Estimating a bivariate density when there are extra data on one or both components

Hall, Peter; Neumeyer, Natalie

Estimating a bivariate density when there are extra data on one or both components

dc.contributor.author	Hall, Peter
dc.contributor.author	Neumeyer, Natalie
dc.date.accessioned	2005-10-12T06:58:23Z
dc.date.available	2005-10-12T06:58:23Z
dc.date.issued	2005-10-12T06:58:23Z
dc.description.abstract	Assume we have a dataset, Z say, from the joint distribution of random variables X and Y , and two further, independent datasets, X and Y, from the marginal distributions of X and Y , respectively. We wish to combine X, Y and Z, so as to construct an estimator of the joint density. This problem is readily solved in some parametric circumstances. For example, if the joint distribution were normal then we would combine data from X and Z to estimate the mean and variance of X; proceed analogously to estimate the mean and variance of Y ; but use data from Z alone to estimate E(XY ). However, the problem is more difficult in a nonparametric setting. There we suggest a copula-based solution, which has potential benefits even when the marginal datasets X and Y are empty. For example, if the copula density is sufficiently smooth in the region where we wish to estimate it, then the effective dimension of the structure that links the marginal distributions is relatively low, and the joint density of X and Y can be estimated with a high degree of accuracy. Similar improvements in performance are available if the marginals are close to being independent. We suggest using wavelet estimators to approximate the copula density, which in cases of statistical interest can be unbounded along boundaries. Our techniques are also useful for solving recently-considered related problems, for example where the marginal distributions are determined by parametric models. Therefore the methodology has application beyond the context which motivated it. The methodology is also readily extended to more general multivariate settings.	de
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dc.format.mimetype	application/pdf
dc.format.mimetype	application/postscript
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dc.identifier.uri	http://hdl.handle.net/2003/21650
dc.identifier.uri	http://dx.doi.org/10.17877/DE290R-14557
dc.language.iso	en
dc.subject	Copula	en
dc.subject	Dimension reduction	en
dc.subject	Independence	en
dc.subject	Kernel method	en
dc.subject	Prediction	en
dc.subject	Threshold	en
dc.subject	Wavelet	de
dc.subject.ddc	004
dc.title	Estimating a bivariate density when there are extra data on one or both components	en
dc.title.alternative	Estimating a bivariate distribution	en
dc.type	Text
dc.type.publicationtype	report	en
dcterms.accessRights	open access