Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data
Penalized B-splines combined with the composite link model are used to estimate a bivariate density from a histogram with wide bins. The goals are multiple: they include the visualization of the dependence between the two variates, but also the estimation of derived quantities like Kendall's tau, conditional moments and quantiles. Two strategies are proposed: the first one is semiparametric with flexible margins modeled using B-splines and a parametric copula for the dependence structure; the second one is nonparametric and is based on Kronecker products of the marginal B-spline bases. Frequentist and Bayesian estimations are described. A large simulation study quantifies the performances of the two methods under different dependence structures and for varying strengths of dependence, sample sizes and amounts of grouping. It suggests that Schwarz's BIC is a good tool for classifying the competing models. The density estimates are used to evaluate conditional quantiles in two applications in social and in medical sciences.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Yang, Mingan & Hanson, Timothy & Christensen, Ronald, 2008. "Nonparametric Bayesian estimation of a bivariate density with interval censored data," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5202-5214, August.
- Hanson, Timothy E., 2006. "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1548-1565, December.
- Jullion, Astrid & Lambert, Philippe, 2007. "Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2542-2558, February.
- Guadalupe Gómez & M. Calle & Ramon Oller, 2004. "Frequentist and Bayesian approaches for interval-censored data," Statistical Papers, Springer, vol. 45(2), pages 139-173, April.
- Tommi Harkanen, 2000. "Caries on Permanent Teeth: A Non-parametric Bayesian Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 577-588.
- Koo, Ja-Yong & Kooperberg, Charles, 2000. "Logspline density estimation for binned data," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 133-147, January.
- Lambert, Philippe & Eilers, Paul H.C., 2009. "Bayesian density estimation from grouped continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1388-1399, February.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:429-445. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.