scholarly journals Non-Parametric Sequential Estimation of a Regression Function Based on Dependent Observations

2013 ◽  
Vol 32 (3) ◽  
pp. 243-266 ◽  
Author(s):  
Dimitris N. Politis ◽  
Vyacheslav A. Vasiliev
Author(s):  
Dafydd Evans ◽  
Antonia J Jones

The aim of non-parametric regression is to model the behaviour of a response vector Y in terms of an explanatory vector X , based only on a finite set of empirical observations. This is usually performed under the additive hypothesis Y = f ( X )+ R , where f ( X )= ( Y | X ) is the true regression function and R is the true residual variable. Subject to a Lipschitz condition on f , we propose new estimators for the moments (scalar response) and covariance (vector response) of the residual distribution, derive their asymptotic properties and discuss their application in practical data analysis.


Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3784 ◽  
Author(s):  
Wenrui Gao ◽  
Weidong Wang ◽  
Hongbiao Zhu ◽  
Guofu Huang ◽  
Dongmei Wu ◽  
...  

This paper addresses a detection problem where sparse measurements are utilized to estimate the source parameters in a mixed multi-modal radiation field. As the limitation of dimensional scalability and the unimodal characteristic, most existing algorithms fail to detect the multi-point sources gathered in narrow regions, especially with no prior knowledge about intensity and source number. The proposed Peak Suppressed Particle Filter (PSPF) method utilizes a hybrid scheme of multi-layer particle filter, mean-shift clustering technique and peak suppression correction to solve the major challenges faced by current existing algorithms. Firstly, the algorithm realizes sequential estimation of multi-point sources in a cross-mixed radiation field by using particle filtering and suppressing intensity peak value, while existing algorithms could just identify single point or spatially separated point sources. Secondly, the number of radioactive sources could be determined in a non-parametric manner as the fact that invalid particle swarms would disperse automatically. In contrast, existing algorithms either require prior information or rely on expensive statistic estimation and comparison. Additionally, to improve the prediction stability and convergent performance, distance correction module and configuration maintenance machine are developed to sustain the multimodal prediction stability. Finally, simulations and physical experiments are carried out in aspects such as different noise level, non-parametric property, processing time and large-scale estimation, to validate the effectiveness and robustness of the PSPF algorithm.


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