Density estimation and regression analysis on hyperspheres in the presence of measurement error
研究了数据在单位超球面上且受测量误差污染时的密度估计与回归分析，提出了新估计量并证明其渐近性质，提供了两种置信区间构建方法，附有模拟和实际数据分析。
Abstract This paper studies density estimation and regression analysis with data observed on a general unit hypersphere and contaminated by measurement errors. We establish novel density and regression estimators, and study their asymptotic properties such as the rates of convergence and asymptotic normality. We also provide two types of asymptotic confidence intervals for both density and regression functions. One type is based on the asymptotic normality of their estimators and the other type is based on the empirical likelihood technique. We present practical details on the implementation of our method as well as simulation studies and real data analysis.