REGRESSION ESTIMATORS: A COMPARATIVE STUDY

By CHARLES GARCIA

CONTENTS ROBUST REGRESSION INTRODUCTION THE ANSCOMBE DATA AND OLS THE ANCOMBE DATA AND QUANTILE REGRESSION REAL DATA EXAMPLES: THE FRENCH DATA THE NETHERLANDS EXAMPLE THE INFLUENCE FUNCTION AND THE DIAGNOSTIC TOOLS DIAGNOSTIC IN THE FRENCH AND THE DUTCH DATA EXAMPLE WITH ERROR CONTAMINATION A SUMMARY OF KEY POINTS REFERENCES APPENDIX: COMPUTER CODES IN STATA QUANTILE REGRESSION AND RELATED METHODS EXPECTILES EXPECTILES AND CONTAMINATED ERRORS FRENCH DATA: INFLUENTIAL OUTLIER IN THE DEPENDENT VARIABLE THE NETHERLANDS EXAMPLE: OUTLIER IN THE EXPLANATORY VARIABLE M-ESTIMATORS M-ESTIMATORS WITH ERROR CONTAMINATION THE FRENCH DATA M-QUANTILES M-QUANTILES ESTIMATES IN THE ERROR-CONTAMINATED MODEL M-QUANTILES IN THE FRENCH AND DUTCH EXAMPLES FURTHER APPLICATIONS: SMALL-AREA ESTIMATION APPENDIX: COMPUTER CODES RESAMPLING, SUBSAMPLING, AND QUANTILE REGRESSION ELEMENTAL SETS BOOTSTRAP AND ELEMENTAL SETS BOOTSTRAP FOR EXTREMAL QUANTILES THE FRENCH DATA SET THE DUTCH DATA SET ASYMPTOTICS FOR CENTRAL-ORDER QUANTILES TREATMENT EFFECT AND DECOMPOSITION QUANTILE TREATMENT EFFECT AND DECOMPOSITION A NOT SO SHORT INTRODUCTION TO LINEAR PROGRAMMING THE LINEAR PROGRAMMING PROBLEM THE STANDARD FORM OF A LINEAR PROGRAMMING PROBLEM ASSUMPTIONS OF A LINEAR PROGRAMMING PROBLEM THE GEOMETRY OF LINEAR PROGRAMMING THE SIMPLEX ALGORITHM BASIC SOLUTIONS OPTIMALITY TEST CHANGE OF THE BASIS: ENTERING VARIABLE AND LEAVING VARIABLE THE CANONICAL FORM OF A LINEAR PROGRAMMING PROBLEM THE TABLEAU VERSION OF THE SIMPLEX ALGORITHM THE TWO–PHASE METHOD CONVERGENCE AND DEGENERATION OF THE SIMPLEX ALGORITHM THE REVISED SIMPLEX ALGORITHM LINEAR PROGRAMMING FOR QUANTILE REGRESSION LP FORMULATION OF THE L1 SIMPLE REGRESSION PROBLEM A FIRST FORMULATION OF THE L1 REGRESSION PROBLEM A MORE CONVENIENT FORMULATION OF THE L1 REGRESSION PROBLEM THE BARRODALE–ROBERTS ALGORITHM FOR L1 REGRESSION LP FORMULATION OF THE QUANTILE REGRESSION PROBLEM GEOMETRIC INTERPRETATION OF THE MEDIAN AND QUANTILE REGRESSION PROBLEM: THE DUAL PLOT CORRELATION AUTOREGRESSIVE MODELS NON-STATIONARITY EXAMPLES OF NON-STATIONARY SERIES INFERENCE IN THE UNIT ROOT MODEL RELATED TESTS FOR UNIT ROOT SPURIOUS REGRESSION COINTEGRATION EXAMPLE OF COINTEGRATED VARIABLES COINTEGRATION TESTS TESTS OF CHANGING COEFFICIENTS EXAMPLES OF CHANGING COEFFICIENTS CONDITIONALLY HETEROSKEDASTIC MODELS EXAMPLE OF A CONDITIONAL HETEROSKEDASTIC MODEL