Lp convergence of reciprocals of sample means with applications to sequential estimation in linear regression

✍ Scribed by N. Etemadi; T.N. Sriram; A.N. Vidyashankar

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 614 KB
• Volume: 65
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(97)00046-3

✦ Synopsis

Let {Z,,; n >~ 1} be a stationary sequence of non-negative random variables with finite first too-. ment. It is known that the sample average 2, converges to a random variable Z with probability one. In this paper we have two objectives: First, we obtain a necessary and sufficient condition for the Lp(p > 0) convergence of 2~ 1 to Z -1. Second, we use this result in the sequential point estimation of the slope parameter in a linear regression model under relative squared error loss. We establish first and second order properties of the stopping times and the sequential procedures involved here.