AISM 53, 370-379

© 2001 ISM

## Statistical inference in a linear model for spatially located sensors and
random input

### Stanislaw Gnot^{1}, Ewaryst Rafajlowicz^{2} and Agnieszka Urbanska-Motyka^{1}

^{1}Pedagogical University, Institute of Mathematics,
pl. Slowianski 9, 65-069 Zielona Góra, Poland

^{2}Wroclaw University of Technology, Institute of
Engineering Cybernetics, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland

(Received June 8, 1998; revised October 18, 1999)

Abstract.
In the paper we consider a random linear model for
observations provided by spatially located sensors measuring signals
coming from one source. For this model a set of sufficient and
complete statistics are found, and it is shown that the maximum
likelihood estimators of unknown parameters (characteristics of the
source) are functions of those statistics. The problem of nonnegative
estimators of variance components of the model is shortly discussed.
Comparisons of the mean squared errors of several estimators are
given. Numerical example concerning hunting for defects in solar cells
is considered in details.

Key words and phrases:
Inverse problem, random linear model, sufficient statistics, variance components,
ML estimators.

**Source**
( TeX , DVI )