An Improved Variable Kernel Density Estimator Based on L 2 Regularization

Yi Jin, Yulin He and Defa Huang
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Yi Jin: Department of Trace Inspection Technology, Criminal Investigation Police University of China, Shenyang 110854, China
Yulin He: Big Data Institute, College of Computer Science & Software Engineering, Shenzhen University, Shenzhen 518060, China
Defa Huang: Big Data Institute, College of Computer Science & Software Engineering, Shenzhen University, Shenzhen 518060, China

Mathematics, 2021, vol. 9, issue 16, 1-12

Abstract: The nature of the kernel density estimator (KDE) is to find the underlying probability density function ( p.d.f ) for a given dataset. The key to training the KDE is to determine the optimal bandwidth or Parzen window. All the data points share a fixed bandwidth (scalar for univariate KDE and vector for multivariate KDE) in the fixed KDE (FKDE). In this paper, we propose an improved variable KDE (IVKDE) which determines the optimal bandwidth for each data point in the given dataset based on the integrated squared error (ISE) criterion with the L 2 regularization term. An effective optimization algorithm is developed to solve the improved objective function. We compare the estimation performance of IVKDE with FKDE and VKDE based on ISE criterion without L 2 regularization on four univariate and four multivariate probability distributions. The experimental results show that IVKDE obtains lower estimation errors and thus demonstrate the effectiveness of IVKDE.

Keywords: probability density function; kernel density estimation; Parzen window; bandwidth; kernel function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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