Сравнительный анализ различных методов оценивания в линейной регрессии

Математические методы анализа решений в экономике, бизнесе и политике. WP7. Издательский дом ВШЭ, 2014. № WP7/2014/07.

Ботвинкин Е. А., Горяинова Е. Р.

This paper focuses on three methods of parameter estimation in linear regression model with unknown distribution of noises. For different distributions of noises there were analytically calculated asymptotic relative efficiencies (ARE) of rank estimations towards LS-estimations and LAD-estimations. There were also simulated regression equations with specific parameters and distributions of noises applying the Monte Carlo method. For datasets with moderate number of entities there were calculated mean values of squared differences between estimation vectors and a real parameter vector over a thousand of simulated regression models. There were made some recommendations on the application of the LS method, the LAD method and the rank method for cases of different distributions of noises. 

Keywords: линейная регрессионная модель, ранговые оценки, МНК-оценки, оценка наименьших модулей, асимптотическая относительная эффективность