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Semiparametric density estimators using copulas. (English) Zbl 1066.62046
Summary: We establish semiparametric density estimators by employing the ideas of copulas and density weighting functions. Results on asymptotic normality and uniform strong consistency are derived. The formula for the asymptotic mean square error is used to get the optimal bandwidth. Moreover, applications to several families of copulas are discussed.

MSC:
62G07 Density estimation
62H12 Estimation in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
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