Estimation of Gaussian parameters in the Neighborhood of No Data

Carlos C. Rodriguez
State University of New York at Albany.
Dept. of Mathematics


Let x be a vector of independent observations from a one dimensional gaussian distribution with unknown parameters. We consider the problem of estimating the mean and the standard deviation when the dimension of x is 0 (no-data), 1, and 2. In particular we show that for a single observation x the following is true: (0,8|x|) has classical probability of covering the true SD of at least 90% and if we know a priori that the mean is within 3 SDs of the origin then, (|x|/4, 8|x|) will be a 90% classical confidence interval for the SD. This is true regardless of the mean and without assuming any specific prior distribution on the parameters. A preliminary version of the paper can be found at (PostScript).
MaxEnt 94 Abstracts /