Accurate Simulation-Based Parametric Inference in High Dimensional Settings

Abstract:

Accurate estimation and inference in finite sample is important for decision making in many experimental and social fields, especially when the available data are complex, like when they include mixed types of measurements, they are dependent in several ways, there are missing data, outliers, etc. Indeed, the more complex the data (hence the models), the less accurate are asymptotic theory results in finite samples.  This is in particular the case, for example, with logistic regression, with possibly also random effects to account for the dependence structure between the outcomes, or more generally, when the likelihood function or the estimating equations have non closed-form expression. Moreover, resampling techniques such as the Bootstrap can also be quite inaccurate in these settings, unless (complex) corrections are provided. We propose instead a simulation based method, the Iterative Bootstrap (IB), that can be used, very generally, to obtain a) unbiased estimators in high dimensional settings, b) finite sample distributions for inference, with, under suitable conditions, the exact probability coverage property. The method is based on an initial estimator, that does not need to be consistent and can hence be chosen for numerical convenience, and/or can have some desirable properties such as robustness. We present the main theoretical results and the relationships with well-established methods, as well as simulation studies involving complex models and different estimators.

About the Speaker:

Maria-Pia Victoria-Feser is currently professor of statistics at the Geneva School of Economics and Management, University of Geneva, Switzerland. She received her Ph.D. in econometrics and statistics from the University of Geneva, and started her carrier as a lecturer at the London School of Economics and Management. She was awarded the Latzis International Prize for her Ph.D. thesis, as well as doctoral and professorial fellowships from the Swiss National Science Foundation.

Maria-Pia Victoria-Feser’s research interests are in statistical methodology (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), and engineering (time series for geo-localization). She has published in leading journals in statistics as well as in related fields.