On asymptotic properties of functional conditional mode estimation with both stationary ergodic and responses MAR

Ling, Nengxiang; Liu, Yang; Vieu, Philippe

doi:10.1007/978-3-319-55846-2_23

Cited by 3 publications

(2 citation statements)

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“…In the analysis of functional data, more complex dependence models arise, involving conditional distributions in abstract spaces. We refer to the reader to the recent contribution by Chaouch, Laib and Louani (2017), on kernel conditional mode estimation, from functional station-ary ergodic data, in the context of random elements in semi-metric abstract spaces (see also Ling, Liu and Vieu, 2017). This paper considers the problem of linear functional multiple regression estimation, when the response takes values in an abstract separable Hilber space H, and the regressors are operators on H. The temporal dependence of the errors is represented, in terms of an ARH(1) time series model.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors

Ruiz-Medina

Miranda

Espejo

2018

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A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic normality and strong consistency is obtained, under suitable conditions. The correlation analysis is based on a componentwise estimator of the residual autocorrelation operator. When the dependence structure of the functional error term is unknown, a plug-in generalized least-squared regression parameter estimator is formulated. Its strong-consistency is proved as well. A simulation study is undertaken to illustrate the performance of the presented approach, under different regularity conditions. An application to financial panel data is also considered.Keywords ARH(1) errors · dynamical functional multiple regression · firm leverage maps · generalized least squared estimator · kernel regressors Mathematics Subject Classification (2010) MSC code1 60G25 · 60G60 and 62J05 · MSC code2 62J10

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%