  We construct a quasi likelihood analysis for diffusions under the
high-frequency sampling over a finite time interval. For this, we prove a
polynomial type large deviation inequality for the quasi likelihood random
field. Then it becomes crucial to prove nondegeneracy of a key index chi_0. By
nature of the sampling setting, chi_0 is random. This makes it difficult to
apply a naive sufficient condition, and requires a new machinery. In order to
establish a quasi likelihood analysis, we need quantitative estimate of the
nondegeneracy of chi_0. The existence of a nondegenerate local section of a
certain tensor bundle associated with the statistical random field solves this
problem.
