Variance estimation with diffuse prior information

✍ Scribed by Barry C. Arnold; Jose A. Villasenor

• Book ID: 104302488
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 276 KB
• Volume: 33
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00107-1

✦ Synopsis

This paper deals with the problem of estimating the variance based on a random sample from a normal distribution with mean /~ and variance a 2 = 1/z. In approaching the problem from a Bayesian point of view, a natural conjugate family of priors for (#, z) consists of z having a gamma distribution and the conditional distribution of/~ given z being normal with precision 6z for 6 > 0 and known. This problem is discussed in the situation where we have no, or choose not to elicit any, prior information about the parameters # and z. It is shown that under various schemes of diffuse prior information of r, the obtained Bayes estimates for tr 2 turn out to be inferior in a mean squared error sense to the known classical estimates. In particular, a uniform prior on a 2 = 1/z yields the worst estimate among the ones under consideration.