Rerandomization Inference on Regression and Shift Effects: Computationally Feasible Methods
Abstract An idea due to Quade (1973) is used to develop a method that reduces the computational load for rerandomization inferences in certain situations, and, for experiments carried out with a sufficiently small reference set of randomizations, makes computations entirely feasible. Consider an experimental design for N units for which an experimental plan E is to be chosen randomly from a set of K plans. Plan E will assign treatment dosage dE,u to unit u with postulated additive effect δdE,u reflected in the observation zu . Rerandomization inferences are to be carried out by means of “pivotal” statistics te,E (z) = [bE (z) - be (z)]/[1 - be (d E )], where z and d E are observation and dosage vectors and be ([mdot]) is the regression (slope) onto d e , the dosages under plan e (∈ ). (a) The P value of a test of the hypotheses δ = Δ versus δ > Δ is essentially the proportion of te,E (z) values, e ∈ , that are at most Δ. (b) If t (l),E (z) is the lth largest of the te,E (z)'s, e ∈ , then a (L - l)/K confi...