Update README.md

Author: Mathias-Fuchs

README.md

@@ -7,7 +7,13 @@ The validity of the confidence interval is confirmed by a coverage probability s
 It works by implementing an unbiased estimator of the variance of the sample variance, and then setting up the standard studentized confidence interval using the square of that unbiased estimator. So far, the strategy is the same as the one used to obtain the confidence interval for the mean, as it is implemented in the t.test function in R, for instance.
 
 There exists a closed form for the variance of this estimator but it involves the square of the underlying distribution's variance. 
-The difficulty is to estimate that square.
+The difficulty is to estimate that square of the variance. There is a U-statistic estimator for it but a naive implementation would be of complexity O(n^4) where n is the sample size which is prohibitively costly. In this package, we solve the problem by reducing the computation to complexity O(n) using a dynamic programming.
+
+# Related work
+There are implementations of confidence intervals but they all suffer from a drawback, either
+* they assume normality of the underlying distribution, basically replacing the fourth moment with a known value.
+* or they use heuristics such as bootstrapping etc., which are only approximately valid.
+Here, we implemement a confidence interval that relies on the universally best (in the least-mean-squared sense) estimator of the variance of the sample variance, it being the U-statistic estimator. So, the validity of the approach is mathematically proven.
 
 # Reference
 The underlying U-statistics variance estimator is a special case of the one underlying this publication [http://dx.doi.org/10.1080/15598608.2016.1158675](http://dx.doi.org/10.1080/15598608.2016.1158675), freely available [https://epub.ub.uni-muenchen.de/27656/7/TR.pdf](here).
@@ -19,7 +25,7 @@ One can easily verify the validity of the confidence interval by choosing a popu
 N <- 1e4
 trueValueCovered <- rep(NA, N)
 for (i in 1:N) {
-    if (i \%\% 1e3 == 0) print(i)
+    if (i %% 1e2 == 0) print(i)
                                         # throw a dice 100 times
     x <- sample(6, 100, replace=TRUE)
                                         # compute our confidence interval