Least square estimates are not robust, So is there any other technique which is used to compute robust estimate in Regression.
What about C-M and S- Estimates ?
In this paper you can find names of some robust regression methods and corresponding referenes to papers where their descriptions can be found:
https://www.researchgate.net/publication/277630626_Blind_Estimation_of_mixed_noise_parameters_in_images_using_robust_regression_curve_fitting
Conference Paper Blind Estimation of mixed noise parameters in images using r...
Abhay -
Perhaps weighted least squares (WLS) is all you need:
https://www.researchgate.net/publication/263036348_Properties_of_Weighted_Least_Squares_Regression_for_Cutoff_Sampling_in_Establishment_Surveys
OLS is just a special case of WLS, with all the weights equal. For cross-sectional surveys I find it inexplicable that OLS is generally the default, when it is often obvious from the data that assuming equal weights is very far from true. A graphical residual analysis will show this.
Here are some ways to estimate heteroscedasticity:
https://www.researchgate.net/publication/263809034_Alternative_to_the_Iterated_Reweighted_Least_Squares_Method_-_Apparent_Heteroscedasticity_and_Linear_Regression_Model_Sampling
https://www.researchgate.net/publication/263032446_Weighting_in_Regression_for_Use_in_Survey_Methodology
Other info:
https://www.researchgate.net/publication/262972023_HETEROSCEDASTICITY_AND_HOMOSCEDASTICITY
https://www.researchgate.net/publication/261596397_Ken_Brewer_and_the_coefficient_of_heteroscedasticity_as_used_in_sample_survey_inference
https://www.researchgate.net/publication/261474011_The_Classical_Ratio_Estimator_Model-Based
And perhaps the top approximately one-third of page 5 in the following, regarding multiple regression, may interest you:
https://www.researchgate.net/publication/261586154_Using_Prediction-Oriented_Software_for_Survey_Estimation
The sigmas are the standard deviations of the random factors of the estimated residuals. An asterisk represents a WLS approximation, employing notation used by G.S. Maddala in econometrics texts.
Note that above papers concentrated on estimating totals from finite populations, but had to also look at individual predictions for cross-sectional surveys. I assume you are looking at individual predictions. For SAS PROC REG, regression weights are entered as "w," and the estimated standard errors of the prediction errors are output as STDI. I assume other software has similar features.
Cheers - Jim
Article Properties of Weighted Least Squares Regression for Cutoff S...
Conference Paper Alternative to the Iterated Reweighted Least Squares Method ...
Article Weighting in Regression for Use in Survey Methodology
Article HETEROSCEDASTICITY AND HOMOSCEDASTICITY
Article Ken Brewer and the coefficient of heteroscedasticity as used...
Article The Classical Ratio Estimator (Model-Based)
Article Using Prediction-Oriented Software for Survey Estimation
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