Economics at your fingertips  

Pseudo phi-divergence test statistics and multidimensional Ito processes

Alessandro De Gregorio and Stefano Iacus ()

No unimi-1083, UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano

Abstract: We consider parametric hypotheses testing for multidimensional It\^o processes, possibly with jumps, observed at discrete time. To this aim, we propose the whole class of pseudo $\phi$-divergence test statistics, which include as a special case the well-known likelihood ratio test but also many other test statistics as well as new ones. Although the final goal is to apply these test procedures to multidimensional It\^o processes, we formulate the problem in the very general setting of regular statistical experiments and then particularize the results to our model of interest. In this general framework we prove that, contrary to what happens to true $\phi$-divergence test statistics, the limiting distribution of the pseudo $\phi$-divergence test statistic is characterized by the function $\phi$ which defines the divergence itself. In the case of contiguous alternatives, it is also possible to study in detail the power function of the test. Although all tests in this class are asymptotically equivalent, we show by Monte Carlo analysis that, in small sample case, the performance of the test strictly depends on the choice of the function $\phi$. In particular, we see that even in the i.i.d. case, the power function of the generalized likelihood ratio test ($\phi=\log$) is strictly dominated by other pseudo $\phi$-divergences test statistics.

Keywords: diffusion processes with jumps; Ito processes; power of the test; parametric hypotheses testing; phi-divergences; generalized likelihood ratio test (search for similar items in EconPapers)
Date: 2009-05-21
Note: oai:cdlib1:unimi-1083
References: Add references at CitEc
Citations: Track citations by RSS feed

Downloads: (external link) (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Access Statistics for this paper

More papers in UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano Contact information at EDIRC.
Bibliographic data for series maintained by Christopher F. Baum ().

Page updated 2019-08-02
Handle: RePEc:bep:unimip:unimi-1083