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["Piercesare" <PSECCHI@eco.unipv.it>]

                    UNIVERSITA' DI PAVIA
  DIPARTIMENTO DI ECONOMIA POLITICA E METODI QUANTITATIVI
  
  
                       Hans Kuensch
                  ETH Zentrum, Zurigo, CH
                  
            SPATIAL POINT PATTERNS AND INFERENCE
            
            Lunedi, 16 Dicembre 1996, h. 11.00
            


We will present both nonparametric and parametric approaches to
the analysis of stationary and isotropic point patterns. Nonparametric
methods are used for exploratory and diagnostic purposes. The most
popular tools are the empty space function (distribution of the
distance from a point in space to the nearest point of the pattern),
the nearest neighbor function (distribution of the distance from
a typical point in the pattern to the nearest other point in the
pattern) and the second moment function. The main problem in estimating
these functions are edge effects due to a finite sampling window.
This causes a censoring of certain distances, and the modern way for
dealing with these edge effects uses the Kaplan Meier estimator
which was developed for censored survival times. We will also 
discuss standard errors of these estimated functions by bootstrap
methods.

For parametric methods the two most frequently used model classes
are the Cox (or doubly stochastic) processes for clustered patterns
and the Gibbs processes for patterns with inhibition. For both
models the exact likelihood function is analytically intractable.
So one has to resort either to Monte Carlo approximations for
the maximum likelihood estimator (MLE) or to simpler estimators like
the Pseudo-MLE or the Takacs-Fiksel estimator. After introducing these
estimators we will finally discuss the problem of obtaining approximate
standard errors based on asymptotic theory.


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Piercesare Secchi
Universita' di Pavia                                         
Dipartimento di Economia Politica e Metodi Quantitativi    
Via San Felice 5                                          
I-27100 Pavia Italy