Local Linear Estimation of the Conditional Cumulative Distribution Function: Censored Functional

Sankhya A ◽  
2022 ◽  
Author(s):  
Saâdia Rahmani ◽  
Oussama Bouanani
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Linear Estimation ◽  
Local Linear ◽  
Local Linear Estimation

scholarly journals kNN local linear estimation of the conditional cumulative distribution function: Dependent functional data case

2018 ◽  
Vol 356 (10) ◽  
pp. 1036-1039 ◽  
Author(s):  
Ibrahim M. Almanjahie ◽  
Zouaoui Chikr Elmezouar ◽  
Ali Laksaci ◽  
Mustapha Rachdi
Keyword(s):  
Distribution Function ◽  
Functional Data ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Linear Estimation ◽  
Local Linear ◽  
Local Linear Estimation

scholarly journals Smooth kNN Local Linear Estimation of the Conditional Distribution Function

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1102
Author(s):  
Ibrahim M. Almanjahie ◽  
Zouaoui Chikr Elmezouar ◽  
Ali Laksaci ◽  
Mustapha Rachdi
Keyword(s):  
Distribution Function ◽  
Conditional Distribution ◽  
Linear Estimation ◽  
Mixing Conditions ◽  
K Nearest Neighbors ◽  
Conditional Distribution Function ◽  
Times Series ◽  
Local Linear ◽  
Cumulative Function ◽  
Local Linear Estimation

Previous works were dedicated to the functional k-Nearest Neighbors (kNN) and the local linearity method estimations of a regression operator. In this paper, a sequence pair of (Xi,Yi)i=1,…,n of functional mixing observations are considered. We treat the local linear estimation of the cumulative function of Yi given functional input variable Xi. Precisely, we combine the kNN method with the local linear algorithm to construct a new and fast efficiency estimator of the conditional distribution function. The main purpose of this paper is to prove the strong convergence of the constructed estimator under mixing conditions. An application to the functional times series prediction is used to compare our proposed estimator with the existing competitive estimators, and show its efficiency and superiority.

scholarly journals Predicting temperature curve based on fast kNN local linear estimation of the conditional distribution function

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11719
Author(s):  
Ibrahim M. Almanjahie ◽  
Zoulikha Kaid ◽  
Ali Laksaci ◽  
Mustapha Rachdi
Keyword(s):  
Distribution Function ◽  
Conditional Distribution ◽  
Meteorological Data ◽  
Linear Estimation ◽  
K Nearest Neighbors ◽  
Conditional Distribution Function ◽  
Modal Interval ◽  
Local Linear ◽  
Local Linear Estimation ◽  
The Impact

Predicting the yearly curve of the temperature, based on meteorological data, is essential for understanding the impact of climate change on humans and the environment. The standard statistical models based on the big data discretization in the finite grid suffer from certain drawbacks such as dimensionality when the size of the data is large. We consider, in this paper, the predictive region problem in functional time series analysis. We study the prediction by the shortest conditional modal interval constructed by the local linear estimation of the cumulative function of $Y$ given functional input variable $X$. More precisely, we combine the $k$-Nearest Neighbors procedure to the local linear algorithm to construct two estimators of the conditional distribution function. The main purpose of this paper is to compare, by a simulation study, the efficiency of the two estimators concerning the level of dependence. The feasibility of these estimators in the functional times series prediction is examined at the end of this paper. More precisely, we compare the shortest conditional modal interval predictive regions of both estimators using real meteorological data.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Functional data: local linear estimation of the conditional density and its application

Statistics ◽  
2013 ◽  
Vol 47 (1) ◽  
pp. 26-44 ◽  
Author(s):  
Jacques Demongeot ◽  
Ali Laksaci ◽  
Fethi Madani ◽  
Mustapha Rachdi
Keyword(s):  
Functional Data ◽  
Conditional Density ◽  
Linear Estimation ◽  
Local Linear ◽  
Local Linear Estimation
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