Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator

• 作者: Cheikh Tidiane Seck Diam Ba Gane Samb L?
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Copula Function Kernel Estimation Local Linear ESTIMATOR Uniform in BANDWIDTH Consistency Simultaneous CONFIDENCE BANDS
• 年，卷（期）: 2015,（12）
• 页码范围: 2077-2095
• 页数: 19页
• 分类号: O1

摘要

In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.