Robust Planning and Analysis of Experiments

Abstract

I: Efficient Inference for Planned Experiments.- 1 Planned Experiments.- 1.1 Deterministic and Random Designs.- 1.2 Linear and Nonlinear Models.- 1.3 Identifiability of Aspects.- 2 Efficiency Concepts for Outlier-Free Observations.- 2.1 Assumptions on the Error Distribution.- 2.2 Optimal Inference for Linear Problems.- 2.3 Efficient Inference for Nonlinear Problems.- II: Robust Inference for Planned Experiments.- 3 Smoothness Concepts of Outlier Robustness.- 3.1 Distributions Modelling Outliers.- 3.2 Smoothness of Estimators and Functionals.- 3.3 Frechet Differentiability of M-Functionals.- 4 Robustness Measures: Bias and Breakdown Points.- 4.1 Asymptotic Bias and Breakdown Points.- 4.2 Bias and Breakdown Points for Finite Samples.- 4.3 Breakdown Points in Linear Models.- 4.4 Breakdown Points for Nonlinear Problems.- 5 Asymptotic Robustness for Shrinking Contamination.- 5.1 Asymptotic Behaviour of Estimators in Shrinking Neighbourhoods.- 5.2 Robust Estimation in Contaminated Linear Models.- 5.3 Robust Estimation of Nonlinear Aspects.- 5.4 Robust Estimation in Contaminated Nonlinear Models.- 6 Robustness of Tests.- 6.1 Bias and Breakdown Points.- 6.2 Asymptotic Robustness for Shrinking Contamination.- III: High Robustness and High Efficiency.- 7 High Robustness and High Efficiency of Estimation.- 7.1 Estimators and Designs with Minimum Asymptotic Bias.- 7.2 Optimal Estimators and Designs for a Bias Bound.- 7.3 Robust and Efficient Estimation of Nonlinear Aspects.- 7.4 Robust and Efficient Estimation in Nonlinear Models.- 8 High Robustness and High Efficiency of Tests.- 8.1 Tests and Designs with Minimum Asymptotic Bias.- 8.2 Optimal Tests and Designs for a Bias Bound.- 9 High Breakdown Point and High Efficiency.- 9.1 Breakdown Point Maximizing Estimators and Designs.- 9.2 Combining High Breakdown Point and High Efficiency.- Outlook.- A.1 Asymptotic Linearity of Frechet Differentiable Functionals.- A.2 Properties of Special Matrices and Functions.- References.- List of Symbols.

Locations

• Library Union Catalog of Bavaria, Berlin and Brandenburg (B3Kat Repository) - View - PDF
• Technometrics - View