The k-nearest neighbors method in single index regression model for functional quasi-associated time series data

Analyzing the co-variability between the Hilbert regressor and the scalar output variable is crucial in functional statistics. In this contribution, the kernel smoothing of the Relative Error Regression (RE-regression) is used to resolve this problem. Precisely, we use the relative square error to establish an estimator of the Hilbertian regression. As asymptotic results, the Hilbertian observations are assumed to be quasi-associated, and we demonstrate the almost complete consistency of the constructed estimator. The feasibility of this Hilbertian model as a predictor in functional time series data is discussed. Moreover, we give some practical ideas for selecting the smoothing parameter based on the bootstrap procedure. Finally, an empirical investigation is performed to examine the behavior of the RE-regression estimation and its superiority in practice.

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“…. Using standard evidence (see Bouzebda et al [17]), we deduce that Theorem 2 is the outcome of Theorem 1 and the two lemmas below. Lemma 3.…”

Section: The Consistency Of the Kernel Estimatormentioning

confidence: 67%

“…In this appendix, we briefly give the proof of preliminary results; the proofs of Lemmas 3 and 4 are omitted, as they can be obtained straightforwardly through the adaptation of the proof of Bouzebda et al [17].…”

Section: Conflicts Of Interestmentioning

confidence: 99%

Scalar-on-Function Relative Error Regression for Weak Dependent Case

Elmezouar

Fatimah

Almanjahie

et al. 2023

Axioms

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“…Another direction for future exploration is the consideration of reducing the predictor's dimensionality by employing a Single Functional Index Model (SFIM) to estimate the regression, as discussed in Refs. [89,90]. SFIM has shown its effectiveness in improving the consistency of the regression operator estimator.…”

Section: Discussionmentioning

confidence: 99%

Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data

Bouzebda,

Souddi,

Madani

2024

Mathematics

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This work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper’s findings enlarge the previous advancements in functional data analysis through the use of empirical process methodologies. These results are shown under specific structural hypotheses regarding entropy and under appealing situations regarding the model. The regression operator’s asymptotic (1−α)-confidence interval is provided for 0<α<1 as an application. Additionally, we offer a classification example to demonstrate the practical importance of the methodology.

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“…In a future investigation, considering the limiting law of the conditional U-statistics regression estimators based on the delta sequence will be of interest. A natural extension of the present investigation is to consider the serial-dependent setting such as the mixing (see [61,62,122]) or the ergodic processes (see [56,123]). In a future investigation of the functional delta sequence local linear approach estimators, it will be natural to think about the possibility of obtaining an alternative estimator that benefits from the advantages of both methods, the local linear method and the delta sequence approach.…”

Section: Discussionmentioning

confidence: 99%

“…Under some mild conditions, a uniform and practically perfect convergence rate of the k-nearest neighbors estimator was established. In the work [59], the authors offer a variety of solutions for limiting laws for the conditional mode in the functional setting for ergodic data; for some current references, see the following: [45,[60][61][62][63][64][65].…”

Section: Introductionmentioning

confidence: 99%

Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences

2022

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U-statistics are a fundamental class of statistics derived from modeling quantities of interest characterized by responses from multiple subjects. U-statistics make generalizations the empirical mean of a random variable X to the sum of all k-tuples of X observations. This paper examines a setting for nonparametric statistical curve estimation based on an infinite-dimensional covariate, including Stute’s estimator as a special case. In this functional context, the class of “delta sequence estimators” is defined and discussed. The orthogonal series method and the histogram method are both included in this class. We achieve almost complete uniform convergence with the rates of these estimators under certain broad conditions. Moreover, in the same context, we show the uniform almost-complete convergence for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Among the potential applications are discrimination problems, metric learning and the time series prediction from the continuous set of past values.

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The k-nearest neighbors method in single index regression model for functional quasi-associated time series data

Cited by 18 publications

References 52 publications

Scalar-on-Function Relative Error Regression for Weak Dependent Case

Scalar-on-Function Relative Error Regression for Weak Dependent Case

Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data

Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences

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