Complete convergence for weighted sums of i.i.d. random variables with applications in regression estimation and EV model

ABSTRACT

In this paper, we obtain complete convergence results for Stout type weighted sums of i.i.d. random variables. A strong law for weighted sums of i.i.d. random variables is also obtained. As the applications of the strong law, the strong consistency and rate of the nonparametric regression estimations and the rates of the strong consistency of LS estimators for the unknown parameters of the simple linear errors in variables (EV) model are given.

KEYWORDS:

• Complete convergence
• EV model
• regression
• strong law
• weighted sums

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60F15
• Secondary 62G05

Funding

The research of Chen is supported by the National Natural Science Foundation of China [grant number 11271161]. The research of Sung is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [grant number 2014R1A1A2058041].