On the robustification of the kernel estimator of the functional modal regression

2021 ◽  
pp. 109256
Author(s):  
Azzi Amel ◽  
Laksaci Ali ◽  
Ould Saïd Elias
Keyword(s):  
Kernel Estimator ◽  
Modal Regression

Resistive Grid Kernel Estimator (RGKE)

1992 ◽  
Author(s):  
Wendy Poston ◽  
George Rogers ◽  
Carey Priebe ◽  
Jeffrey Solka
Keyword(s):  
Kernel Estimator

scholarly journals An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions

Stats ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 1-17
Author(s):  
Samuele Tosatto ◽  
Riad Akrour ◽  
Jan Peters
Keyword(s):  
Upper Bound ◽  
Prediction Error ◽  
Kernel Estimator ◽  
Asymptotic Bias ◽  
Surgical Robots ◽  
Related Literature ◽  
Asymptotic Nature ◽  
Potential Applications ◽  
Self Driving Cars ◽  
Automated Decision Making

The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in several related literature. However, given its asymptotic nature, it gives no access to a hard bound. The increasing popularity of predictive tools for automated decision-making surges the need for hard (non-probabilistic) guarantees. To alleviate this issue, we propose an upper bound of the bias which holds for finite bandwidths using Lipschitz assumptions and mitigating some of the prerequisites of Rosenblatt’s analysis. Our bound has potential applications in fields like surgical robots or self-driving cars, where some hard guarantees on the prediction-error are needed.

scholarly journals On the Convergence Rate for a Kernel Estimate of the Regression Function

2016 ◽  
Vol 5 (2) ◽  
pp. 29
Author(s):  
Mounir ARFI
Keyword(s):  
Convergence Rate ◽  
Uniform Convergence ◽  
Kernel Estimator ◽  
Regression Function ◽  
Kernel Estimate ◽  
Compact Sets

We give the rate of the uniform convergence for the kernel estimate of the regression function over a sequence of compact sets which increases to $\mathbb{R}^{d}$ when $n$ approaches the infinity and when the observed process is $\varphi$-mixing. The used estimator for the regression function is the kernel estimator proposed by Nadaraya, Watson (1964).

scholarly journals Predicting frequency distribution and influence of sociodemographic and behavioral risk factors of Schistosoma mansoni infection and analysis of co-infection with intestinal parasites

2015 ◽  
Vol 10 (1) ◽  
Author(s):  
Carla V.V. Rollemberg ◽  
Marília M.B.L. Silva ◽  
Karla C. Rollemberg ◽  
Fábio R. Amorim ◽  
Nayanna M.N. Lessa ◽  
...  
Keyword(s):  
Schistosoma Mansoni ◽  
Low Income ◽  
Intestinal Parasites ◽  
Kernel Estimation ◽  
Kernel Estimator ◽  
Integrated Approach ◽  
Parasitic Infections ◽  
Behavioral Risk ◽  
Water Contact ◽  
Untreated Water

Geospatial analysis was used to study the epidemiology of <em>Schistosoma mansoni</em>, intestinal parasites and co-infections in an area (Ilha das Flores) in Sergipe, Brazil. We collected individually georeferenced sociodemographic, behavioral and parasitological data from 500 subjects, analyzed them by conventional statistics, and produced risk maps by Kernel estimation. The prevalence rates found were: <em>S. mansoni</em> (24.0%), <em>Trichuris trichiura</em> (54.8%), <em>Ascaris lumbricoides</em> (49.2%), Hookworm (17.6%) and <em>Entamoeba histolytica</em> (7.0%). Only 59/500 (11.8%) individuals did not present any of these infections, whereas 279/500 (55.8%) were simultaneously infected by three or more parasites. We observed associations between <em>S. mansoni</em> infection and various variables such as male gender, being rice farmer or fisherman, low educational level, low income, water contact and drinking untreated water. The Kernel estimator indicated that high-risk areas coincide with the poorest regions of the villages as well as with the part of the villages without an adequate sewage system. We also noted associations between both <em>A. lumbricoides</em> and hookworm infections with low education and low income. <em>A. lumbricoides</em> infection and <em>T. trichiura</em> infection were both associated with drinking untreated water and residential open-air sewage. These findings call for an integrated approach to effectively control multiple parasitic infections.

scholarly journals Spatial distribution of schistosomiasis and geohelminthiasis cases in the rural areas of Pernambuco, Brazil

2012 ◽  
Vol 45 (5) ◽  
pp. 633-638 ◽  
Author(s):  
Verônica Santos Barbosa ◽  
Karina Conceição Araújo ◽  
Onicio Batista Leal Neto ◽  
Constança Simões Barbosa
Keyword(s):  
Spatial Distribution ◽  
Rural Areas ◽  
Public Health Problem ◽  
Secondary Data ◽  
Kernel Estimator ◽  
Distribution Patterns ◽  
Number Of Children ◽  
Density Maps ◽  
Significant Public Health Problem ◽  
Significant Public Health

INTRODUCTION: The prevalence and intensity of geohelminth infections and schistosomiasis remain high in the rural areas of Zona da Mata, Pernambuco (ZMP), Brazil, where these parasites still represent a significant public health problem. The present study aimed to spatially assess the occurrences of schistosomiasis and geohelminthiasis in the ZMP. METHODS: The ZMP has a population of 1,132,544 inhabitants, formed by 43 municipalities. An ecological study was conducted, using secondary data relating to positive human cases and parasite loads of schistosomiasis and positive human cases of geohelminthiasis that were worked up in Excel 2007. We used the coordinates of the municipal headquarters to represent the cities which served as the unit of analysis of this study. The Kernel estimator was used to spatially analyze the data and identify distribution patterns and case densities, with analysis done in ArcGIS software. RESULTS: Spatial analysis from the Kernel intensity estimator made it possible to construct density maps showing that the northern ZMP was the region with the greatest number of children infected with parasites and the populations most intensely infected by Schistosoma mansoni. In relation to geohelminths, there was higher spatial distribution of cases of Ascaris lumbricoides and Trichuris trichiura in the southern ZMP, and greater occurrence of hookworms in the northern/central ZMP. CONCLUSIONS: Despite several surveys and studies showing occurrences of schistosomiasis and geohelminthiasis in the ZMP, no preventive measures that are known to have been effective in decreasing these health hazards have yet been implemented in the endemic area.

scholarly journals Estimating a Distribution Function at the Boundary

2020 ◽  
Vol 49 (1) ◽  
pp. 1-23
Author(s):  
Shunpu Zhang ◽  
Zhong Li ◽  
Zhiying Zhang
Keyword(s):  
Distribution Function ◽  
Kernel Estimation ◽  
Kernel Estimator ◽  
Distribution Functions ◽  
Practical Application ◽  
Real World Applications ◽  
Distribution Kernel ◽  
Estimation Of Distribution ◽  
Simulation Results ◽  
Boundary Correction

Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

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