Shapley Value Confidence Intervals for Attributing Variance Explained

Confidence intervals for Shapley value in Markovian dynamic games

We consider a dynamic multiagent system in which several states succeed each other, following a Markov chain process. In each state, a different single stage game among the agents, or players, is played, and cooperation among subsets of players can arise in order to achieve a common goal. We assume that each coalition can ensure a certain value for itself. The Shapley value is a well known meth...

Variance Allocation and Shapley Value

Motivated by the problem of utility allocation in a portfolio under a Markowitz meanvariance choice paradigm, we propose an allocation criterion for the variance of the sum of n possibly dependent random variables. This criterion, the Shapley value, requires to translate the problem into a cooperative game. The Shapley value has nice properties, but, in general, is computationally demanding. Th...

Honest Confidence Intervals for the Error Variance in Stepwise Regression

An honest confidence interval for the error variance in a stepwise regression is a one-sided interval that adjusts for the effects of variable selection. The endpoint of this interval may be many times larger than the usual endpoint. Such adjustments are most important when selecting variables from a large number of available predictors, particularly in situations with more available predictors...

Explicit Nonparametric Confidence Intervals for the Variance with Guaranteed Coverage

_________________________________________________________________ In this paper, we provide a method for constructing confidence intervals for the variance that exhibit guaranteed coverage probability for any sample size, uniformly over a wide class of probability distributions. In contrast, standard methods achieve guaranteed coverage only in the limit for a fixed distribution or for any sampl...

Variance Estimation and Construction of Confidence Intervals for GEE Estimator