In this thesis we consider the following. We choose the random variable θ, which has some fixed but unknown distribution with a finite second moment. We observe the value x, of a preliminary random variable X, which has an unknown distribution which is conditional on θ. Using x and our past experience we are asked to estimate the value of θ with a squared error loss function. After we have made our decision we are given the value, y, of a detailed random variable Y, which has an unknown distribution conditional on θ. The random variable X and Y are assumed independent given a particular θ. Our past experience is made up of the values of preliminary and detailed random variables from previous decision problems which are independent of but similar to the present one.
With the risk defined in the usual way the Bayes decision function is the expected value of θ given that X = x. Since the distributions are unknown, the use of the two sample nonparametric empirical Bayes decision function is proposed. With the regret defined in the usual way it can be shown that the two sample nonparametric empirical Bayes decision function is asymptotically optimal, i.e. for a large number of past decision problems, the regret in using the two nonparametric empirical Bayes decision function tends to zero, and it is the main purpose of this thesis to verify this property by using a hypothetical numerical example. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/74613 |
| Date | January 1965 |
| Creators | Wang, Alan Then-Kang |
| Contributors | Statistics |
| Publisher | Virginia Polytechnic Institute |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Thesis, Text |
| Format | 36 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 20623106 |
Page generated in 0.0017 seconds