Results of the simulations with normal distributions.

For simulation setting (3), shown are the RSSEs of the estimated joint probabilities to the true values (A) as a function of sample sizes with a fixed number of categories, and (B) as a function of various numbers of categories with a fixed sample size. For simulation setting (4), shown are the estimation RSSEs (C) as a function of sample sizes and (D) as a function of numbers of categorical values. The RSSEs of the proposed method are shown in solid lines, and those of conventional combination-wise estimation are shown in dashed lines. The average RSSEs from 100 repeated simulations are shown with dots and the standard deviation is shown with error bars.