Bayesian dynamic modeling of latent trait distributions by Dunson D.B.

By Dunson D.B.

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Define W = i=1 Xi , n W (i) = W − Xi , λ = i=1 pi and Z to be a Poisson random variable with mean λ. Let fh be the solution (which is unique except at 0) of the Stein equation λf (w + 1) − wf (w) = h(w) − Eh(Z) where h is a bounded real-valued function defined on Z+ = {0, 1, 2, . }. 1) i=1 where f (w) = f (w + 1) − f (w). A result of Barbour and Eagleson (1983) states that fh ∞ ≤ 2(1 ∧ λ−1 ) h ∞ . 2) i=1 where dT V denotes the total variation distance. It is known that the absolute constant 1 is best possible and the factor (1 ∧ λ−1 ) has the correct order for both small and large values of λ.

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