Showing papers by "Rahul Mukerjee published in 2022"
TL;DR: This paper investigates randomization based causal inference in split-plot designs that are possibly unbalanced and proposes a construction procedure that generates an estimator with minimax bias, which becomes unbiased under milder conditions.
Abstract: Split-plot designs find wide applicability in multifactor experiments with randomization restrictions Practical considerations often warrant the use of unbalanced designs This paper investigates randomization based causal inference in split-plot designs that are possibly unbalanced Extension of ideas from the recently studied balanced case yields an expression for the sampling variance of a treatment contrast estimator as well as a conservative estimator of the sampling variance However, the bias of this variance estimator does not vanish even when the treatment effects are strictly additive A careful and involved matrix analysis is employed to overcome this difficulty, resulting in a new variance estimator, which becomes unbiased under milder conditions A construction procedure that generates such an estimator with minimax bias is proposed
2 citations
TL;DR: In this paper , a stick is broken at random at n-1 points to form n pieces, and the problem of forming k-gons with k out of these n pieces is considered.
Abstract: Let a stick be broken at random at n-1 points to form n pieces. We consider three problems on forming k-gons with k out of these n pieces, and show how a statistical approach, through a linear transformation of variables, yields simple solutions that also allow fast computation.
09 Jul 2022
TL;DR: This paper extends and generalizes a variance analysis proposed in Elvira et al (2019), providing novel proofs that allow to determine the variance relations among MIS schemes.
Abstract: : Multiple importance sampling (MIS) is an increasingly used methodology where several proposal densities are used to approximate integrals, generally involving target probability density functions. The use of several proposals allows for a large variety of sampling and weighting schemes. Then, the practitioner must choose a given scheme, i.e., sampling mechanism and weighting function. A variance analysis has been proposed in Elvira et al (2019, Statistical Science 34 , 129-155), showing the superiority of the balanced heuristic estimator with respect to other competing schemes in some scenarios. However, some of their results are valid only for two proposals. In this paper, we extend and generalize these results, providing novel proofs that allow to determine the variance relations among MIS schemes.