Premium
Density estimation for circular data observed with errors
Author(s) -
Di Marzio Marco,
Fensore Stefania,
Panzera Agnese,
Taylor Charles C.
Publication year - 2022
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13431
Subject(s) - estimator , equivalence (formal languages) , kernel density estimation , kernel (algebra) , deconvolution , mathematics , series (stratigraphy) , simple (philosophy) , algorithm , euclidean geometry , computer science , statistics , geometry , discrete mathematics , epistemology , biology , paleontology , philosophy
Until now the problem of estimating circular densities when data are observed with errors has been mainly treated by Fourier series methods. We propose kernel‐based estimators exhibiting simple construction and easy implementation. Specifically, we consider three different approaches: the first one is based on the equivalence between kernel estimators using data corrupted with different levels of error. This proposal appears to be totally unexplored, despite its potential for application also in the Euclidean setting. The second approach relies on estimators whose weight functions are circular deconvolution kernels. Due to the periodicity of the involved densities, it requires ad hoc mathematical tools. Finally, the third one is based on the idea of correcting extra bias of kernel estimators which use contaminated data and is essentially an adaptation of the standard theory to the circular case. For all the proposed estimators, we derive asymptotic properties, provide some simulation results, and also discuss some possible generalizations and extensions. Real data case studies are also included.