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turnbull: Update documentation to discuss Anderson–Björck algorithm

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@ -53,7 +53,7 @@
Alternatively, when \textit{--se-method oim-drop-zeros} is passed, columns/rows of $\nablasub{\hat{\symbf{F}}} \mathcal{L}$ corresponding with intervals where $\hat{s}_i = 0$ are dropped before the matrix is inverted, which enables greater numerical stability but whose theoretical justification is not well explored [3]. Alternatively, when \textit{--se-method oim-drop-zeros} is passed, columns/rows of $\nablasub{\hat{\symbf{F}}} \mathcal{L}$ corresponding with intervals where $\hat{s}_i = 0$ are dropped before the matrix is inverted, which enables greater numerical stability but whose theoretical justification is not well explored [3].
In the further alternative, when \textit{--se-method likelihood-ratio} is passed, confidence intervals for $\hat{\symbf{F}}$ are computed by inverting a likelihood ratio test at each point, as described by Goodall, Dunn \& Babiker~[3]. In the further alternative, when \textit{--se-method likelihood-ratio} is passed, confidence intervals for $\hat{\symbf{F}}$ are computed by inverting a likelihood ratio test at each point, as described by Goodall, Dunn \& Babiker~[3]. The confidence limits are computed using the Anderson–Björck root-finding algorithm [4], which is more efficient than the interval bisection method described by Goodall, Dunn \& Babiker.
{\vspace{0.5cm}\scshape\centering References\par} {\vspace{0.5cm}\scshape\centering References\par}
%{\pagebreak\scshape\centering References\par} %{\pagebreak\scshape\centering References\par}
@ -62,6 +62,7 @@
\item Turnbull BW. The empirical distribution function with arbitrarily grouped, censored and truncated data. \textit{Journal of the Royal Statistical Society, Series B (Methodological)}. 1976;38(3):290–5. \href{https://doi.org/10.1111/j.2517-6161.1976.tb01597.x}{doi: 10.1111\slash j.2517-6161.1976.tb01597.x} \item Turnbull BW. The empirical distribution function with arbitrarily grouped, censored and truncated data. \textit{Journal of the Royal Statistical Society, Series B (Methodological)}. 1976;38(3):290–5. \href{https://doi.org/10.1111/j.2517-6161.1976.tb01597.x}{doi: 10.1111\slash j.2517-6161.1976.tb01597.x}
\item Anderson-Bergman C. An efficient implementation of the EMICM algorithm for the interval censored NPMLE. \textit{Journal of Computational and Graphical Statistics}. 2017;26(2):463–7. \href{https://doi.org/10.1080/10618600.2016.1208616}{doi: 10.1080\slash 10618600.2016.1208616} \item Anderson-Bergman C. An efficient implementation of the EMICM algorithm for the interval censored NPMLE. \textit{Journal of Computational and Graphical Statistics}. 2017;26(2):463–7. \href{https://doi.org/10.1080/10618600.2016.1208616}{doi: 10.1080\slash 10618600.2016.1208616}
\item Goodall RL, Dunn DT, Babiker AG. Interval-censored survival time data: confidence intervals for the non-parametric survivor function. \textit{Statistics in Medicine}. 2004;23(7):1131–45. \href{https://doi.org/10.1002/sim.1682}{doi: 10.1002\slash sim.1682} \item Goodall RL, Dunn DT, Babiker AG. Interval-censored survival time data: confidence intervals for the non-parametric survivor function. \textit{Statistics in Medicine}. 2004;23(7):1131–45. \href{https://doi.org/10.1002/sim.1682}{doi: 10.1002\slash sim.1682}
\item Anderson N, Björck Å. A new high order method of regula falsi type for computing a root of an equation. \textit{BIT}. 1973;13(3):253–64. doi: \href{https://doi.org/10.1007/BF01951936}{doi: 10.1007\slash BF01951936}
\end{enumerate} \end{enumerate}
\end{document} \end{document}