Imperfect Supervision Research Articles

Incentives and supervision in hierarchies

This paper describes a simple, and therefore limited, model for incentives design under imperfect hierarchical supervision, in order to explain certain empirical evidence on the relative importance of bonuses and salaries for the compensation of managers. Some theoretical implications are also derived from the model: first we find that improvements in the activity of supervision do not always imply higher salaries and less incentives, as is implicitly recognized in certain agency models; secondly, the introduction of incentives in a hierarchy which is performing imperfect supervision may not be sufficient to remove the limits to the firm's size which is attributed to this imperfection.

Efficiency of learning with imperfect supervision

We consider the problem of supervision errors in training samples in two-group discriminant analysis based on normal distributions. Using a model for training sample misclassification, we derive Efron's Asymptotic Relative Efficiency (ARE) of the discriminant function estimated under this model, relative to the case when classification is perfect. We tabulate this ARE for certain values of the Mahalanobis distance between the groups and for various levels of supervision errors. We show that training samples are useful even if prone to a certain amount of misclassification. Our formulae and tables give, for a training sample prone to a certain amount of error, sample size equivalent to that of one error-free training sample as well as that of an unsupervised sample, the equivalence being in terms of estimation efficiency.

ANDAL: A Nonparametric Discrimination And Learning Algorithm for Recognition in Imperfectly Supervised Environments

The problem of recognition in nonparametric environments under imperfect supervision is not amenable to solution through classical statistical approaches based on identification of finite mixtures, which require an a priori knowledge of the probabilistic descriptions of the classes. Accordingly, the problem is viewed in this study as one of optimal linear/nonlinear partitioning of the imperfectly labeled training sample set. This optimal partitioning is accomplished by defining an appropriate optimality criterion, which takes into account the imperfectness of supervision, and solving the resultant optimization problem through the Improved Flexible Polyhedron Method (IFPM). Possible alternatives to compensate for the inherent bias in this criterion towards equipopulation clusters are developed and evaluated using an illustrative example. Details of the methodology involved in implementing the approach are presented. Results of simulation experiments, which confirm the validity and effectiveness of this new technique in accomplishing optimal, linear/nonlinear discriminant learning in imperfectly supervised, nonparametric environments, are included.