In this paper, we propose a class of simulation-based estimators that are, in general, numerically simple to implement and fast to compute and also set suitable (and mild) conditions for consistency and finite sample bias reduction and coverage probability for inference. This class can be used in complex settings, including high dimensional ones (e.g $p$ large relative to $n$), with regularized (shrinkage) methods and robust estimation and inference. The inferential framework is rooted in the one of indirect inference combined with Fisher's switching principle for inferential purposes. The links with other simulation-based inferential methods such as the bootstrap and the approximated Bayesian computing are formally made and lead to the conclusion that SwiZs brings clear advantages in terms of computational efficiency, bias reduction, and probability coverage, with finite (and small) sample sizes. Moreover, the SwiZs outperforms asymptotic correction methods designed for the same purposes. We illustrate the theoretical results by means of exact derivations and simulations in complex settings.

Maria graduated from the University of Geneva (Ph. D. in econometrics and statistics) in 1993, Maria-Pia  Victoria-Feser has held several positions in different institutions or Departments. She was appointed as lecturer in statistics at the London School of Economics (1993-1996), as assistant and associate professor in statistics (part-time) at the Faculty of psychology and educational sciences at the University of Geneva (1997-2005), financed by a Swiss National Science Found grant, full professor in statistics at the University of Geneva since 2001. She has also acted for the foundation and as founding dean (2013-2017) of the Geneva School of Economics and Management (GSEM) of the University of Geneva, and as founding director of the Research Center for Statistics of the University of Geneva (created in 2011). Maria-Pia Victoria-Feser’s research interests are in fundamental statistics (robust statistics, model selection and simulation-based inference in high dimensions for complex models) with applications in economics (welfare economics, extremes), psychology and social sciences (generalized linear latent variable models, media analytics), and engineering (time series for geo-localization). She has published in leading journals in statistics as well as in related fields.