###
ON ASYMPTOTIC NORMALITY OF PSEUDO LIKELIHOOD

ESTIMATES FOR PAIRWISE INTERACTION PROCESSES

###
JENS LEDET JENSEN^{1} AND
HANS R. KÜNSCH^{2}

^{1} *Department of Theoretical Statistics, Institute of Mathematics,*

University of Aarhus, DK-8000 Aarhus C, Denmark

^{2} *Seminar für Statistik, ETH, CH-8092 Zürich, Switzerland*
(Received February 22, 1993; revised August 26, 1993)

**Abstract.**
We consider point processes defined
through a pairwise interaction potential and admitting a
two-dimensional sufficient statistic. It is shown that the
pseudo maximum likelihood estimate can be stochastically
normed so that the limiting distribution is a standard
normal distribution. This result is true irrespectively of
the possible existence of phase transitions. The work here
is an extension of the work Guyon and Künsch (1992,
*Lecture Notes in Statist.*, **74**, Springer,
New York) and is based on viewing a point process
interchangeably as a lattice field.

*Key words and phrases*:
Asymptotic normality,
Gibbs processes, lattice field, phase transitions, pseudo
likelihood, stochastically normed.

**Source**
( TeX ,
DVI ,
PS )