A Bayesian procedure for bandwidth selection in circular kernel density estimation

References

[1] E. Batschelet, Circular Statistics in Biology, Academic Press, London, 1981. Search in Google Scholar

[2] N. Belaid, S. Adjabi, N. Zougab and C. C. Kokonendji, Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions, J. Korean Statist. Soc. 45 (2016), no. 4, 557–567. 10.1016/j.jkss.2016.04.001Search in Google Scholar

[3] M. J. Brewer, A modelling approach for bandwidth selection in kernel density estimation, Proceedings of the 13th Symposium on computational Statistics—COMPSTAT, Physica, Heidelberg (1998), 203–208. 10.1007/978-3-662-01131-7_22Search in Google Scholar

[4] M. Di Marzio, A. Panzera and C. C. Taylor, Local polynomial regression for circular predictors, Statist. Probab. Lett. 79 (2009), no. 19, 2066–2075. 10.1016/j.spl.2009.06.014Search in Google Scholar

[5] M. Di Marzio, A. Panzera and C. C. Taylor, Kernel density estimation on the torus, J. Statist. Plann. Inference 141 (2011), no. 6, 2156–2173. 10.1016/j.jspi.2011.01.002Search in Google Scholar

[6] N. I. Fisher, Statistical Analysis of Circular Data, Cambridge University, Cambridge, 1993. 10.1017/CBO9780511564345Search in Google Scholar

[7] E. García-Portugués, Exact risk improvement of bandwidth selectors for kernel density estimation with directional data, Electron. J. Stat. 7 (2013), 1655–1685. 10.1214/13-EJS821Search in Google Scholar

[8] P. H. Garthwaite, Y. Fan and S. A. Sisson, Adaptive optimal scaling of Metropolis–Hastings algorithms using the Robbins–Monro process, Comm. Statist. Theory Methods 45 (2016), no. 17, 5098–5111. 10.1080/03610926.2014.936562Search in Google Scholar

[9] P. Hall, G. S. Watson and J. Cabrera, Kernel density estimation with spherical data, Biometrika 74 (1987), no. 4, 751–762. 10.1093/biomet/74.4.751Search in Google Scholar

[10] J. Klemelä, Estimation of densities and derivatives of densities with directional data, J. Multivariate Anal. 73 (2000), no. 1, 18–40. 10.1006/jmva.1999.1861Search in Google Scholar

[11] C. N. Kuruwita, K. B. Kulasekera and W. J. Padgett, Density estimation using asymmetric kernels and Bayes bandwidths with censored data, J. Statist. Plann. Inference 140 (2010), no. 7, 1765–1774. 10.1016/j.jspi.2010.01.001Search in Google Scholar

[12] S. Li, M. J. Silvapulle, P. Silvapulle and X. Zhang, Bayesian approaches to nonparametric estimation of densities on the unit interval, Econometric Rev. 34 (2015), no. 3, 394–412. 10.1080/07474938.2013.807130Search in Google Scholar

[13] M. Oliveira, R. M. Crujeiras and A. Rodríguez-Casal, A plug-in rule for bandwidth selection in circular density estimation, Comput. Statist. Data Anal. 56 (2012), no. 12, 3898–3908. 10.1016/j.csda.2012.05.021Search in Google Scholar

[14] M. Oliveira, R. M. Crujeiras and A. Rodríguez-Casal, Nonparametric circular methods for exploring environmental data, Environ. Ecol. Stat. 20 (2013), no. 1, 1–17. 10.1007/s10651-012-0203-6Search in Google Scholar

[15] M. Oliveira, R. M. Crujeiras, A. Rodríguez-Casal, NPCirc: An R Package for nonparametric circular methods, J. Statist. Softw. 61 (2014), 1–26. 10.18637/jss.v061.i09Search in Google Scholar

[16] M. Oliveira, R. M. Crujeiras, A. Rodríguez-Casal, NPCirc: Nonparametric Circular Methods. R package version 2.0.1, 2014, http://www.CRAN.R-project.org/package=NPCirc. 10.18637/jss.v061.i09Search in Google Scholar

[17] G. O. Roberts and J. S. Rosenthal, Examples of adaptive MCMC, J. Comput. Graph. Statist. 18 (2009), no. 2, 349–367. 10.1198/jcgs.2009.06134Search in Google Scholar

[18] T. Senga Kiessé, N. Zougab and C. C. Kokonendji, Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data, Comput. Statist. 31 (2016), no. 1, 189–206. 10.1007/s00180-015-0627-1Search in Google Scholar

[19] B. W. Silverman, Density Estimation for Statistics and Data Analysis, Monogr. Statist. Appl. Probab., Chapman & Hall, London, 1986. Search in Google Scholar

[20] C. C. Taylor, Bootstrap choice of the smoothing parameter in kernel density estimation, Biometrika 76 (1989), no. 4, 705–712. 10.1093/biomet/76.4.705Search in Google Scholar

[21] C. C. Taylor, Automatic bandwidth selection for circular density estimation, Comput. Statist. Data Anal. 52 (2008), no. 7, 3493–3500. 10.1016/j.csda.2007.11.003Search in Google Scholar

[22] C. C. Taylor, K. V. Mardia, M. Di Marzio and A. Panzera, Validating protein structure using kernel density estimates, J. Appl. Stat. 39 (2012), no. 11, 2379–2388. 10.1080/02664763.2012.710898Search in Google Scholar

[23] X. Zhang, M. L. King and R. J. Hyndman, A Bayesian approach to bandwidth selection for multivariate kernel density estimation, Comput. Statist. Data Anal. 50 (2006), no. 11, 3009–3031. 10.1016/j.csda.2005.06.019Search in Google Scholar

[24] X. Zhang, M. L. King and H. L. Shang, A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density, Comput. Statist. Data Anal. 78 (2014), 218–234. 10.1016/j.csda.2014.04.016Search in Google Scholar

[25] Y. Ziane, N. Zougab and S. Adjabi, Birnbaum–Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy tailed data, Comput. Statist. 33 (2018), no. 1, 299–318. 10.1007/s00180-017-0712-8Search in Google Scholar

[26] N. Zougab, S. Adjabi and C. C. Kokonendji, Comparison study to bandwidth selection in binomial kernel estimation using Bayesian approaches, J. Stat. Theory Pract. 10 (2016), no. 1, 133–153. 10.1080/15598608.2015.1098579Search in Google Scholar