Transformations to symmetry and homoscedasticity

Abstract This article considers transformations in regression to eliminate skewness and heteroscedasticity of the response. We work with the transform-both-sides model where the relationship between the median response and the independent variables has been identified, at least tentatively. To preserve this relationship, the response and the regression model are transformed in the same way. Extending the work of others for the location parameter case, we propose an estimator that eliminates skewness. We also develop an estimator to eliminate heteroscedasticity and an estimator that attempts to induce both symmetry and homoscedasticity. Both and appear new. By comparing and we develop a test of the null hypothesis that there exists a transformation to both symmetry and homoscedasticity. We study the question When does the estimator of λ behave (in terms of asymptotic variance) as if the regression parameter β were known (and vice versa)? The results are of use for telling when the optimal estimator of λ do...

[1]  Noel A Cressie,et al.  A Transformation/Weighting Model for Estimating Michaelis-Menten Parameters, , 1989 .

[2]  D. Ruppert,et al.  Random-Effect Models in Nonlinear Regression with Applications to Bioassay , 1989 .

[3]  D. Ruppert,et al.  Transformation and Weighting in Regression , 1988 .

[4]  D. Ruppert,et al.  Diagnostics and robust estimation when tranforming the regression model and the response , 1987 .

[5]  Changbao Wu,et al.  Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis , 1986 .

[6]  Ronald D. Snee,et al.  An Alternative Approach to Fitting Models When Re-expression of the Response is Useful , 1986 .

[7]  F. Mosteller,et al.  Exploring Data Tables, Trends and Shapes. , 1986 .

[8]  Chih-Ling Tsai,et al.  Residuals in nonlinear regression , 1985 .

[9]  D. Ruppert,et al.  Data Transformations in Regression Analysis with Applications to Stock—Recruitment Relationships , 1985 .

[10]  David Ruppert,et al.  Power Transformations When Fitting Theoretical Models to Data , 1984 .

[11]  S. Weisberg,et al.  Diagnostics for heteroscedasticity in regression , 1983 .

[12]  David Ruppert,et al.  Robust Estimation in Heteroscedastic Linear Models. , 1982 .

[13]  David Ruppert,et al.  On prediction and the power transformation family , 1981 .

[14]  P. Bickel,et al.  An Analysis of Transformations Revisited , 1981 .

[15]  Richard A. Johnson,et al.  The Large-Sample Behavior of Transformations to Normality , 1980 .

[16]  Raymond J. Carroll,et al.  On Estimating Variances of Robust Estimators When the Errors are Asymmetric , 1979 .

[17]  P. Bickel,et al.  Using Residuals Robustly I: Tests for Heteroscedasticity, Nonlinearity , 1975 .

[18]  W. Ricker,et al.  A Revised Interpretation of the History of the Skeena River Sockeye Salmon (Oncorhynchus nerka) , 1975 .

[19]  David V. Hinkley,et al.  On power transformations to symmetry , 1975 .

[20]  Efficiency robustness of estimators , 1972 .

[21]  P. J. Huber.  The behavior of maximum likelihood estimates under nonstandard conditions , 1967 .

[22]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[23]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .

[24]  F. J. Anscombe,et al.  Examination of Residuals , 1961 .

[25]  W. Ricker.  Stock and Recruitment , 1954 .