Show that the kernel estimator (15.9) is the same as the Bayes estimator (15.3) for the Dirichlet prior with { i = n/(1 )N}.

Show that the kernel estimator (15.9) is the same as the Bayes estimator (15.3) for the Dirichlet prior with {β_i = αn/(1 – α)N}. Using this result, suggest a way of letting the data determine the value of α in the kernel estimator.