Search

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]

Well‐recommended methods of forming "confidence intervals" for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal confidence level. The methods are favoured because their intervals have a shorter average length than the Clopper–Pearson (gold‐standard) method, whose intervals really are confidence intervals. As the definition of a confidence interval is not being adhered to, another criterion for forming interval estimates for a binomial proportion is needed. In this paper, we suggest a new criterion for forming one‐sided intervals and equal‐tail two‐sided intervals. Methods which meet the criterion are said to yield locally correct confidence intervals. We propose a method that yields such intervals and prove that its intervals have a shorter average length than those of any other method that meets the criterion. Compared with the Clopper–Pearson method, the proposed method gives intervals with an appreciably smaller average length. For confidence levels of practical interest, the mid‐p method also satisfies the new criterion and has its own optimality property. It gives locally correct confidence intervals that are only slightly wider than those of the new method. [ABSTRACT FROM AUTHOR]

In this paper, we propose new asymptotic confidence intervals for extreme quantiles, that is, for quantiles located outside the range of the available data. We restrict ourselves to the situation where the underlying distribution is heavy‐tailed. While asymptotic confidence intervals are mostly constructed around a pivotal quantity, we consider here an alternative approach based on the distribution of order statistics sampled from a uniform distribution. The convergence of the coverage probability to the nominal one is established under a classical second‐order condition. The finite sample behavior is also examined and our methodology is applied to a real dataset. [ABSTRACT FROM AUTHOR]