors local linear regression for functional and missing data at random

Rachdi

Laksaci

Kaid

et al. 2020

Statistica Neerlandica

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We combine the k‐Nearest Neighbors (kNN) method to the local linear estimation (LLE) approach to construct a new estimator (LLE‐kNN) of the regression operator when the regressor is of functional type and the response variable is a scalar but observed with some missing at random (MAR) observations. The resulting estimator inherits many of the advantages of both approaches (kNN and LLE methods). This is confirmed by the established asymptotic results, in terms of the pointwise and uniform almost complete consistencies, and the precise convergence rates. In addition, a numerical study (i) on simulated data, then (ii) on a real dataset concerning the sugar quality using fluorescence data, were conducted. This practical study clearly shows the feasibility and the superiority of the LLE‐kNN estimator compared to competitive estimators.

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Section: Introductionmentioning

confidence: 94%

Section: Appendixmentioning

confidence: 99%

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k‐Nearest neighbors local linear regression for functional and missing data at random

Rachdi

Laksaci

Kaid

et al. 2020

Statistica Neerlandica

Self Cite

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“…To the best of the authors' knowledge, the number of existing papers on regression of MI 𝛼,𝑌 (𝑥) is relatively small, and the existing papers are mainly either simple line charts [33]- [35], kernel density estimation methods [36], [37], local linear regression methods [38], [39], or random forest methods [40], [41]. These existing methods are still insufficient to flexibly express the true smooth curves 𝑚 low 𝛼,𝑌 (𝑥) and 𝑚 up 𝛼,𝑌 (𝑥) especially when 𝑁 is not so large.…”

Section: Modal Intervalmentioning

confidence: 99%

Modal Interval Regression Based on Spline Quantile Regression

YAO

Kitahara

Kuroda

et al. 2023

IEICE Trans. Fundamentals

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The mean, median, and mode are usually calculated from univariate observations as the most basic representative values of a random variable. To measure the spread of the distribution, the standard deviation, interquartile range, and modal interval are also calculated. When we analyze continuous relations between a pair of random variables from bivariate observations, regression analysis is often used. By minimizing appropriate costs evaluating regression errors, we estimate the conditional mean, median, and mode. The conditional standard deviation can be estimated if the bivariate observations are obtained from a Gaussian process. Moreover, the conditional interquartile range can be calculated for various distributions by the quantile regression that estimates any conditional quantile (percentile). Meanwhile, the study of the modal interval regression is relatively new, and spline regression models, known as flexible models having the optimality on the smoothness for bivariate data, are not yet used. In this paper, we propose a modal interval regression method based on spline quantile regression. The proposed method consists of two steps. In the first step, we divide the bivariate observations into bins for one random variable, then detect the modal interval for the other random variable as the lower and upper quantiles in each bin. In the second step, we estimate the conditional modal interval by constructing both lower and upper quantile curves as spline functions. By using the spline quantile regression, the proposed method is widely applicable to various distributions and formulated as a convex optimization problem on the coefficient vectors of the lower and upper spline functions. Extensive experiments, including settings of the bin width, the smoothing parameter and weights in the cost function, show the effectiveness of the proposed modal interval regression in terms of accuracy and visual shape for synthetic data generated from various distributions. Experiments for real-world meteorological data also demonstrate a good performance of the proposed method.

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“…As countries around the world are experiencing economic stagnation following the COVID-19 outbreak, tourism, catering and accommodation industries have been hit particularly hard [1] . In the face of economic recession, governments often resort to large-scale fiscal policies and other measures to boost the economy, such as direct income subsidies to residents or consumption vouchers.…”

Section: Introductionmentioning

confidence: 99%

Consumption Subsidies, Residents' Welfare and Industrial Support: Based on the Comparison of Efficiency of Various Consumption Subsidies

2022

FSST

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This paper discusses the effects of cash subsidies, cash coupons and discount coupons on improving residents' welfare and supporting specific industries by constructing a theoretical model. The conclusion is that there is no difference between different subsidy methods when the amount of subsidy is small, and the efficiency of subsidy does not change with the amount of subsidy. On the contrary, cash subsidy is more conducive to improving residents' welfare, while consumption coupons are more conducive to supporting specific industries. Especially when the amount of subsidy is large, discount vouchers are better than cash vouchers in industrial support, while cash vouchers can improve residents' welfare more effectively than discount vouchers. This research contributes to the development of subsidy policies and seems to provide an explanation for the differences in consumption subsidy patterns and economic performance of governments around the world.

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FDA: theoretical and practical efficiency of the local linear estimation based on the kNN smoothing of the conditional distribution when there are missing data

Cited by 5 publications

References 27 publications

k‐Nearest neighbors local linear regression for functional and missing data at random

k‐Nearest neighbors local linear regression for functional and missing data at random

Modal Interval Regression Based on Spline Quantile Regression

Consumption Subsidies, Residents' Welfare and Industrial Support: Based on the Comparison of Efficiency of Various Consumption Subsidies

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