Estimation of Dirichlet process priors with monotone missing data
Lei Yang, Xianyi Wu · Journal of nonparametric statistics · 2013
This article investigates the estimation of Dirichlet process priors DP(α, α¯) of a random (J+1)-dimensional distribution by monotone missing observations, where the precision parameter α is a positive scalar and α¯ a probability measure on ℝJ+1. While α is estimated by maximising a particularly designed likelihood function, α¯ is estimated using kernel smoothing. The asymptotic properties show that the estimate of α is strongly consistent and asymptotically normally distributed. For the estimate of α¯, the L1 consistency and the optimal bandwidths under an asymptotic mean integrated squared error criterion are examined. Finally, the performance of these estimates are analysed by means of a small simulation.