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\underset{\theta\in\Theta}{\operatorname{max}}\sum_{i=1}^N\sum_{t=1}^T \log f_t(y_{it} \mid x_{it}; \theta) </math>
In this formulation, the joint conditional density of ''y<sub>i</sub>'' given ''x<sub>i</sub>'' is modeled as ''Π<sub>t</sub>'' ''f<sub>t</sub>'' (''y<sub>it</sub>'' | ''x<sub>it</sub>'' ; θ). We assume that ''f<sub>t</sub> (y<sub>it</sub> |x<sub>it</sub> ; θ)'' is correctly specified for each ''t'' = 1,
But, it is not assumed that the joint conditional density is correctly specified. Under some regularity conditions, partial MLE is consistent and asymptotically normal.
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==References==
{{Reflist}}
{{improve categories|date=April 2018}}
[[Category:Panel data]]
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