The functional kNN estimator of the conditional expectile: Uniform consistency in number of neighbors

The main purpose of the present paper is to investigate the problem of the nonparametric estimation of the expectile regression in which the response variable is scalar while the covariate is a random function. More precisely, an estimator is constructed by using the k Nearest Neighbor procedures (kNN). The main contribution of this study is the establishment of the Uniform consistency in Number of Neighbors (UNN) of the constructed estimator. The usefulness of our result for the smoothing parameter automatic selection is discussed. Short simulation results show that the finite sample performance of the proposed estimator is satisfactory in moderate sample sizes. We finally examine the implementation of this model in practice with a real data in financial risk analysis.

Bootstrap With Cluster‐Dependence in Two or More Dimensions

We propose a bootstrap procedure for data that may exhibit cluster‐dependence in two or more dimensions. The asymptotic distribution of the sample mean or other statistics may be non‐Gaussian if observations are dependent but uncorrelated within clusters. We show that there exists no procedure for estimating the limiting distribution of the sample mean under two‐way clustering that achieves uniform consistency. However, we propose bootstrap procedures that achieve adaptivity with respect to different uniformity criteria. Important cases and extensions discussed in the paper include regression inference, U‐ and V‐statistics, subgraph counts for network data, and non‐exhaustive samples of matched data.