Vegas, Esteban; del Castillo, Joan; Ocaña, Jordi Efficiency and exponential models in a variance-reduction technique for dichotomous response variables. (English) Zbl 1054.62012 J. Stat. Plann. Inference 85, No. 1-2, 61-74 (2000). Summary: The statistical properties of a variance-reduction technique, applicable to simulations with dichotomous response variables, are examined from the standpoint of exponential models, that is, distribution families whose log-likelihood is a linear function of a sufficient statistic of fixed dimension. It is established that this variance-reduction technique induces some distortion that is explainable in terms of the statistical curvature of the resulting exponential model. The curvature concept used here is a multiparametric generalization of Efron’s definition. It is calculated explicitly and its relation to the amount of variance reduction and to the asymptotic distribution of the relevant statistics is discussed. It is concluded that Efrons’s criteria for low curvature (associated with nice statistical properties) are valid in this context and generally met for the usual sample sizes in simulation (some thousands of replicates). Cited in 1 Document MSC: 62E10 Characterization and structure theory of statistical distributions 62F12 Asymptotic properties of parametric estimators Keywords:Curved exponential models; Fisher’s information; Score function; Statistical curvature PDF BibTeX XML Cite \textit{E. Vegas} et al., J. Stat. Plann. Inference 85, No. 1--2, 61--74 (2000; Zbl 1054.62012) Full Text: DOI References: [3] Efron, B., Defining the curvature of a statistical problem (with application to second order efficiency) (with discussion), Ann. Statist., 3, 1189-1242 (1975) · Zbl 0321.62013 [4] Grab, E. L.; Savage, R., Tables of the expected value of \(1/X\) for positive Bernouilli and Poisson variables, J. Amer. Statist. Assoc., 49, 169-177 (1954) · Zbl 0055.12702 [6] Ocaña, J.; Vegas, E., Variance reduction for Bernoulli response variables in simulation, Comput. Statist. Data Anal., 19, 631-640 (1995) · Zbl 0875.62094 [7] Rothery, P., The use of control variates in Monte Carlo estimation of power, Appl. Statist., 31, 125-129 (1982) · Zbl 0482.65076 [10] Wooff, D. A., Bounds on reciprocal moments with applications and developments in Stein estimation and post-stratification, J.R. Statist. Soc. Serie B, 47, 362-371 (1985) · Zbl 0603.62016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.