Title: On a representation of fractional Brownian motion and the limit distributions of statistics arising in cusp statistical models,
Abstract: We discuss some extensions of results from the recent paper by Chernoyarov et
al. (Ann. Inst. Stat. Math., October 2016) concerning limit distributions of
Bayesian and maximum likelihood estimators in the model "signal plus white
noise" with irregular cusp-type signals. Using a new representation of
fractional Brownian motion (fBm) in terms of cusp functions we show that as the
noise intensity tends to zero, the limit distributions are expressed in terms
of fBm for the full range of asymmetric cusp-type signals correspondingly with
the Hurst parameter H, 0<H<1. Simulation results for the densities and
variances of the limit distributions of Bayesian and maximum likelihood
estimators are also provided.