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This paper describes the results of a Monte Carlo study of certain aspects of robust regression confidence region estimation for linear models with one, five, and seven parameters. One-step sine estimators (c = l.42) were used with design matrices consisting of short-tailed, Gaussian, and long-tailed columns. The samples were generated from a variety of contaminated Gaussian distributions. A number of proposals for covariance matrices were tried, including forms derived from asymptotic considerations and from weighted-least squares with data dependent weights. Comparisons with: the Monte Carlo "truth" were made using generalized eigenvalues. In order to measure efficiency and compute approximate t-values, linear combinations of parameters corresponding to the largest eigenvalues of the "truth" were examined. For design matrices with columns of modest kurtosis, the covariance estimators all give reasonable results and, after adjusting for asymptotic bias, some useful approximate t-values can be obtained. This implies that the standard weighted least-squares output using data-dependent weights need only be modified slightly to give useful robust confidence intervals. When design matrix kurtosis is high and severe contamination is present in the data, these simple approximations are not adequate.
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What are the statistical and computational problems associated with robust nonlinear regression? This paper presents a number of possible approaches to these problems and develops a particular algorithm based on the work of Powell and Dennis.
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Regression Analysis --- Correlation (Statistics) --- Regression analysis --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- Least squares --- Mathematical statistics --- Probabilities --- Statistics --- Instrumental variables (Statistics) --- Graphic methods
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Trend surface analysis --- Mathematical geography --- Analysis, Trend surface --- Regression analysis --- Spatial analysis (Statistics) --- Statistics --- Geography, Mathematical --- Geography --- Astronomical geography --- Geodesy --- Geographical positions --- Graphic methods
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330.115 --- Econometrics --- Regression analysis --- Statistics --- 519.2 --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- Economics, Mathematical --- Econometrie --- Probability. Mathematical statistics --- Econometrics. --- Regression analysis. --- Statistics. --- 519.2 Probability. Mathematical statistics --- 330.115 Econometrie --- Statistique mathématique --- Mathematical statistics --- Statistique mathématique. --- Statistique mathématique --- Mathematical statistics. --- Économétrie
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Human geography --- -Anthropo-geography --- Anthropogeography --- Geographical distribution of humans --- Social geography --- Anthropology --- Geography --- Human ecology --- Mathematical models --- Regression analysis --- Spatial analysis (Statistics) --- Analysis, Spatial (Statistics) --- Correlation (Statistics) --- Spatial systems --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- Anthropo-geography --- Regression Analysis --- Human geography - Mathematical models
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Statistique --- Informatique appliquée --- Mathematical statistics --- Data processing --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Computer. Automation --- Statistique mathématique --- Informatique --- Regression analysis --- Analyse de régression --- Statistique mathématique --- Computer science --- Mathematical statistics - Data processing
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Multivariate analysis --- 519.233 --- 519.237 --- 57.087.1 --- 519.233 Parametric methods --- Parametric methods --- 519.237 Multivariate statistical methods --- Multivariate statistical methods --- 57.087.1 Biometry. Statistical study and treatment of biological data --- Biometry. Statistical study and treatment of biological data --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Mathematical statistics --- Matrices --- #ABIB:abos --- #ABIB:astp --- #ABIB:dd.prof.E.TOLLENS --- 304.0 --- 306.5 --- AA / International- internationaal --- Zuivere statistische analyse (algemene naslagwerken). Tijdreeksen --- Statistische analyse (methodologie) --- Statistics as Topic --- Multivariate Analysis --- Multivariate analysis. --- Basic Sciences. Statistics --- Statistical Analysis. --- Multivariate Statistics. --- Analyse multivariée --- Statistics --- Regression analysis --- Factor analysis --- Analyse multivariée. --- Statistique. --- Statistiques --- Analyse de régression --- Analyse factorielle. --- Analyse de variance. --- Tests --- Analyse de régression. --- Tests.
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