Nonparametric estimation of a conditional density
详细信息 查看全文
- 作者：Ann-Kathrin Bott ; Michael Kohler
- 关键词：Conditional density estimation ; \(L_1\) ; error ; Consistency ; Rate of convergence
- 刊名：Annals of the Institute of Statistical Mathematics
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：69
- 期：1
- 页码：189-214
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance;
- 出版者：Springer Japan
- ISSN：1572-9052
- 卷排序：69
文摘
In this paper, we estimate a conditional density. In contrast to standard results in the literature in this context we assume that for each observed value of the covariate we observe a sample of the corresponding conditional distribution of size larger than one. A density estimate is defined taking into account the data from all the samples by computing a weighted average using weights depending on the covariates. The error of the density estimate is measured by the \(L_1\)-error. Results concerning consistency and rate of convergence of the estimate are presented, and the performance of the estimate for finite sample size is illustrated using simulated data. Furthermore, the estimate is applied to a problem in fatigue analysis.