A Perturbation Technique for Sample Moment Matching in Kernel Density Estimation

2005 ◽  
Vol 56 (1-4) ◽  
pp. 161-188
Author(s):  
Arnab Maity ◽  
Debapriya Sengupta
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Smoothing ◽  
Perturbation Technique ◽  
Kernel Density ◽  
Moment Matching ◽  
Data Perturbation ◽  
Density Estimates ◽  
Kernel Density Estimates ◽  
Sample Moment

Summary The fundamental idea of kernel smoothing technique can be recognized as one-parameter data perturbation with a smooth density. The usual kernel density estimates might not match arbitrary sample moments calculated from the unsmoothed data. A technique based on two-parameter data perturbation is developed for sample moment matching in kernel density estimation. It is shown that the moments calculated from the resulting tuned kernel density estimate can be made arbitrarily close to the raw sample moments. Moreover, the pointwise rate of MISE of the resulting density estimates remains optimal. Relevant simulation studies are carried out to demonstrate the usefulness and other features of this technique.

Kernel Density Techniques as a Tool for Estimating and Comparing Income Distributions: A Cross European–Country Study

2004 ◽  
Author(s):  
Christos Papatheodorou ◽  
Paraskevi Peristera ◽  
Anastasia Kostaki
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Density Estimates ◽  
Income Distributions ◽  
The United Kingdom ◽  
Kernel Density Estimates ◽  
Income Polarization ◽  
Country Study ◽  
The Impact

This paper compares and assesses the income inequality between five European countries in the mid 1990’s, employing the non-parametric technique of kernel density estimation. The countries used in this inequality exercise were Germany, Hungary, Luxembourg, Poland and the United Kingdom, and the analysis was based on comparative data and variables provided by the PACO project. Kernel density estimates were found particularly revealing for comparing the shape of income distributions between populations, and for mapping the impact that differences in income polarization and concentration in various subgroups have on the overall income distribution of a country.

scholarly journals Automated differentiation of Alzheimer’s condition using Kernel Density Estimation based texture analysis of single slice brain MR images

2021 ◽  
Vol 7 (2) ◽  
pp. 747-750
Author(s):  
Amrutha Veluppal ◽  
Deboleena Sadhukhan ◽  
Venugopal Gopinath ◽  
Ramakrishnan Swaminathan
Keyword(s):  
Texture Analysis ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Computer Assisted ◽  
Mr Images ◽  
Density Estimates ◽  
Single Slice ◽  
Brain Mr Images ◽  
Textural Changes

Abstract Computer-assisted tools can aid in the detection of Alzheimer disease (AD) which is a progressive neurodegenerative disorder that can lead to cognitive impairments and eventually death. The accumulated effects due to AD can cause changes in the appearance of grey matter, white matter and cerebrospinal fluid in brain Magnetic Resonance (MR) images. This study aims to use Kernel Density Estimation (KDE) technique to analyse the textural changes from single slice brain MR images for the detection of AD. The preprocessed, skull stripped T1-weighted MR brain images are obtained from the publicly available OASIS database. A single axial slice per subject is chosen from a volumetric image for further processing to reduce the computational load. Multivariate KDE technique is applied to each pixel, by considering the changes in the neighbourhood based on selected bandwidth to obtain corresponding density estimates. Statistical features quantifying the distribution of density estimates are extracted to characterise textural variations in images. Linear discriminant analysis (LDA) classifier is implemented with ten-fold cross-validation for detecting AD. An optimum bandwidth of 18 for the KDE technique is selected based on the classification performance. Out of seven extracted texture features, three are found to be statistically significant in distinguishing AD. The classification with LDA yields an accuracy of 72.3% with a sensitivity of 80.6% for identifying AD from healthy subjects. The proposed method is efficient in detecting AD by revealing the textural changes within the brain slice without the involvement of any segmentation technique. Thus, the novel KDE-based texture analysis proves to be an effective tool for the automated diagnosis of AD from single slice brain MR images.

scholarly journals Author Correction: An extended Weight Kernel Density Estimation model forecasts COVID-19 onset risk and identifies spatiotemporal variations of lockdown effects in China

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Wenzhong Shi ◽  
Chengzhuo Tong ◽  
Anshu Zhang ◽  
Bin Wang ◽  
Zhicheng Shi ◽  
...  
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Spatiotemporal Variations ◽  
Estimation Model

A Correction to this paper has been published: https://doi.org/10.1038/s42003-021-01924-6

scholarly journals Identifying the density of grassland fire points with kernel density estimation based on spatial distribution characteristics

2021 ◽  
Vol 13 (1) ◽  
pp. 796-806
Author(s):  
Zhen Shuo ◽  
Zhang Jingyu ◽  
Zhang Zhengxiang ◽  
Zhao Jianjun
Keyword(s):  
Spatial Distribution ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Function Method ◽  
Kernel Density ◽  
Fire Occurrence ◽  
Distribution Characteristics ◽  
Fire Point ◽  
Spatial Distribution Characteristics ◽  
Grassland Fire

Abstract Understanding the risk of grassland fire occurrence associated with historical fire point events is critical for implementing effective management of grasslands. This may require a model to convert the fire point records into continuous spatial distribution data. Kernel density estimation (KDE) can be used to represent the spatial distribution of grassland fire occurrences and decrease the influences historical records in point format with inaccurate positions. The bandwidth is the most important parameter because it dominates the amount of variation in the estimation of KDE. In this study, the spatial distribution characteristic of the points was considered to determine the bandwidth of KDE with the Ripley’s K function method. With high, medium, and low concentration scenes of grassland fire points, kernel density surfaces were produced by using the kernel function with four bandwidth parameter selection methods. For acquiring the best maps, the estimated density surfaces were compared by mean integrated squared error methods. The results show that Ripley’s K function method is the best bandwidth selection method for mapping and analyzing the risk of grassland fire occurrence with the dependent or inaccurate point variable, considering the spatial distribution characteristics.

scholarly journals Foraging range and habitat use by Cape Vulture Gyps coprotheres from the Msikaba colony, Eastern Cape province, South Africa

Koedoe ◽  
2015 ◽  
Vol 57 (1) ◽  
Author(s):  
Morgan B. Pfeiffer ◽  
Jan A. Venter ◽  
Colleen T. Downs
Keyword(s):  
South Africa ◽  
Protected Areas ◽  
Breeding Season ◽  
Movement Ecology ◽  
Kernel Density ◽  
Eastern Cape Province ◽  
Eastern Cape ◽  
Convex Polygons ◽  
Density Estimates ◽  
Kernel Density Estimates

Despite the extent of subsistence farmland in Africa, little is known about endangered species that persist within them. The Cape Vulture (Gyps coprotheres) is regionally endangered in southern Africa and at least 20% of the population breeds in the subsistence farmland area previously known as the Transkei in the Eastern Cape province of South Africa. To understand their movement ecology, adult Cape Vultures (n = 9) were captured and fitted with global positioning system/global system for mobile transmitters. Minimum convex polygons (MCPs),and 99% and 50% kernel density estimates (KDEs) were calculated for the breeding and non breeding seasons of the Cape Vulture. Land use maps were constructed for each 99% KDE and vulture locations were overlaid. During the non-breeding season, ranges were slightly larger(mean [± SE] MCP = 16 887 km2 ± 366 km2) than the breeding season (MCP = 14 707 km2 ± 2155 km2). Breeding and non-breeding season MCPs overlapped by a total of 92%. Kernel density estimates showed seasonal variability. During the breeding season, Cape Vultures used subsistence farmland, natural woodland and protected areas more than expected. In the non-breeding season, vultures used natural woodland and subsistence farmland more than expected, and protected areas less than expected. In both seasons, human-altered landscapes were used less, except for subsistence farmland.Conservation implications: These results highlight the importance of subsistence farm land to the survival of the Cape Vulture. Efforts should be made to minimise potential threats to vultures in the core areas outlined, through outreach programmes and mitigation measures.The conservation buffer of 40 km around Cape Vulture breeding colonies should be increased to 50 km.

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