Fixed Width Confidence Region for the Mean of a Multivariate Normal Distribution

✍ Scribed by Hisao Nagao; M.S. Srivastava

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 130 KB
• Volume: 81
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.2001.2006

✦ Synopsis

Srivastava gave an asymptotically efficient and consistent sequential procedure to obtain a fixed-width confidence region for the mean vector of any p-dimensional random vector with finite second moments. For normally distributed random vectors, Srivastava and Bhargava showed that the specified coverage probability is attained independent of the width, the mean vector, and the covariance matrix by taking a finite number of observations over and above T prescribed by the sequential rule. However, the problem of showing that E(T -n 0 ) is bounded, where n 0 is the sample size required if the covariance matrix were known, has not been available. In this paper, we not only show that it is bounded but obtain sharper estimates of E(T) on the lines of Woodroofe. We also give an asymptotic expansion of the coverage probability. Similar results have recently been obtained by Nagao under the assumption that the covariance matrix S=; k i=1 s i A i and ; k i=1 A i =I, where A i 's are known matrices. We obtain the results of this paper under the sole assumption that the largest latent root of S is simple.