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Fitting Time Series Models
Published in Tucker S. McElroy, Dimitris N. Politis, Time Series, 2019
Tucker S. McElroy, Dimitris N. Politis
It is interesting that this estimator can be negative, even though the estimand is always non-negative – sometimes estimators of positive quantities have better bias properties when they are allowed to take on negative values. The following result (see McElroy and Roy (2018)) gives the asymptotic behavior of ζ^.
Toward Optimal Variance Reduction in Online Controlled Experiments
Published in Technometrics, 2023
In this article, we target at the natural but unanswered question: With access to a set of covariates that are independent of the treatment in the experiment, what is the optimal estimator for comparing the outcomes of treatment and control groups? We study the optimal variance reduction procedures for both count and ratio metrics that are ubiquitous in online controlled experiments in the industry. The optimality we focus on is semiparametric efficiency (Bickel et al. 1993). Given an estimand that arises from the comparison of experiment outcomes, our goal is to develop an estimator with the smallest asymptotic variance among all asymptotically unbiased estimators. We propose procedures that reduce the variance of treatment effect estimation by incorporating flexible ML regressors with rigorous statistical guarantee. Based on classical semiparametric statistics theory, we establish the optimality of our procedures under mild conditions. For ratio metrics, in addition to the optimal (and perhaps nonlinear) approaches, we also propose a computationally efficient linear adjustment method which, to the best of our knowledge, is not available in the literature.
Assessment of structural interventions using Bayesian updating and subspace-based fault detection methods: the case study of S. Maria di Collemaggio basilica, L’Aquila, Italy
Published in Structure and Infrastructure Engineering, 2021
Angelo Aloisio, Luca Di Battista, Rocco Alaggio, Elena Antonacci, Massimo Fragiacomo
Let be the unknown damage indicator variance. The joint posterior density of Id and given initial information I and actual data D, may be factored in Gelman et al. (2013) where is the joint prior density and the likelihood function. The population mean, Id, could be assumed as the estimand of interest, and so the objective of Bayesian analysis is the marginal posterior distribution of Id, which can be obtained by integrating the joint posterior density over