A more general central limit theorem for m-dependent random variables with unbounded m

✍ Scribed by Joseph P. Romano; Michael Wolf

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 108 KB
• Volume: 47
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00146-7

✦ Synopsis

In this article, a general central limit theorem for a triangular array of m-dependent random variables is presented. Here, m may tend to inÿnity with the row index at a certain rate. Our theorem is a generalization of previous results. Some examples are given that show that the generalization is useful. In particular, we consider the limiting behavior of the sample mean of a combined sample of independent long-memory sequences, the limiting behavior of a spectral estimator, and the moving blocks bootstrap distribution. The examples make it clear the consideration of asymptotic behavior with the amount of dependence m increasing with n is useful even when the underlying processes are weakly dependent (or even independent), because certain natural statistics that arise in the analysis of time series have this structure. In addition, we provide an example to demonstrate the sharpness of our result.