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Naâmane Laïb,Djamal Louani 한국통계학회 2016 Journal of the Korean Statistical Society Vol.45 No.1
The aim of this paper is to establish the uniform consistency with rate over a bandwidth interval of the kernel conditional mode estimate whenever functional stationary ergodic data are considered. This kind of result is immediately applicable to proving uniform consistency of kernel-type estimators when the bandwidth h is a function of the data or the location x. Notice that our uniform in bandwidth results are the first ones to be established in this setting. Moreover, the ergodic setting offers a more general framework in regards to the practice than the usual mixing structure.
Vector-on-function quantile regression for stationary ergodic processes
Mohamed Chaouch,Naâmane Laïb 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.2
This paper deals with quantile regression of a vector response (Y ∈ Rq, q ≥ 2) on a functional covariate X that takes values in an infinite dimensional space. The main purpose is to introduce a kernel-type estimator of the conditional geometric quantiles whenever functional strictly stationary ergodic data are considered. We established the strong consistency with rate of the proposed estimator as well as the asymptotic distribution that leads to build a confidence region for the multivariate quantile regression. We gave also an application to joint horizon time series forecasting.