Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1149190 | Journal of Statistical Planning and Inference | 2010 | 10 Pages |
Abstract
In this paper we propose the use of Ïâdivergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt=b(Xt,α)dt+Ï(Xt,β),αâRp,βâRq,p,q>=1, from discrete observations {Xti,i=0,â¦,n} with ti=iÎn, i=0,1,â¦,n, under the asymptotic scheme Înâ0, nÎnââ and nÎn2â0. The class of Ïâdivergences is wide and includes several special members like Kullback-Leibler, Rényi, power and αâdivergences. We derive the asymptotic distribution of the test statistics based on the estimated Ïâdivergences. The asymptotic distribution depends on the regularity of the function Ï and in general it differs from the standard Ï2 distribution as in the i.i.d. case. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Alessandro De Gregorio, Stefano M. Iacus,