Yuri Belyaev

Dept. of mathematics and mathematical statistics Umeå University  

Dept. of forest economics  SLU   Umeå   
	
Resampling methods in selection of linear regression functions
and in assessing accuracy of the OLS-estimators

Abstract

Heteroscedastic linear regression models will be considered.  We
suppose that an unknown polynomial is the true regression
function. For any taken polynomial it is possible formally to find the
OLS-estimates of its coefficients and find the related residuals.
Under the natural assumptions resamplings from the residuals can give
us information that we have over-parametrization, correct
parametrization or under-parametrization case. In the correct or
over-parametrization cases it is possible to obtain consistent
estimators of the c.d.f.s of deviations of the OLS-estimators from the
true unknown parameters as data size n go to infinity. Their analysis
gives us an objective method for selection of the true linear
regeression function.