# Estimation of Gaussian parameters in the Neighborhood of No
Data

## Carlos C. Rodriguez

State University of New York at Albany.

Dept. of Mathematics

`carlos@math.albany.edu`

### Abstract

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
http://omega.albany.edu:8008/confint.ps
(PostScript).

MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk