On Convergence Rates of Mixtures of Polynomial Experts

In this letter, we consider a mixture-of-experts structure where
m
experts are mixed, with each expert being related to a polynomial regression model of order
k
. We study the convergence rate of the maximum likelihood estimator in terms of how fast the Hellinger distance of the estimated density converges to the true density, when the sample size
n
increases. The convergence rate is found to be dependent on both
m
and
k
, while certain choices of
m
and
k
are found to produce near-optimal convergence rates.