Nonparametric regression estimation for functional stationary ergodic data with missing at random

Ling, Nengxiang; Liang, Longlong; Vieu, Philippe

doi:10.1016/j.jspi.2015.02.001

Cited by 52 publications

(28 citation statements)

References 16 publications

(5 reference statements)

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“…They established the asymptotic properties of the regression operator estimator when the functional regressor is completely observed and a part of the responses are MAR. Taking into account the functional ergodic time series data, Ling, Liu, and Vieu (2015) proved the asymptotic normality of the estimator proposed by Ferraty et al (2013). We also cite Ling, Liu, and Vieu (2016) for the kernel estimation of the conditional mode for functional ergodic time series data with MAR responses and Ibrahim, Hassan, Demongeot, and Rachdi (2020) for surrogate data.…”

Section: Introductionmentioning

confidence: 84%

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: 84%

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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“…In this comparison, we consider model_1 and model_2 described above and the final sample sizes are 50, 100 and 200. We consider 100 replications of the Monte-Carlo procedure and compute the average mean square error defined in (22). The results are displayed in Figure 2.…”

Section: Comparison Of Recursive and Nonrecursive Estimatorsmentioning

confidence: 99%

“…Recently, Laïb and Louani [17,18] studied the conditional bias of the regression estimator (3) and established the almost sure uniform consistency rate as well as the asymptotic normality for stationary and ergodic processes. For further theoretical and practical motivations to consider ergodic data, reader is advised to see [12,17,[19][20][21][22], among others.…”

Section: Introductionmentioning

confidence: 99%

Real-time estimation for functional stochastic regression models

Aboubacar

Chaouch

2020

Journal of Statistical Computation and Simulation

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In this paper, a heteroscedastic functional regression model with martingale difference errors is considered. We are interested in realtime estimation of the regression as well as the conditional variance operators when the response is a real-valued random variable and the covariate belongs to an infinite-dimensional space. A Robbins-Monro-type estimator of the conditional variance is introduced when a sample is collected from an underlying stationary and ergodic process. First, a local uniform L q-consistency (for q ≥ 2) rate of the recursive estimator of the regression operator is established. Then, a pointwise mean-square consistency rate of the conditional variance is given when the regression function is supposed to be known and when it is estimated recursively. Simulation studies are conducted to assess the proposed estimator's performance, in terms of reducing the computational time without affecting significantly the accuracy, compared to its natural competitor. An application to real environmental data is also carried out to illustrate the real-time on day ahead prediction of the maximum ozone concentration in Mexico city as well as its volatility.

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“…Assumption (2.4), which represents a weak dependence condition using a physical dependence measure, may be viewed as a substitute for classical mixing conditions. Mixing conditions in function spaces have been successfully employed to study consistency and asymptotic normality in the presence of dependence in numerous settings, for example in nonparametric regression; see [37,17,33,35]. The relationship between classical mixing conditions and conditions along the lines of (2.4) in function spaces is discussed in [23].…”

Section: Asymptotic Normality Ofĉmentioning

confidence: 99%

On the asymptotic normality of kernel estimators of the long run covariance of functional time series

Berkes

Horváth

Rice

2016

Journal of Multivariate Analysis

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a b s t r a c tWe consider the asymptotic normality in L 2 of kernel estimators of the long run covariance of stationary functional time series. Our results are established assuming a weakly dependent Bernoulli shift structure for the underlying observations, which contains most stationary functional time series models, under mild conditions. As a corollary, we obtain joint asymptotics for functional principal components computed from empirical long run covariance operators, showing that they have the favorable property of being asymptotically independent.

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Nonparametric regression estimation for functional stationary ergodic data with missing at random

Cited by 52 publications

References 16 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

Real-time estimation for functional stochastic regression models

On the asymptotic normality of kernel estimators of the long run covariance of functional time series

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