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# sampling from conditonal distribution of missing random vector given a complete random vector

Tue 29 Nov, 2016 02:50 pm
suppose i have complete random variable vector $Y$ with size $n$
and this random vector $Y$ is partitioned into observed and missing vector
as follows $Y =[Y_{obsv}, Y_{mis}]$, where missing is foloowing a dropout pattern, $Y_{mis}$ is of size $s$ and $Y_{obsv}$ is of size $n-s$ and we are interested of the first dropout which its missing is rely on the previous obsereved value and the missing value itselef via a logit model for probabiltiy
of missing at occasion $i =1 :n$
$logit(p_{i}) = \phi_{1} +\phi_{2}Y_{i-1}+\phi_{3}Y_{i}$, Also missing is based on missing-mechanism $R_{i}$ which is equal one if value is missing and equal zero if value is observed. the missing mechanism is distributed as multi-nomial. Also The complete Vector $Y$ has the following relation $Y = X+Z$, WHERE $X$ and $z$ are independent random vector variables and $X$ is distributed as multivariate noraml and $z$ is distributed as multivariate t
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