Kernel Estimate
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2021 ◽  
Vol 37 (8) ◽  
pp. 1205-1218
Lu Li ◽  
Zhen Lei Zhang

2021 ◽  
Vol 11 (3) ◽  
pp. 217-227
Tomasz Gałkowski ◽  
Adam Krzyżak ◽  
Zofia Patora-Wysocka ◽  
Zbigniew Filutowicz ◽  
Lipo Wang

Abstract In the paper we develop an algorithm based on the Parzen kernel estimate for detection of sudden changes in 3-dimensional shapes which happen along the edge curves. Such problems commonly arise in various areas of computer vision, e.g., in edge detection, bioinformatics and processing of satellite imagery. In many engineering problems abrupt change detection may help in fault protection e.g. the jump detection in functions describing the static and dynamic properties of the objects in mechanical systems. We developed an algorithm for detecting abrupt changes which is nonparametric in nature and utilizes Parzen regression estimates of multivariate functions and their derivatives. In tests we apply this method, particularly but not exclusively, to the functions of two variables.

2018 ◽  
Vol 115 (40) ◽  
pp. 9956-9961 ◽  
Xianli Zeng ◽  
Yingcun Xia ◽  
Howell Tong

Quantifying the dependence between two random variables is a fundamental issue in data analysis, and thus many measures have been proposed. Recent studies have focused on the renowned mutual information (MI) [Reshef DN, et al. (2011)Science334:1518–1524]. However, “Unfortunately, reliably estimating mutual information from finite continuous data remains a significant and unresolved problem” [Kinney JB, Atwal GS (2014)Proc Natl Acad Sci USA111:3354–3359]. In this paper, we examine the kernel estimation of MI and show that the bandwidths involved should be equalized. We consider a jackknife version of the kernel estimate with equalized bandwidth and allow the bandwidth to vary over an interval. We estimate the MI by the largest value among these kernel estimates and establish the associated theoretical underpinnings.

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