The inference in multi-state models is traditionally performed under
             a Markov assumption that claims that past and future of the process
             are independent given the present state. In this package, we 
             consider tests of the Markov assumption that are applicable to 
             general multi-state models. Three approaches using existing 
             methodology are considered: a simple method based on including
             covariates depending on the history in Cox models for the transition
             intensities; methods based on measuring the discrepancy of the 
             non-Markov estimators of the transition probabilities to the 
             Markov Aalen-Johansen estimators; and, finally, methods that were
             developed by considering summaries from families of log-rank 
             statistics where patients are grouped by the state occupied of the
             process at a particular time point (see Soutinho G, Meira-Machado L
             (2021) <doi:10.1007/s00180-021-01139-7> and Titman AC, Putter H
             (2020) <doi:10.1093/biostatistics/kxaa030>).

The Markowitz criterion is a multicriteria decision-making method that stands out in risk and uncertainty analysis in contexts where probabilities are known. This approach represents an evolution of Pascal's criterion by incorporating the dimension of variability. In this framework, the expected value reflects the anticipated return, while the standard deviation serves as a measure of risk. The 'markowitz' package provides a practical and accessible tool for implementing this method, enabling researchers and professionals to perform analyses without complex calculations. Thus, the package facilitates the application of the Markowitz criterion. More details on the method can be found in Octave Jokung-Nguéna (2001, ISBN 2100055372).

A collection of tools for analyzing significance of 
    Markowitz portfolios, using the delta method on the second moment
    matrix, <arxiv:1312.0557>.