2012/09/08 by Kinjal Basu, Basu, Kinjal, Debapriya Sengupta +1
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Bilinear interpolation #Classification of discontinuities #Combinatorics #Computation (stat.CO) #Computer science #Control Systems and Identification #Density estimation #Discontinuity (linguistics) #Engineering #FOS: Computer and information sciences #Image and Signal Denoising Methods #Kernel (algebra) #Kernel density estimation #Kernel method #Mathematical analysis #Mathematics #Methodology (stat.ME) #Parametric statistics #Probability density function #Smoothing #Smoothing spline #Spline (mechanical) #Spline interpolation #Statistical Methods and Inference #Statistics #Support vector machine #Variable kernel density estimation #stat.CO #stat.ME
paper · pdf · doi:10.48550/arxiv.1209.1740
published in arXiv (Cornell University) (Cornell University) · 34 pages, 8 figures
arxiv created 2012/09/08 · openalex publication_date 2012/09/08 · arxiv updated 2016/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the problem when X1,X2,..., Xn are distributed on a circle following an unknown distribution F on S1. In this article we have consider the absolute general set-up where the density can have local features such as discontinuities and edges. Furthermore, there can be outlying data which can follow some discrete distributions. The traditional Kernel Density Estimation methods fail to identify such local features in the data. Here we device a non-parametric density estimate on S1, by the use of a novel technique which we term as Fourier Spline. We have also tried to identify and incorporate local features such as support, discontinuity or edges in the final density estimate. Several new results are proved in this regard. Simulation studies have also been performed to see how our methodology works. Finally a real life example is also shown.