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Seminar on Probability and Statistics Wednesday December 17 2008 Tokyo 002 3:00-4:10 pm
Divergences Test Statistics for Discretely Observed Diffusion Processes
Stefano Maria Iacus Universita degli Studi di Milano Abstract In this paper we propose the use of $\phi$-divergences as test
statistics to verify simple hypotheses about a one-dimensional
parametric diffusion process dXt = b(Xt, theta)dt + sigma(Xt, theta)
dWt, from discrete observations at times ti = i*Dn, i=0, 1, ..., n,
under the asymptotic scheme Dn - 0, n*Dn - +oo and n*Dn^2 - 0. The
class of phi-divergences is wide and includes several special members
like Kullback-Leibler, Renyi, power and alpha-divergences. We derive
the asymptotic distribution of the test statistics based on phi-
divergences. The limiting law takes different forms depending on the
regularity of phi. These convergence differ from the classical results
for independent and identically
distributed random variables. Numerical analysis is used to show the
small sample properties of the test statistics in terms of estimated
level and power of the test.
joint work with A. De Gregorio |
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