After testing for biased treatment assignment in an observational study using an unaffected outcome, the sensitivity analysis is constrained to be compatible with that test.  The package uses the optimization software gurobi obtainable from <https://www.gurobi.com/>, together with its associated R package, also called gurobi; see: <https://www.gurobi.com/documentation/7.0/refman/installing_the_r_package.html>.  The method is a substantial computational and practical enhancement of a concept introduced in Rosenbaum (1992) Detecting bias with confidence in observational studies Biometrika, 79(2), 367-374  <doi:10.1093/biomet/79.2.367>.

Estimation of the most-left informative set of gross returns 
             (i.e., the informative set).
             The procedure to compute the informative set adjusts the method 
             proposed by 
             Mariani et al. (2022a) <doi:10.1007/s11205-020-02440-6> 
             and 
             Mariani et al. (2022b) <doi:10.1007/s10287-022-00422-2> 
             to gross returns of financial assets. 
             This is accomplished through an adaptive algorithm
             that identifies sub-groups of gross returns in 
             each iteration by approximating their distribution with a
             sequence of two-component log-normal mixtures. 
             These sub-groups emerge when a significant change
             in the distribution occurs below the median of the 
             financial returns, with their boundary termed as
             the “change point" of the mixture. 
             The process concludes when no further change points are detected.
             The outcome encompasses parameters of the leftmost mixture 
             distributions and change points of the
             analyzed financial time series.

Implements various measures of information theory based on several entropy estimators.

Estimates the probability of informed trading (PIN) initially introduced by Easley et. al. (1996) <doi:10.1111/j.1540-6261.1996.tb04074.x> . Contribution of the package is that it uses likelihood factorizations of Easley et. al. (2010) <doi:10.1017/S0022109010000074> (EHO factorization) and Lin and Ke (2011) <doi:10.1016/j.finmar.2011.03.001> (LK factorization). Moreover, the package uses different estimation algorithms. Specifically, the grid-search algorithm proposed by Yan and Zhang (2012) <doi:10.1016/j.jbankfin.2011.08.003> , hierarchical agglomerative clustering approach proposed by Gan et. al. (2015) <doi:10.1080/14697688.2015.1023336> and later extended by Ersan and Alici (2016) <doi:10.1016/j.intfin.2016.04.001> .