Journal of the
Korean Mathematical Society JKMS

In this paper we derive the central limit theorem for $\sum_{i=1}^n a_{ni}\xi_i$, where $\{a_{ni}, 1\leq i \leq n \}$ is a triangular array of nonnegative numbers such that $\sup_n \sum_{i=1}^n a_{ni}^2<\infty,~~\max_{1\leq i \leq n} a_{ni}\rightarrow 0~~\text{as}~~n \rightarrow \infty$ and $\xi_i^{'}s$ are a linearly positive quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process of the form $X_n=\sum_{j=-\infty}^\infty a_{k+j}\xi_j$.

Keywords: central limit theorem, linear process, linearly positive quadrant dependent, uniformly integrable, triangular array