A broad class of smooth empirical copulas that contains the empirical beta copula proposed by Segers, Sibuya and Tsukahara is studied. Conditions under which the corresponding sequential empirical copula processes converge weakly are provided. Specific members of this general class of smooth estimators that depend on a scalar parameter determining the amount of marginal smoothing and a functional parameter controlling the shape of the smoothing region are proposed. The empirical investigation of the influence of these parameters suggests to focus on a subclass of data-adaptive smooth nonparametric copulas. To allow the use of the proposed class of smooth estimators in inference procedures on an unknown copula, including in change-point analysis, natural smooth extensions of the sequential dependent multiplier bootstrap are asymptotically validated and their finite-sample performance is studied through Monte Carlo experiments.
翻译:研究的是Segers、Sibuya和Tsukahara提出的大量光滑的经验性阴极,其中包含Segers、Sibuya和Tsukahara提出的实验性阴极; 研究相应的相继试验性阴极过程在哪些条件下比较薄弱; 这一一般的光滑测算器类别的具体成员,这些成员依赖一个确定边际平滑量的标尺参数和一个控制平滑区域形状的功能性参数; 对这些参数的影响进行的经验性调查表明,这些参数的影响将集中于一个数据适应性平滑的非参数性对立的相阴极亚类; 允许在未知的阴极上使用拟议的平滑测算器计算程序类别,包括在变化点分析中,顺序依附的增殖靴的自然平稳扩展将不同时得到验证,并通过蒙特卡洛实验研究其有限的增殖性性性表现。