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...dent about our parameter estimates. To correct for this bias, following Ezell, Land, and Cohen (2003), I construct and utilize a modified sandwich variance estimator. Sandwich estimators (Huber 1967; =-=White 1980-=-) are now very commonly utilized in econometrics and statistics when researchers are unsure about the complete specification of the distribution in a fully parametric model but are fairly sure that th...

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...ivial and will be discussed later. 12s{p0 j }, then an equivalent problem is to minimize the Kullback-Leibler directed divergence, or Cross Entropy, between the prior and the posterior probabilities (=-=Kullback 1959-=-; Good 1963). The Cross Entropy is defined as CE = � j p j log(p j/p0 j ) if p0 j are the priors. Furthermore, if the prior probabilities p0 j are assumed to be uniform, then the Cross Entropy formali...

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...overly confident about our parameter estimates. To correct for this bias, following Ezell, Land, and Cohen (2003), I construct and utilize a modified sandwich variance estimator. Sandwich estimators (=-=Huber 1967-=-; White 1980) are now very commonly utilized in econometrics and statistics when researchers are unsure about the complete specification of the distribution in a fully parametric model but are fairly ...

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...py formalism reduces to the Maximum Entropy formalism. Not surprisingly, both the CE and the H objectives are related and really special cases of the family of Cressie Read power divergence measures (=-=Cressie and Read 1984-=-). Notwithstanding the diverse types of constraints that theory may suggest (e.g., geometric moment, higher order moment, inequality constraints, etc.) and whether or not we believe their sample analo...

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...be discussed later. 12s{p0 j }, then an equivalent problem is to minimize the Kullback-Leibler directed divergence, or Cross Entropy, between the prior and the posterior probabilities (Kullback 1959; =-=Good 1963-=-). The Cross Entropy is defined as CE = � j p j log(p j/p0 j ) if p0 j are the priors. Furthermore, if the prior probabilities p0 j are assumed to be uniform, then the Cross Entropy formalism reduces ...

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...allows us to re-write these constraints as: � � � xkrnarn = zmdrmnsrmn ∀k ∈ K (2.9) rn rn xkrn m We now have, what is termed, an ill-posed inversion problem—more unknowns than equations linking them (=-=Levine, 1980-=-). In the non-parametric hazard model case, we solved this problem by assuming that srmn = srm ∀n and we only summed within each r and m pairs. In other words, we had exactly the same number of unknow...

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...a large literature in criminology that aims to model the trajectories of offending patterns over the life course of individuals using group based modeling techniques (Nagin 2005; Nagin and Land 1993; =-=Land and Nagin 1996-=-). Responding to concerns raised by Hagan and Palloni (1988), in particular, Land and Nagin (1996) demonstrated that group-based trajectory models are well suited to take into account the order of arr...

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...patterns over time. There exists a large literature in criminology that aims to model the trajectories of offending patterns over the life course of individuals using group based modeling techniques (=-=Nagin 2005-=-; Nagin and Land 1993; Land and Nagin 1996). Responding to concerns raised by Hagan and Palloni (1988), in particular, Land and Nagin (1996) demonstrated that group-based trajectory models are well su...