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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. [ABSTRACT FROM AUTHOR]

Through exploiting information from the source data to improve the fit performance on the target data, transfer learning estimations for high‐dimensional linear regression models have drawn much attention recently, but few studies focus on statistical inference and robust learning in the presence of heavy‐tailed/asymmetric errors. Using adaptive Huber regression (AHR) to achieve the bias and robustness tradeoff, in this paper we propose a robust transfer learning algorithm with high‐dimensional covariates, then construct valid confidence intervals and hypothesis tests based on the debiased lasso approach. When the transferable sources are known, a two‐step ℓ1$$ {\ell}_1 $$‐penalized transfer AHR estimator is firstly proposed and the error bounds are established. To correct the biases caused by the lasso penalty, a unified debiasing framework based on the decorrelated score equations is considered to establish asymptotic normality of the debiased lasso transfer AHR estimator. Confidence intervals and hypothesis tests for each component can be constructed. When the transferable sources are unknown, a data‐driven source detection algorithm is proposed with theoretical guarantee. Numerical studies verify the performance of our proposed estimator and confidence intervals, and an application to Genotype‐Tissue Expression data is also presented. [ABSTRACT FROM AUTHOR]