Strong uniform consistency of a nonparametric estimator of a conditional quantile for censored dependent data and functional regressors

2011 ◽  
Vol 19 (2) ◽  
pp. 131-156 ◽  
Author(s):  
Walid Horrigue ◽  
Elias Ould Saïd
Keyword(s):  
Dependent Data ◽  
Nonparametric Estimator ◽  
Uniform Consistency ◽  
Conditional Quantile ◽  
Strong Uniform Consistency

scholarly journals Strong uniform consistency rates of conditional quantile estimation in the single functional index model under random censorship

2018 ◽  
Vol 6 (1) ◽  
pp. 197-227 ◽  
Author(s):  
Nadia Kadiri ◽  
Abbes Rabhi ◽  
Amina Angelika Bouchentouf
Keyword(s):  
Cumulative Distribution Function ◽  
Complete Convergence ◽  
Asymptotic Properties ◽  
Cumulative Distribution ◽  
Index Structure ◽  
Functional Index ◽  
Conditional Quantile ◽  
Index Model ◽  
Strong Uniform Consistency ◽  
Mixing Sequence

AbstractThe main objective of this paper is to non-parametrically estimate the quantiles of a conditional distribution in the censorship model when the sample is considered as an -mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we estimate the quantiles by inverting this estimated cond-cdf and state the asymptotic properties when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. This approach can be applied in time series analysis.

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