For censored data.(adsbygoogle = window.adsbygoogle || []).push({});

Random sample X1,...,Xn

Censored such that x1,...xm are observed but xm+1,...,xn are not - we just know they exceed T.

fx = exponential = theata exp(-theta.x)

L = ∏ (from 1 going to m) f(x;theta) ∏ (m+1 - n) 1 - F(T;theta)

Using F = int f I get

L = ∏∅exp(-∅x) ∏ exp(-∅T)

I can now work out the MLE but I want to use EM method.

Reading online I get that this censor (or right censor) would give E(X|X≥T) = T + 1/∅ and I get it but dont really know how to show it. Im not sure how to write the complete data likelihood or log-likelihood for this EM (im more used to mixed distributions or id just solve MLE).

I just dont really know how to set up the E step or M step. It should be quite trivial given what I know already but I just keep confusing myself with the whole

Q(∅,∅i) = E[l(∅;x1,...,xn)|∅i;x1,...,xm).

i have some intial data and then iterating using the M step should also be trivial, im just falling down at the one of the first hurdles.

Thanks in advance.

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# EM Method for censored data - Statistical Inference

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