In this paper we establish moderate deviations of regression function estimator on functional data. The pointwise moderate deviation principles of Nadaraya–Watson type estimator is considered by exponential equivalence. Depending on the Vapnik–Chervonenkis size of the class, the uniform...

We studied the sharp large deviations for the log-likelihood ratio of an α-Brownian bridge. The full expansion of the tail probability for the log-likelihood ratio was obtained by using a change of measure.

Applying the large deviations and moderate deviations for the log-likelihood ratio of the Jacobi model, we give negative regions in testing Jacobi model, and get the decay rates of the error probabilities.