Speckman, P, Lee, J. and Sun, D. (1999). Existence of the MLE and the propriety of posteriors for a general multinomial choice model. Discussion Paper 99-19, ISDS, Duke University.  Home/Search   Document Details and Download   Summary   Related Articles

....the partial likelihood as the profile likelihood. See Anderson et al. 1993) for detail. 3.2 The Prior We recommend subjective proper prior for fi, when prior information is available for fi. The constant prior for fi can be used, but one needs to be careful about the propriety of the posterior. Speckman, Lee and Sun (1999) considered a general multinomial regression model 9 and gave a necessary and sufficient condition for the propriety of the posterior when the prior of regression coefficients is constant. Their conditions can be applied to the Bayesian bootstrap with the PFBB likelihood with slight modification ....

....20 PFBB posterior distribution of p n(fi Gamma fi) to the distribution of X. Applying theorem 2 of Sethuraman (1961) completes the proof. Theorem 3 and 5 still hold with the constant prior on fi. The argument of the proof for this case is essentially the same as the proof of theorem 8 in Speckman, Lee and Sun (1999). For the proofs of theorem 3 and 4, we start with a theorem in Tsiatis (1981) Theorem 6 (Tsiatis) fi fi 0 with probability one. Lemma 1 Suppose g(z; fi) is a continuous function in z and fi and has a first derivative g 0 (z; fi) g(z; fi) fi. Assume that there exists a neighborhood O ....

Speckman, P, Lee, J. and Sun, D. (1999). Existence of the MLE and the propriety of posteriors for a general multinomial choice model. Discussion Paper 99-19, ISDS, Duke University.

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