Estimation of Dirichlet process priors with monotone missing data

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 ℝ^J+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.