Say I have a lifetime variable with survival probability $S(t|\theta)$, and I estimate this probability by $$\hat{S}(t|\theta)=S(t|\hat{\theta})$$ How would we go about deriving the standard error of this estimate? Is there a general procedure to follow, or does it depend on the form of the hazard function of $T$?
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1$\begingroup$ It may help to clarify how you would like to estimate $S$: is this the Kaplan Meier estimator you are interested in? Cox-PH model with Kaplan Meier base distribution? Or a fully parametric model? $\endgroup$– Cliff ABJan 17, 2017 at 15:20
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$\begingroup$ I am working with a semiparametric additive model, specifically with hazard $\lambda(t|\alpha,\beta(t))=X^T\beta(t)+g(Y^T\alpha)$ $\endgroup$– user128836Jan 17, 2017 at 15:39
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