The simplex CLT

Topic: Categorical data and the Dirichlet distribution · more questions on this topic
‹ Small concentrations Dirichlet updating ›

Starting from \operatorname{Cov}(X_j,X_k)=-np_jp_k for j\neq k and \operatorname{Var}(X_k)=np_k(1-p_k), derive the covariance matrix of \sqrt n(\widehat{\boldsymbol{p}}-{\boldsymbol{p}}). Show that multiplication by the all-ones vector gives zero.

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