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On optimal re-randomization designs
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.ORCID iD: 0000-0002-1260-7737
Tsinghua University, Beijing, China.
Number of Authors: 32019 (English)Report (Other academic)
Abstract [en]

Blocking is commonly used in randomized experiments to increase efficiency of estimation. A generalization of blocking is to remove allocations with imbalance in covariates between treated and control units, and thenrandomize within the set of allocations with balance in these covariates. This idea of rerandomization was formalized by [5], who suggested using the affinely invariant Mahalanobis distance between treated and control covariate means as the criterion for removing unbalanced allocations. [3] proposed reducing the set of balanced allocations to the minimum. Here we discuss the implication of such an ‘optimal’ rerandomization design for inferences to the units inthe sample and to the population from which the units in the sample were randomly drawn. We argue that, in general, it is a bad idea to seak the optimal design for an inference to the population because that inference typically only reflects uncertainty from the usually hypothetical random sampling, and not the randomization of treatment versus control.

Place, publisher, year, edition, pages
2019. , p. 20
Series
Working paper / Department of Statistics, Uppsala University ; 2019:3
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-381381OAI: oai:DiVA.org:uu-381381DiVA, id: diva2:1303234
Available from: 2019-04-09 Created: 2019-04-09 Last updated: 2019-09-27Bibliographically approved
In thesis
1. Causal Inference in Observational Studies and Experiments: Theory and Applications
Open this publication in new window or tab >>Causal Inference in Observational Studies and Experiments: Theory and Applications
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of six papers that study the design of observational studies and experiments.

Paper I proposes strategies to consistently estimate the average treatment effect of the treated using information derived from a large number of pre-treatment measurements of the outcome. The key to this strategy is to use two-level time-series model estimates to summarize the inter-unit heterogeneity in the sample. It is illustrated how this approach is in line with the conventional identifying assumptions, and how sensitivity analyses of several key assumptions can be performed.

Paper II contains an empirical application of the identification strategy proposed in Paper I. This study provides the first causal analysis of the demand response effects of a billing demand charge involuntarily introduced to small and medium sized electricity users.

Paper III proposes strategies for rerandomization. First, we propose a two-stage allocation sample scheme for randomization inference to the units in balanced experiments that guarantees that the difference-in-means estimator is an unbiased estimator of the sample average treatment effect for any experiment, conserves the exactness of randomization inference, and halves the time consumption of the rerandomization design. Second, we propose a rank-based covariate-balance measure which can take into account the estimated relative weight of each covariate.

Paper IV discusses the concept of optimal rerandomization. It is shown that depending on whether inference is to be drawn to the units of the sample or the population, the notion of optimal differs. We show that it is often advisable to aim for a design that is optimal for inference to the units of the sample, as such a design is often near-optimal also for inference to the units of the population.

Paper V summarizes the current knowledge on asymptotic inference for rerandomization designs and proposes some simplifications for practical applications. Drawing on previous work, we show that the non-normal sampling distribution of the difference-in-means test statistic approaches normal as the rerandomization criterion approaches zero. Furthermore, the difference between the correct non-normal distribution and the proposed approximation based on a normal distribution is in many situations negligible even for near optimal rerandomization criteria.

Paper VI investigates and clarifies the relation between the traditional blocked designs and rerandomization. We show that blocking and rerandomization is very similar, and in some special cases identical. Moreover, it is shown that combining blocking and rerandomization is always at least as efficient as using only rerandomization, but the difference is in many cases small.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. p. 36
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 172
Keywords
experimental design, identification, observational studies, rerandomization
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-393810 (URN)978-91-513-0762-6 (ISBN)
Public defence
2019-12-06, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2019-11-05 Created: 2019-09-27 Last updated: 2019-11-27

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Johansson, PerSchultzberg, Mårten

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