Optimal Multiple Decision Statistical Procedure for Inverse Covariance Matrix

Multiple testing with optimal individual tests in Gaussian graphical model selection

“…To construct optimal individual tests for the problem (2) we use a tests of the Neyman structure [Lehmann and Romano 2005], [Koldanov and Koldanov 2014]. Let f (x; θ) be the density of the exponential family:…”

Nonparametric procedure for comparing the performance of divisions of a network organization

“…Such methods are divided into: ♦ parametric, relying on a specific probabilistic model of the analyzed indicators. In this case, the normal distribution is most often used as a probabilistic model [4,5],…”

“…This type of problem arose in [17] when discussing the problem of testing hypotheses of homogeneity of at least three populations and was called the incompatibility problem. Applied tasks in which the incompatibility problem arises (the problem of inconsistently combining the results of comparing effectiveness of the pairs of departments) were considered in [4,5] within the framework of the normal model. The solution to the incompatibility problem was based on the introduction of an additional parameter ∆ and the transition to tasks of comparing the effectiveness of two divisions with accuracy ∆.…”

“…In this work, unlike [4,5], the assumption of a normal distribution of the number of sales is not used. Pairwise comparison of the effectiveness of two units is based on the use of Mann-Whitney tests.…”

“…This uses a graphical representation, which is convenient for visualizing emerging incompatibility problems. The proposed nonparametric procedure is applied to the analysis of data reported in [4], and an example is given in which the inconsistency problem is overcome by analyzing p-values and appropriately selecting significance levels for pairwise comparison tests. A comparison is made with the results obtained within the normal model.…”