Large sample behavior of the Bernstein copula estimator

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• 作者：Paul Janssen^a ; ^{paul.janssen@uhasselt.be} ; Jan Swanepoel^b ; ^{jan.swanepoel@nwu.ac.za} ; Noë ; l Veraverbeke^a ; ^{noel.veraverbeke@uhasselt.be}
• 关键词：Asymptotic properties ; Bernstein estimator ; Copula estimator ; Mean squared error
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2012
• 出版时间：May 2012
• 年：2012
• 卷：142
• 期：5
• 页码：1189-1197
• 全文大小：172 K

文摘

Bernstein polynomial estimators have been used as smooth estimators for density functions and distribution functions. The idea of using them for copula estimation has been given in . In the present paper we study the asymptotic properties of this estimator: almost sure consistency rates and asymptotic normality. We also obtain explicit expressions for the asymptotic bias and asymptotic variance and show the improvement of the asymptotic mean squared error compared to that of the classical empirical copula estimator. A small simulation study illustrates this superior behavior in small samples.