Robust Planning and Analysis of Experiments

ISBN-13: 9780387982236 / Angielski / Miękka / 1997 / 234 str.

Christine H. Muller; Christine H. Mueller

Opis

Author-approved bcc: Robust statistics and the design of experiments are two of the fastest growing fields in contemporary statistics. Up to now, there has been very little overlap between these fields. In robust statistics, robust alternatives to the nonrobust least squares estimator have been developed, while in experimental design, designs for the efficient use of the least square estimator have been developed. This volume is the first to link these two areas by studying the influence of the design on the efficiency and robustness of robust estimators and tests. It shows that robust statistical procedures profit by an appropriate choice of the design and that efficient designs for a robust statistical analysis are more applicable. The classical approaches of experimental design and robust statistics are introduced before the areas are linked. Dr. Christine H. M ller teaches at the Department of Mathematics and Computer Science of the Free University of Berlin and is a member of the research project on "Efficient Experiments in Industrial Production." From 1988-1991, she worked as a biometrician at the Medical Department of the Free University of Berlin.

Spis treści

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.