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.