Estimation of Dirichlet process priors with monotone missing data

摘要

This article investigates the estimation of Dirichlet process priors DP(α,α-bar) of a random (J+1)-dimensional distribution by monotone missing observations, where the precision parameter α is a positive scalar and α-bar a probability measure on R~(J+1) While α is estimated by maximising a particularly designed likelihood function, α-bar 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-bar, the L_1 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.