Kernel regression with functional response

Ferraty, Frédéric; Laksaci, Ali; Tadj, Amel; Vieu, Philippe

doi:10.1214/11-ejs600

Cited by 69 publications

(36 citation statements)

References 11 publications

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“…In most of applications in functional regression the explanatory variable is a one dimensional curve (see for instance [20], [21], [12], [16]) and the response is scalar. The nonparametric methodology has been extended and used also to responses being also a one dimensional curve (see eg [11] or [10]), but in the situation depicted in this paper both the explanatory variables (which is a compact two dimensional set) and the response one (which is a bivariate density) are not simple one-dimensional curves. Fig.…”

Section: Discussionmentioning

confidence: 99%

“…The asymptotic properties of the estimated operatorR h,α can be derived directly from the recent advances obtained in nonparametric regression when both explanatory and response variables are functional (see for instance [11] for asymptotic normality and [10] for uniform rates of convergence). These consistency results are not our purpose here since we wish rather to discuss how this method may allow us to select the probability content α.…”

Section: Theorem 1 Under the Conditions (A4)-(a12) One Hasmentioning

confidence: 99%

“…These consistency results are not our purpose here since we wish rather to discuss how this method may allow us to select the probability content α. The technical assumptions necessary for ensuring consistency properties of the estimated operatorR h,α are recalled below (see [10]). …”

Section: Theorem 1 Under the Conditions (A4)-(a12) One Hasmentioning

confidence: 99%

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Choosing the most relevant level sets for depicting a sample of densities

Delicado

Vieu

2017

Comput Stat

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When exploring a sample composed with a set of bivariate density functions, the question of the visualisation of the data has to front with the choice of the relevant level set(s). The approach proposed in this paper consists in defining the optimal level set(s) as being the one(s) allowing for the best reconstitution of the whole density. A fully data-driven procedure is developed in order to estimate the link between the level set(s) and their corresponding density, to construct optimal level set(s) and to choose automatically the number of relevant level set(s). The method is based on recent advances in functional data analysis when both response and predictors are functional. After a wide description of the methodology, finite sample studies are presented (including both real and simulated data) while theoretical studies are reported to a final appendix.

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Section: Discussionmentioning

confidence: 99%

Section: Theorem 1 Under the Conditions (A4)-(a12) One Hasmentioning

confidence: 99%

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Choosing the most relevant level sets for depicting a sample of densities

Delicado

Vieu

2017

Comput Stat

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“…A kernel regression estimator when both the response and the explanatory variables are functional was also recently considered [21]. Thinking of the explanatory variables being quantitative, such as, daily temperature, daily humidity, daily wind speed, etc., the resulting functional kernel regression approach could be used for STLF.…”

Section: A Existing Approachesmentioning

confidence: 99%

Short-Term Load Forecasting: The Similar Shape Functional Time-Series Predictor

Paparoditis

Sapatinas

2013

IEEE Trans. Power Syst.

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A novel functional time-series methodology for shortterm load forecasting is introduced. The prediction is performed by means of a weighted average of past daily load segments, the shape of which is similar to the expected shape of the load segment to be predicted. The past load segments are identified from the available history of the observed load segments by means of their closeness to a so-called reference load segment. The latter is selected in a manner that captures the expected qualitative and quantitative characteristics of the load segment to be predicted. As an illustration, the suggested functional time-series forecasting methodology is applied to historical daily load data in Cyprus. Its performance is compared with some recently proposed alternative methodologies for short-term load forecasting.

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“…Extend to nonparametric functional regression model with functional responses (see for example, Ferraty et al, 2011Ferraty et al, , 2012 As a sequel of the simulation study, we also investigate the MSE and MISE of five other error densities, as shown in Tables (.6) and (.7). The first four error densities are simulated from mixtures of Gaussian densities selected from Marron and Wand (1992), while the last one is simulated from a non-Gaussian error density.…”

Section: Conclusion and Some Open Questionsmentioning

confidence: 99%

Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density

Shang

2013

Computational Statistics & Data Analysis

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Error density estimation in a nonparametric functional regression model with functional predictor and scalar response is considered. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance as a constant parameter. This proposed mixture error density has a form of a kernel density estimator of residuals, where the regression function is estimated by the functional Nadaraya-Watson estimator. A Bayesian bandwidth estimation procedure that can simultaneously estimate the bandwidths in the kernel-form error density and the functional Nadaraya-Watson estimator is proposed. A kernel likelihood and posterior for the bandwidth parameters are derived under the kernel-form error density. A series of simulation studies show that the proposed Bayesian estimation method performs on par with the functional cross validation for estimating the regression function, but it performs better than the likelihood cross validation for estimating the regression error density. The proposed Bayesian procedure is also applied to a nonparametric functional regression model, where the functional predictors are spectroscopy wavelengths and the scalar responses are fat/protein/moisture content, respectively.

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Kernel regression with functional response

Cited by 69 publications

References 11 publications

Choosing the most relevant level sets for depicting a sample of densities

Choosing the most relevant level sets for depicting a sample of densities

Short-Term Load Forecasting: The Similar Shape Functional Time-Series Predictor

Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density

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