Merge pull request #10 from durandg12/9-implement-requested-changes-by-reviewer-vh7p

Implement requested changes by reviewer vh7p

Author: durandg12

_quarto.yml

@@ -7,7 +7,8 @@ diagram:
       header-includes:
         - '\usetikzlibrary{arrows}'
 
-title: "Fast confidence bounds for the false discovery proportion over a path of hypotheses"
+title: "Fast confidence bounds for the false discovery proportion 
+  over a path of hypotheses"
 # subtitle: ""
 author:
   - name: Guillermo Durand
@@ -22,8 +23,20 @@ author:
 date: last-modified
 date-modified: last-modified
 abstract: >+
-  This paper presents a new algorithm (and an additional trick) that allows to compute fastly an entire curve of post hoc bounds for the False Discovery Proportion when the underlying bound $V^*_{\mathfrak{R}}$ construction is based on a reference family $\mathfrak{R}$ with a forest structure à la @MR4178188. By an entire curve, we mean the values $V^*_{\mathfrak{R}}(S_1),\dotsc,V^*_{\mathfrak{R}}(S_m)$ computed on a path of increasing selection sets $S_1\subsetneq\dotsb\subsetneq S_m$, $|S_t|=t$. The new algorithm leverages the fact that going from $S_t$ to $S_{t+1}$ is done by adding only one hypothesis.
-keywords: [multiple testing, algorithmic, post hoc inference, false discovery proportion, confidence bound]
+  This paper presents a new algorithm (and an additional trick) 
+  that allows to compute fastly 
+  an entire curve of post hoc bounds for the False Discovery Proportion when the 
+  underlying bound $V^*_{\mathfrak{R}}$ construction is based on a reference 
+  family $\mathfrak{R}$ with a forest structure à la @MR4178188. 
+  By an entire curve, we mean the values 
+  $V^*_{\mathfrak{R}}(S_1),\dotsc,V^*_{\mathfrak{R}}(S_m)$ computed on a path 
+  of increasing selection sets $S_1\subsetneq\dotsb\subsetneq S_m$, $|S_t|=t$. 
+  The new algorithm leverages the fact that going from $S_t$ to $S_{t+1}$ 
+  is done by adding only one hypothesis. Compared to a more naive approach,
+  the new algorithm has a complexity in $O(|\mathcal K|m)$ instead of
+  $O(|\mathcal K|m^2)$, where $|\mathcal K|$ is the cardinality of the family.
+keywords: [multiple testing, algorithmic, post hoc inference, 
+  false discovery proportion, confidence bound]
 citation:
   type: article-journal
   container-title: "Computo"