Inthis paper, we study the precise large deviations of sums of two-dimensional random vectors with two dependent and real-valued components. In the presence of heavy tails, we obtain some uniformly asymptotic results for the bivariate case, which can provide novel insights into dependence structure between two marginal components.

We consider the transfer learning problem in the linear regression model, where the source domain and target domain have different features and the model exhibits heteroscedasticity. The existing homogeneous transfer learning methods cannot yet handle this type of problem. In this work, a transfer learning algorithm is proposed, which integrates data of varying dimensions and accounts for heteroscedasticity, thereby yielding a data-pooling estimator. The algorithm is simple to implement and easy to operate. The theoretical properties of the proposed estimator are established, including an upper bound on the generalization error and robustness against negative transfer. Simulation studies indicate that the proposed method performs well in terms of parameter estimation. The effectiveness of the proposed method is also validated using real-life datasets in UCI public repository, demonstrating favorable performance compared to the existing methods.