Parametric estimation for planar random flights observed at discrete times
Alessandro De Gregorio, Università di Milano, Italy
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ABSTRACT:
We deal with a planar random flight
{(X (t), Y (t)), 0 < t ? T }
observed at n + 1 equidistant times ti = i?n , i = 0, 1, ..., n. The
aim of this paper is to estimate the unknown value of the parameter
?, the underlying rate of the Poisson process. The planar random
flights are not markovian, then we use an alternative argument to
derive a pseudo-maximum likelihood estimator ˆ? of the parameter ?.
We consider two different types of asymptotic schemes and show the
consistency, the asymptotic normality and efficiency of the estimator
proposed. A Monte Carlo analysis for small sample size n permits us
to analyze the empirical performance of ˆ?.
A different approach permits us to introduce an alternative estima-
tor of ? which is consistent, asymptotically normal and asymptotically
efficient without the request of other assumptions.
SUGGESTED CITATION:
Alessandro De Gregorio,
"Parametric estimation for planar random flights observed at discrete times"
(March 2007).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 22.
http://services.bepress.com/unimi/statistics/art22
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